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Why are mathematicians so bad at arithmetic? (2017)

110 points by tomerv 5y ago

cesarosum 5y ago
Thanks for sharing this. I feel seen :)
dwohnitmok 5y ago
Yeah a lot of pure mathematics education very much emphasizes the learning the "spirit" or fundamental concepts of certain things rather than computation, sometimes to the extreme when compared even with applied mathematics. This is especially obvious in anything that even approached calculus. In the math courses I took in college, if we e.g. ever had a differential equation we needed to solve on a problem set "looked up the answer on Wolfram Alpha" was a perfectly reasonable response. Same for differentiation or integration. In some intro courses you'd be ask to prove that certain differentiation or integration techniques had mathematically rigorous backing, but never had to do the rote work of actually memorizing and using those techniques ever again. Again "looked up the answer on Wolfram Alpha" was a perfectly reasonable response. It was a far cry from the applied mathematics department. Another huge discrepancy was in linear algebra, where very little time was spent on matrix computation other than again proving that matrix operations and invariants preserved properties of linear maps and vector spaces and almost all the time of the course was spent on the linear maps and vector spaces themselves, whereas linear algebra in the applied math department was almost entirely about matrices and the intricacies of various matrix computations and decompositions and subjects like dual spaces or other things that couldn't be represented with normal matrix computation (e.g. infinite dimensional vector spaces) were omitted.
- gjulianm 5y ago
  To add to this comment, a lot of times we didn't even care what the solution was, only that it existed, was unique, or was bounded by some constant (and we didn't usually care about the value either). The more you advance into pure mathematics, the less you care about specific functions or values.
  - raverbashing 5y ago
    And I suspect, this is what makes math grind its own gears. The way math is "built", with too generalizing theorems, non-constructive statements, etc makes it fall into traps like the Russel's Paradox (which literally cannot exist "in real life" - not even for the very wide definition of mathematical real life). Building math on saying "this exists" without actually building towards what it is, is a bit of a "sin".
    - gjulianm 5y ago
      > The way math is "built", with too generalizing theorems, non-constructive statements, etc makes it fall into traps like the Russel's Paradox I don't think Russel's paradox is a problem with ZFC set theory. Building sets out of "the set of everything" is not used, and even people are careful to specify when the axiom of choice is being used. > Building math on saying "this exists" without actually building towards what it is, is a bit of a "sin". It's actually not. The idea is that you prove only what you actually need for the next step. A nice example is again in the field of differential equations. Ultimately people are interested in a solution, but to get that solution you need an approximation method, and to get an approximation method you need to know when does it work and how fast does it work, and to know that you need to know when a solution can be found and what properties does it have. Constructivism is something that in theory might sound interesting, but forcing all mathematics to fit that model only servers to make certain proofs of true and useful statements far more complicated or even impossible.
      - lupire 5y ago
        It's rather unscientific to say that we believe things because we want them to be true and not because they are inherently true.
        gjulianm 5y ago
        Nothing is inherently true, things are only true based on some axioms and hypothesis. What I meant with "results that are true" is things that are consistent with our physical world.
- ls15 5y ago
  My university had exams that involved arithmetic, matrix computation and differential equations, but no access to Wolfram Alpha though. It was impossible to pass the exams without prior training.
- hn_go_brrrrr 5y ago
  Once I got past calculus, it seemed like we stopped caring about numbers. Plenty of 0s and 1s, the occasion 2, but rarely a 3 or higher. I remember one theorem had a 24 in the derivation (Stone-Weierstrass, I want to say?) and we were all amazed. Given that, who needs arithmetic?
goldenkey 5y ago
Mathematics is about abstraction, it's literally the study of objects. Different foundations of math define the fundamental objects of the universe in different ways. You have set theory, where everything must be constructed from the empty set, and operations of union, intersection, complement, and inclusion/comprehension. https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers https://en.wikipedia.org/wiki/Set-theoretic_definition_of_na... You might say, how the hell do I get an ordered pair (x,y) from sets? Well, this was solved in a myriad of ways. https://en.m.wikipedia.org/wiki/Ordered_pair#Defining_the_ordered_pair_using_set_theory https://en.m.wikipedia.org/wiki/Ordered_pair#Defining_the_or... You also have category theory where everything is a graph and you start with the global object: 1 -> N then build all numbers recursively. https://en.wikipedia.org/wiki/Natural_numbers_object https://en.wikipedia.org/wiki/Natural_numbers_object And then you keep on using these complex objects to build even more complex ones. So you have a consistent system. And you derive truths about the system, these get called proofs. Arithmetic is child's play - it has nothing to do with consequence or truth. Math is all about starting with agreeable rules and deriving profound consequences that are a kind of umbrella that those rules cover, and sprout from. Canonically, these get called axioms. And we like to choose ones that agree with our common perception of the world -- ie. the Peano axioms for how objects physically work when you combine them, split them, try to group them into rows and columns (prime factorization), etc.. Numbers are one of the simplest and fascinating abstractions because they take the idea of object and unify everything under it -- so two cats and two dogs get typecast to two objects and two objects, then you can add them and get 4 objects. Numbers are basically a reflection of the most primitive type cast possible in our universe of thought. Such, number theory is called the Queen of Mathematics. Because number theory seems to relate much closer to our actual physicality than other axiomatic systems.
TrackerFF 5y ago
What I liked about math in engineering school was that after a certain point, it was really all about numerical methods. Because it is such an applied field, of course you want actual numbers - that's your bread and butter. You first learn the basics, the same way a mathematician learns something, but afterwards it's all simulation and approximations. During grad school, however, there was a complete shift from this - IMO. You suddenly had more classes with with math for mathematicians. Of course, this was because you took a lot more advanced and cutting edge classes, which were often built on various fields of math. New tech often follows that route...breakthrough discoveries in math or physics, which is often described in dense mathematical language. Before it eventually gets more applied and approximated forms, which are more suited for real-life uses. I've also noticed that working engineers tend to be much better at mental computation, than most researchers / scientists. But that obviously comes from years of work experience.
- ReleaseCandidat 5y ago
  > Because it is such an applied field, of course you want actual numbers That's why you're an engineer and not a mathematician ;) Because, no, _I_ do not want numbers if I can avoid them. Proofing that something has one (and exactly one) solution is (for example) way more interesting than actually computing the result - this is that boring that even computers can do (some of) the work for us.
emptybits 5y ago
Seems plausible. Similarly, a computer scientist may be bad at writing computer programs. (And this may also surprise someone outside the field.)
jesperlang 5y ago
Isn't this a little bit like "Why are computer scientists so bad at fixing my router / printer / virus infected windows laptop?" :)
- grenoire 5y ago
  Oh, you computer scientists!
- mdp2021 5y ago
  Because something broke inside following the times in which they were requested to help with your "virus infected mouse device". (Sorry.) Or those times "What do you mean do not open the virus? I tried to open it, I clicked on it a thousand times, nothing happened!". (Both are very real and lived, I am afraid.)
- Koshkin 5y ago
  Simple: we all know that Computer science is no more about computers than astronomy is about telescopes. (Something like that can be said about mathematics, I am sure.)
- technothrasher 5y ago
  When I was in school back in the 90's and worked for the computing center supporting Unix workstations on campus, it was always funny to get called over to the CS department to fix a professor's workstation and discover once again that they had zero clue how to use their machine. These were the same professors I had in my CS classes, who were fantastic. They were 100% theory and not at all practical, and actually weren't the least bit ashamed to admit it.
  - mathattack 5y ago
    One of my professors answered “How do you go about debugging your programs?” with “I don’t debug, I prove my code correct before typing it in.” Not very useful.
    - xgkickt 5y ago
AllegedAlec 5y ago
For the same reason a biologist doesn't know the names of all trees by sight.
lordnacho 5y ago
What we need now is someone giving an anecdote about how they're a published math researcher but at the job interview they screened him with Times Table Rock Star and gave him a take home to solve 20 quadratic equations.
- pooper 5y ago
  > Times Table Rock Star When I was a child, the schools tried to get me to memorize the multiplication tables. At least through ten, teachers would say. I thought it was pretty silly. You shouldn't force memorization. It should come naturally as you use certain things many times. If you use 7x6 often, you will remember it. If not, you will forget it. That should be totally fine. Why should it matter if you memorized 7x6 or you had to go the long way and say 7x5 is 35 so add 7 to 35 and you'll get 7x6? Imagine if you said, good programmers are often fast typists and some idiot decided to add a touch typing test to their hiring process. » Goodhart's law is an adage often stated as "When a measure becomes a target, it ceases to be a good measure". Edit turn asterisks to x. Please read x as multiply.
  - lordnacho 5y ago
    > It should come naturally as you use certain things many times. But if it's not second nature, you may decide not to do it many times. Is it "need this -> gets memorized" or "memorized -> can use as tool"? Personally I've never been a proponent of memorizing things, preferring to Google when needed, but I can see how the argument runs.
  - mdp2021 5y ago
    I Disagree. This "you only need one eye and one ear - two is redundant" approach to memorization is a root with the dire situation of today, in which I know youngsters with some diploma who can go "I thought that 5x8 was [any number]. Really it is 40?!". While studying, in general, mnemonic hooks pose a foundation for further notions to become solid. Then, the whole of them become available micro-tools for reasoning.
  - jimhefferon 5y ago
    I'm a mathematician. When I was in grade school they told us to memorize up to twelve. But I figured I could skip the evens, because doubling is easy, so I would just memorize the odds. One is trivial, three and five are simple, as is eleven. There is an easy algorithm for mine. So I memorized seven and called it done. When I think of the thousands of multiplications I've done since then, it's clear I was a dope and my teachers were perfectly right.
roenxi 5y ago
The mathematicians are probably wrong. Mathematicians will have above average ability with arithmatics, but they're going to be meeting people who memorise pi to 50 decimal places or happen to calculate the sum of small cubic numbers for fun to pass the time and are really good at arithmetic. What the mathematicians are probably cluing in to is the fact that around half of mathematicians are below median arithmetic ability in their immidiate academic community.
- gjulianm 5y ago
  > but they're going to be meeting people who memorise pi to 50 decimal places or happen to calculate the sum of small cubic numbers for fun to pass the time and are really good at arithmetic. Not really. The "above average ability" depends on the population: if you compare mathematicians with other college educated people, I'd guess they'd be at the bottom among the STEM fields. It wasn't weird to see people (or myself) having the occasional "wait, what's 5 times 7". And it shouldn't be surprising if people knew that 99% of the arithmetic operations done in math degrees are things like "2+1" or "2·3".
  - lupire 5y ago
    It's unsurprising that abstract mathematicians are worse at engineering math than engineers, and vice versa for abstract math.
- watwut 5y ago
  > Mathematicians will have above average ability with arithmatics They dont. My family has multiple ma mathematicians in it and as a kid I spent a lot of time with their colleagues on activities. Many do regularly huge mistakes in basic arithmetic like multiplication or addition. Some of them do "memorise pi to 50 decimal places" or learn some other "stunt" for fun of it or in order to impress people. But they all treat it more of as a stunt then something meaningful. It just does not matter for work of mathematician whether you are good with arithmetic. So they dont care about becoming good at it. They just joke about it when someone makes mistake yet again.
jonathanstrange 5y ago
I doubt that the premise is true. Self-reporting is not a reliable indicator of actual performance in this case. It seems plausible that an empirical study would find mathematicians way above the average in elementary arithmetic, though possibly trumped by waiters and cashiers who often have to calculate without aid. Of course, without an actual study this is just speculation.
anoplus 5y ago
I think this is a crucial message for young students who feel inferior to that human calculator classmate.
harshreality 5y ago
Contest-style rapid numeric calculation is a special case of "math". Many kids in math clubs focus on both — a significant part of contest math is word problems that have to be interpreted correctly and then calculated correctly, under time pressure — but calculation has little to do with higher math other than being able to validate symbolic results. Fast calculation is about drilling and learning tricks. People can get pretty accurate and fast at simple arithmetic as long as numbers fit (or they've learned tricks to chunk them) into their working memories. If there's no inherent motivation or necessity to maintain those skills after school, they'll decay. As the article points out, accountants and engineers are likely to be better at being human calculators. I'd guess accountants first, because engineers do more complex calculations and it'd be much more efficient to rely on computers for most of that. Accounting is focused almost entirely on arithmetic that's possible to be really good at without computers, and less on developing complex formulas where it's simpler to write them out on a computer and then let the computer plug in values and solve. For simpler math, inputting and transcribing numbers from a calculator or computer could end up being the limiting factor. The other aspect to being good at arithmetic is not being particularly good or fast at doing the exact calculation, but rather at estimating what the results should be, so that if the computer gives them the wrong answer, they know almost immediately that they typed something wrong.
immmmmm 5y ago
i learned multiplication table up to 10 time 10 during my phd, while doing 100+ pages long tensor/spinor calculations. at some point it looked more effective learning 6x7 by heart that using a calculator.
rich_sasha 5y ago
I think it’s also that mathematicians rarely care about the answer, more about the process. Figuring out the volume of a complex shape with size scale x? Yes please! Missed a factor of pi/2? Meh who cares? Multiplying two numbers? Oh look one is twice the other one, so it’s a perfect square times 2. Got the squaring wrong? Meh who cares. Then even if you do care, it’s hard to shake old habits. I can’t imagine an accountant saying “ooh here’s an interesting method for multiplying times the tax rate of 13.75%. Got the counting wrong? Meh”.
anthony_r 5y ago
Because arithmetic is completely solved and boring, duh. There was a time when it was at least a little bit interesting, and many mathematicians were actually quite good at it.
- ogogmad 5y ago
  There are clever techniques for doing multiplication like: Logarithm tables, prosthaphaeresis ("trigonometric logarithm tables"), quarter-square tables, abacuses. More recently (that is, within the last 60 years) faster than O(n^2) algorithms have been found as well, with a time complexity of O(n log n) having been achieved. These last algorithms range from being impractical to do by hand, to being outright galactic.
  - jart 5y ago
    I was just about to post this. Arithmetic starts going to the moon once you're dealing with larger than 64-bit numbers. Stuff like Karatsuba's algorithm or you can read all the fourier transform convolution hacks libraries like mpdecimal use. Arithmetic is also very dominant in any sort of low-level programming. It's just that it isn't the same kind of arithmetic that math is used to dealing with, or even likes dealing with, since it's usually over a field that mixes boolean logic with arithmetic. It actually ended up being a security issue because malware authors would find ways to obfuscate their programs using types of math that haven't traditionally been studied, so math tools would be completely powerless to make sense of them. So definitely not a solved problem.
  - kragen 5y ago
    I didn't know about prosthaphaeresis! Thank you! Richard Guy developed a single-scale nomogram based on elliptic curves in 01953: https://www.jstor.org/stable/3609499 https://www.jstor.org/stable/3609499 His explanation is wonderfully simple; quoting the beginning: "Since the equation x³ + ax + b = 0 has zero for the sum of its roots, the x-coordinates of the three intersections of the line y = mx + c and the curve y = x³ + px + q add to zero." It may be entertaining to attempt to derive the rest of the nomogram from that sentence and the use of logarithms before consulting the (one-page) paper. A nice advantage of Guy's contrivance over slide rules is its facility with squares and square roots. On a conventional Oughtred slide rule you can easily enough read off the square root of a number on the A or B scales by reading across the hairline to the D or C scales, respectively; but if your square had been computed on C or D, you are out of luck. Guy's nomogram has some similar limitations, but you can in general easily take the square root of any point on it.
yobbo 5y ago
The reason is that arithmetic is a muscle memory that atrophies without use, and no one outside of school benefits from doing arithmetic by hand. The same is true for algebra and calculus. Mathematicians who teach keep their memories fresh, but no one can pass calculus exams without practising.
stared 5y ago
I am waiting for a follow up: "Why are accountants so bad at proving theorems?"
lmilcin 5y ago
The simple reason is that what you think is math is actually not math at all. When I started studying theoretical math, on my first day, I was told to completely forget what I have learned in school because "it is not math". And then when we talked with our professors about them giving lectures for other students (studying electrical engineering or physics, etc.) we would hear from them something like "Yeah, these guys think math is hard but they don't actually study math". In short -- adding or multiplying things, applying numbers to formulae -- isn't math. Actual mathematicians do not need to calculate a lot of stuff in their heads (though estimating things is sometimes helpful) and don't need to remember formulae (although if you spend any time doing actual math you will learn a lot of formulae). And if they need to they are just as likely to pull out a calculator or Google as any other person. And funny thing is -- before I went to study math I have attended trade school. There, besides a lot of useful topics like economics, accounting, law, touchtyping, etc., we had one semester of actual arithmetic. Which was actually about calculating stuff in your head, fast. We would spend ENTIRE time learning tricks to calculate things faster. And the exams would consist solely of sheets of paper with columns of things to calculate (multiply these three six-digit numbers, etc.) which we had to do in memory.
hdivider 5y ago
Forget arithmetic; I remember conversations with exceptionally capable academic mathematicians who in many cases couldn't count without making mistakes. The likely reason: every number triggers a symphony of mathematical results and complicated ideas in their minds, from both memory of association as well as logic itself, and by necessity their minds also conjure up new concepts every now and then. All this added mathematical machinery interferes with the actual counting process at hand. In an extremely interdependent field like mathematics, maybe the more you know, the harder simple operations become, because our short term memory inevitably gets occupied and interrupted with all the more complicated stuff.
- mbeex 5y ago
  Sometimes a cigar Is just a cigar. I'm a mathematician, I love numbers. But believe me, many do not. And even in a considerably insistent way, they define themselves literally about it.
Koshkin 5y ago
Arnold may have partially explained it in https://www.math.fsu.edu/~wxm/Arnold.htm https://www.math.fsu.edu/~wxm/Arnold.htm
Someone 5y ago
How can you write such an article without mentioning the Grothendieck prime? https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf https://www.ams.org/notices/200410/fea-grothendieck-part2.pd...: One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.” But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. “He doesn’t think concretely.” Consider by contrast the Indian mathematician Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. “He really never worked on examples,” Mumford observed. “I only understand things through examples and then gradually make them more abstract. I don’t think it helped Grothendieck in the least to look at an example.
- danidiaz 5y ago
  Maybe Grothendieck, like Avicenna's conception of God, only knew particulars "in as much as they are universal". Grothendieck once flunked an exam due to—in his own words— "une erreur idiote de calcul numérique".
- davidivadavid 5y ago
  For those who can read French, probably as good a place as any to mention Grothendieck's journal Récoltes et semailles recently got published by Gallimard: https://www.gallimard.fr/Catalogue/GALLIMARD/Tel/Recoltes-et-Semailles-I-II https://www.gallimard.fr/Catalogue/GALLIMARD/Tel/Recoltes-et...
mcv 5y ago
I believe it. I remember from my student days, a couple of M&CS students were playing some game, and afterwards, the mathematician managed to fill an entire A4 sheet trying to add up the scores.
mi_lk 5y ago
why are (some) computer scientists so bad at software engineering?
tpoacher 5y ago
What a great example of the Bulverism fallacy! Love it!
quux 5y ago
This rings true to me. I'm a good software engineer, decent at "real math" and close to hopeless at arithmetic to a level that has had me wondering if I suffer from some version of dyscalculia. This is very confusing to friends and family who assume I should be some kind of savant with numbers until I explain "oh no, in fact the first practical program I wrote as a kid was one to do all my second or third grade math homework for me."
charlieyu1 5y ago
You need mental energy for arithmetic. Mostly gone when you are old enough to be called mathematican
gordaco 5y ago
That's funny. I have a degree in maths, which I guess qualifies me as a mathematician, although I've always worked as a software developer. So, the thing is that I'm not a good mathematician, but I happen to be good at arithmetic. By this I mean that I'm good with mental math (of the "square a 4-digit number in ten seconds or less" type; I'm not nearly as good as the savants out there who perform operations with many more digits, and much more quickly), but also that I like playing with numbers and I've came up with a ton of silly "theorems" [1] (I'm not sure if they even deserve that name) that are mostly based on basic modular arithmetics, so any actual mathematician might find them amusing but nothing more, while a layperson is often amazed. So, mental arithmetic can be useful to make people believe that you are smarter than you actually are :) . I'm not fond of doing this, by the way. But it's a thing that happens. [1] Here goes an example. Take a number that is a multiple of 73, that has exactly seven digits, and that has a zero somewhere in the middle. Say, 73*75391 = 5503543. Then you can exchange whatever goes before and after the zero, and the result is also a multiple of 73: 3543055/73 = 48535. For added WTF, I'd like to mention that it also works with 137: 137*8621 = 1181077, and then, 7701181/137=56213. The proof is surprisingly simple, but you need to know what to look for.
- openknot 5y ago
  A great book for this is "Secrets of Mental Math" by Benjamin and Shermer [0]. I remember a feeling of fun when I memorized the tricks many years ago, but unfortunately I lost the digital flash card deck for reviewing them, so I've forgotten them now. I should recreate it. [0] Goodreads link: https://www.goodreads.com/book/show/83585.Secrets_of_Mental_Math https://www.goodreads.com/book/show/83585.Secrets_of_Mental_...
  - ziml77 5y ago
    I came up with my own shortcuts for mental math back when I was in middle school. But since then whenever I've needed to do anything more than a simple calculation I've just reached for a calculator and have basically lost the ability to do the longer work in my head. While it would have been nice to retain that ability without continued practice, pulling out my phone's calculator is simply faster and won't make an error like I can easily in my head when trying to remember the all the intermediate numbers I'm calculating.
thatjoeoverthr 5y ago
Why would anyone be good at arithmetic? Who does their own arithmetic? I understand that before smartphones it was less common to have a calculator in your literal pocket all the time, but you’d have one at work. You’d have one doing your taxes. Even you child would have one at the bottom of the toy box or left on the floor somewhere. That was the state of things for decades. I recently taught my daughter long division. Home schooling; it’s a requirement. I have to be honest, so I can’t tell her it’s important. She wants to know why it’s in the requirements. My best guess is that it was a job skill in the 1970s and that the education system has a lot of bureaucratic inertia.
- erehweb 5y ago
  While you certainly can calculate everything easily on a calculator, I think there's a value to being able to do your own arithmetic easily, in that this transfers over to good estimation skills and having a sense for when you typed the wrong thing into the calculator. Not something I have a proof of, though.
  - BeFlatXIII 5y ago
    My teachers used to call that intuition "number sense".
- kragen 5y ago
  I did long division on paper yesterday, to convert swimming-pool evaporation rates given as millimeters per day to nanometers per second. Probably a skill I use every week or two. It's true that I could do it faster with a calculator. Perhaps a more practical example was that the day before yesterday my father told me that the recent collapse of an ice shelf off Antarctica was likely to raise sea levels by 27 inches in the next three to five years by debuttressing [what turned out to be] the Thwaites Glacier, so possibly the seaside camping spot he was enjoying that day would be under a foot of water in a few years. I immediately protested that this could not be correct; he must have misunderstood the research, because it was the wrong order of magnitude for such a short time period. And in fact it was the wrong order of magnitude, and the article he had read was deliberately sensationalized by juxtaposing sea-level rises that might occur over the next 80 years with events that will happen over the next three to five years. So his campsite will be fine. Didn't need mental long division for that, though.
calebm 5y ago
I do math art (https://gods.art https://gods.art) and Machine Learning, but I pull out my phone calculator to tips, and my most hated class in school ever was 5th grade math (long division).
dwater 5y ago
Arithmetic (mental math) is a skill that must be practiced like juggling. I used to be a high school math teacher and spent a few hours a day working problems on the board. I got to the point where I could work through stats problems with 3 decimal places about as fast as the students could do them with calculators, and I didn't need to write out my work (although I did). Now 5 years after leaving I prefer to reach for a calculator when adding or subtracting 2 numbers, just to make sure I don't make a mistake.
- IncRnd 5y ago
  > Why Are Mathematicians So Bad at Arithmetic? Why are Programmers So Bad at Programming Bug-Free?
  - sumtechguy 5y ago
    Because we spend 90% of our time in meetings?
    - deleted 5y ago
      [deleted]
- kragen 5y ago
  Watching math professors working problems on the blackboard I am constantly amazed at how rapid they are. They have the training advantage that when they make a mistake, which is not uncommon, someone in the class will immediately point it out.
  - savingsPossible 5y ago
    Also, we do them often. Some problems we use every year (CS teacher here, but I assume the same applies)
- CoastalCoder 5y ago
  I'm curious how much of that is attributable to aging.
deleted 5y ago
[deleted]
usrbinbash 5y ago
For the same reason why my reply to the question: "Hey, can you fix my printer" has always been: "No, I cannot." Just because some things are very losely related, doesn't mean the skills between the two are transferable.
- spywaregorilla 5y ago
  You don't think you could troubleshoot an average printer problem?
  - ninkendo 5y ago
    If the person asking me to help them couldn't figure it out, why would I have a better chance?
    - spywaregorilla 5y ago
      Because they presumably asked you because they think you can do it.
  - usrbinbash 5y ago
    No, I don't, because "an average printer problem" usually translates to "I bought these ink/toner cartridges from one website, and the sledge they go into from another one, and I managed to wedge them into the printer somehow even though now the hatch no longer closes properly and it makes funny noises when I start it, but the light is slighly more orange than last time, so that's a good sign, but it cannot fetch paper from the tray now, could you have a look at it? Because you're so good with the tech stuff..." Sorry, but my proficiency in software engineering doesn't exactly qualify me for handling things like hatches, hinges, tiny gears, levers, springs and plastic boxes that don't fit well together.
dynamic_sausage 5y ago
Not all mathematicians are bad at arithmetic. Both Euler and Gauss were brilliant calculators. Another comment mentions Ramanujan. In more recent history, Arnold in his exams would give problems with plenty of arithmetic estimates, that had to be performed orally and be within 10% of the exact answer. In a surprising turn of events, people studying mathematics are a large group, and some of them are indeed incapable of factoring 57.
- wrycoder 5y ago
  51 looks kinda prime, too.
  - mdp2021 5y ago
    Well, theoretical studies teach you about navigating, managing and creating complex structures; life teaches you to distrust and verify all appearances.
- __MatrixMan__ 5y ago
  The question in the article title sounds to me like: > Why are people from the USA bad at navigating the New York subway? And you're right to point out: > People from New York aren't. If people are surprised by the idea that many mathematicians are bad at arithmetic, then I'm guessing they also think that arithmetic is taught first because it's fundamentally foundational, rather than something to do with Diophantus having lived before Erdős.
umvi 5y ago
> When I began to teach 3D vectors two years ago, I realized I first had to teach it to myself, because I’d never actually learned it. My college courses skipped straight to “n-dimensional vectors.” This sums up why I disliked higher level math classes in college so much. We never actually did anything _useful_ with the math, we never actually applied it to real life, we always just rapidly advanced to the general case ("n-dimensions"), took a test, then moved onto the next topic.
- dash2 5y ago
  That's just why some people like it. My favourite review on Amazon, of Rudin's Principles of Mathematical Analysis (https://www.amazon.com/gp/customer-reviews/R23MC2PCAJYHCB/ref=cm_cr_getr_d_rvw_ttl?ie=UTF8&ASIN=0070856133 https://www.amazon.com/gp/customer-reviews/R23MC2PCAJYHCB/re...): > It is not possible to overstate how good this book is. I tried to give it uncountably many stars but they only have five. Five is an insult. I'm sorry Dr. Rudin.... > "The material is not motivated." Not motivated? Judas just stick a dagger in my heart. This material needs no motivation. Just do it. Faith will come. He's teaching you analysis. Not selling you a used car. By the time you are ready to read this book you should not need motivation from the author as to why you need to know analysis. You should just feel a burning in you chest that can only be quenched by arguments involving an arbitrary sequence {x_n} that converges to x in X. >... if you'r a student and find the book too hard? Try harder. That's the point. If you did not crave intellectual work why are you sitting in an analysis course? Dig in. It will make you a better person. Trust me. > Or you could just change your major back to engineering. It's more money and the books always have lots of nice pictures.
  - wrycoder 5y ago
    Bourbaki themself wrote a review on Amazon? {x-n}
herodotus 5y ago
Stanislaw Ulam (from his book Adventures of a Mathematician): "There are three types of mathematicians. Those that can count and those that can not."
mathteddybear 5y ago
But is there a perception that they are? I mean, in my home country, the stereotypes about mathematicians usually involve them being out-of-touch with the material world, so to speak.
aught 5y ago
arithmetic is a subset of mathematics but its a part that gets in the way of understanding you cant prove things abstractly using numbers for the most part, you can test cases in a very glib way: arithmetic: 1,2,3,… i bet you i can count really high. Arithmetic is integers and while those are cool they are ordered mathematics: what kind of objects behave this way can i prove there are finitely many or infinity many. The field of complex numbers is not ordered very different there hasn’t been a universal mathematician for a very long time and you must choose for your own sanity and productivity what you’re gonna spend your energy on are you going to calculate then don’t go into “modern” abstract mathematics you have to choose what you’re priorities are going to be and everything else has to take a backseat
asow92 5y ago
Does anyone else feel like we should be teaching programming in math classes and implementing proofs instead of writing out arithmetic?
allo37 5y ago
It's funny, in grade school we used to have "speed tests" where you had to add, subtract, multiply numbers as quickly as possible. I used to always do terribly, easily one of the slowest in the class. Then I remember we got into high school and started doing more abstract math. The kids who were amazing at doing math quickly seemed to struggle with this, but I did just fine. I'm not a mathematician or anything, but this article at least validates my belief that doing arithmetic fast in your head and doing more analytical math involve two completely different parts of your brain.
nelgaard 5y ago
Well, not mathematicians. But I once was a physics student. We had a professor which was usually brilliant. But we had a few classes involving arithmetic: Dimensional analysis or practical examples. He would scorn students that took out their calculator and say that any decent physicist could work it out within a few percents margin. Then he would work it out on the blackboard, and every single time he would be wrong by orders of magnitude and we all tried our best not to laugh.
JoeAltmaier 5y ago
Mensa members - 25% can't do math, 10% can't do arithmetic. From a 'Mensa puzzle-a-day' book with answers in the back and percentages of Mensa members getting them right.
tzs 5y ago
Relevant Asimov: https://urbigenous.net/library/power.html https://urbigenous.net/library/power.html

110 points by tomerv 5y ago

Thanks for sharing this. I feel seen :)

Yeah a lot of pure mathematics education very much emphasizes the learning the "spirit" or fundamental concepts of certain things rather than computation, sometimes to the extreme when compared even with applied mathematics. This is especially obvious in anything that even approached calculus. In the math courses I took in college, if we e.g. ever had a differential equation we needed to solve on a problem set "looked up the answer on Wolfram Alpha" was a perfectly reasonable response. Same for differentiation or integration. In some intro courses you'd be ask to prove that certain differentiation or integration techniques had mathematically rigorous backing, but never had to do the rote work of actually memorizing and using those techniques ever again. Again "looked up the answer on Wolfram Alpha" was a perfectly reasonable response. It was a far cry from the applied mathematics department. Another huge discrepancy was in linear algebra, where very little time was spent on matrix computation other than again proving that matrix operations and invariants preserved properties of linear maps and vector spaces and almost all the time of the course was spent on the linear maps and vector spaces themselves, whereas linear algebra in the applied math department was almost entirely about matrices and the intricacies of various matrix computations and decompositions and subjects like dual spaces or other things that couldn't be represented with normal matrix computation (e.g. infinite dimensional vector spaces) were omitted.

gjulianm 5y ago
To add to this comment, a lot of times we didn't even care what the solution was, only that it existed, was unique, or was bounded by some constant (and we didn't usually care about the value either). The more you advance into pure mathematics, the less you care about specific functions or values.
- raverbashing 5y ago
  And I suspect, this is what makes math grind its own gears. The way math is "built", with too generalizing theorems, non-constructive statements, etc makes it fall into traps like the Russel's Paradox (which literally cannot exist "in real life" - not even for the very wide definition of mathematical real life). Building math on saying "this exists" without actually building towards what it is, is a bit of a "sin".
  - gjulianm 5y ago
    > The way math is "built", with too generalizing theorems, non-constructive statements, etc makes it fall into traps like the Russel's Paradox I don't think Russel's paradox is a problem with ZFC set theory. Building sets out of "the set of everything" is not used, and even people are careful to specify when the axiom of choice is being used. > Building math on saying "this exists" without actually building towards what it is, is a bit of a "sin". It's actually not. The idea is that you prove only what you actually need for the next step. A nice example is again in the field of differential equations. Ultimately people are interested in a solution, but to get that solution you need an approximation method, and to get an approximation method you need to know when does it work and how fast does it work, and to know that you need to know when a solution can be found and what properties does it have. Constructivism is something that in theory might sound interesting, but forcing all mathematics to fit that model only servers to make certain proofs of true and useful statements far more complicated or even impossible.
    - lupire 5y ago
      It's rather unscientific to say that we believe things because we want them to be true and not because they are inherently true.
      - gjulianm 5y ago
        Nothing is inherently true, things are only true based on some axioms and hypothesis. What I meant with "results that are true" is things that are consistent with our physical world.
ls15 5y ago
My university had exams that involved arithmetic, matrix computation and differential equations, but no access to Wolfram Alpha though. It was impossible to pass the exams without prior training.
hn_go_brrrrr 5y ago
Once I got past calculus, it seemed like we stopped caring about numbers. Plenty of 0s and 1s, the occasion 2, but rarely a 3 or higher. I remember one theorem had a 24 in the derivation (Stone-Weierstrass, I want to say?) and we were all amazed. Given that, who needs arithmetic?

goldenkey 5y ago

Mathematics is about abstraction, it's literally the study of objects. Different foundations of math define the fundamental objects of the universe in different ways. You have set theory, where everything must be constructed from the empty set, and operations of union, intersection, complement, and inclusion/comprehension. https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers https://en.wikipedia.org/wiki/Set-theoretic_definition_of_na... You might say, how the hell do I get an ordered pair (x,y) from sets? Well, this was solved in a myriad of ways. https://en.m.wikipedia.org/wiki/Ordered_pair#Defining_the_ordered_pair_using_set_theory https://en.m.wikipedia.org/wiki/Ordered_pair#Defining_the_or... You also have category theory where everything is a graph and you start with the global object: 1 -> N then build all numbers recursively. https://en.wikipedia.org/wiki/Natural_numbers_object https://en.wikipedia.org/wiki/Natural_numbers_object And then you keep on using these complex objects to build even more complex ones. So you have a consistent system. And you derive truths about the system, these get called proofs. Arithmetic is child's play - it has nothing to do with consequence or truth. Math is all about starting with agreeable rules and deriving profound consequences that are a kind of umbrella that those rules cover, and sprout from. Canonically, these get called axioms. And we like to choose ones that agree with our common perception of the world -- ie. the Peano axioms for how objects physically work when you combine them, split them, try to group them into rows and columns (prime factorization), etc.. Numbers are one of the simplest and fascinating abstractions because they take the idea of object and unify everything under it -- so two cats and two dogs get typecast to two objects and two objects, then you can add them and get 4 objects. Numbers are basically a reflection of the most primitive type cast possible in our universe of thought. Such, number theory is called the Queen of Mathematics. Because number theory seems to relate much closer to our actual physicality than other axiomatic systems.

TrackerFF 5y ago

What I liked about math in engineering school was that after a certain point, it was really all about numerical methods. Because it is such an applied field, of course you want actual numbers - that's your bread and butter. You first learn the basics, the same way a mathematician learns something, but afterwards it's all simulation and approximations. During grad school, however, there was a complete shift from this - IMO. You suddenly had more classes with with math for mathematicians. Of course, this was because you took a lot more advanced and cutting edge classes, which were often built on various fields of math. New tech often follows that route...breakthrough discoveries in math or physics, which is often described in dense mathematical language. Before it eventually gets more applied and approximated forms, which are more suited for real-life uses. I've also noticed that working engineers tend to be much better at mental computation, than most researchers / scientists. But that obviously comes from years of work experience.

ReleaseCandidat 5y ago
> Because it is such an applied field, of course you want actual numbers That's why you're an engineer and not a mathematician ;) Because, no, _I_ do not want numbers if I can avoid them. Proofing that something has one (and exactly one) solution is (for example) way more interesting than actually computing the result - this is that boring that even computers can do (some of) the work for us.

emptybits 5y ago

Seems plausible. Similarly, a computer scientist may be bad at writing computer programs. (And this may also surprise someone outside the field.)

jesperlang 5y ago

Isn't this a little bit like "Why are computer scientists so bad at fixing my router / printer / virus infected windows laptop?" :)

grenoire 5y ago
Oh, you computer scientists!
mdp2021 5y ago
Because something broke inside following the times in which they were requested to help with your "virus infected mouse device". (Sorry.) Or those times "What do you mean do not open the virus? I tried to open it, I clicked on it a thousand times, nothing happened!". (Both are very real and lived, I am afraid.)
Koshkin 5y ago
Simple: we all know that Computer science is no more about computers than astronomy is about telescopes. (Something like that can be said about mathematics, I am sure.)
technothrasher 5y ago
When I was in school back in the 90's and worked for the computing center supporting Unix workstations on campus, it was always funny to get called over to the CS department to fix a professor's workstation and discover once again that they had zero clue how to use their machine. These were the same professors I had in my CS classes, who were fantastic. They were 100% theory and not at all practical, and actually weren't the least bit ashamed to admit it.
- mathattack 5y ago
  One of my professors answered “How do you go about debugging your programs?” with “I don’t debug, I prove my code correct before typing it in.” Not very useful.
  - xgkickt 5y ago

AllegedAlec 5y ago

For the same reason a biologist doesn't know the names of all trees by sight.

lordnacho 5y ago

What we need now is someone giving an anecdote about how they're a published math researcher but at the job interview they screened him with Times Table Rock Star and gave him a take home to solve 20 quadratic equations.

pooper 5y ago
> Times Table Rock Star When I was a child, the schools tried to get me to memorize the multiplication tables. At least through ten, teachers would say. I thought it was pretty silly. You shouldn't force memorization. It should come naturally as you use certain things many times. If you use 7x6 often, you will remember it. If not, you will forget it. That should be totally fine. Why should it matter if you memorized 7x6 or you had to go the long way and say 7x5 is 35 so add 7 to 35 and you'll get 7x6? Imagine if you said, good programmers are often fast typists and some idiot decided to add a touch typing test to their hiring process. » Goodhart's law is an adage often stated as "When a measure becomes a target, it ceases to be a good measure". Edit turn asterisks to x. Please read x as multiply.
- lordnacho 5y ago
  > It should come naturally as you use certain things many times. But if it's not second nature, you may decide not to do it many times. Is it "need this -> gets memorized" or "memorized -> can use as tool"? Personally I've never been a proponent of memorizing things, preferring to Google when needed, but I can see how the argument runs.
- mdp2021 5y ago
  I Disagree. This "you only need one eye and one ear - two is redundant" approach to memorization is a root with the dire situation of today, in which I know youngsters with some diploma who can go "I thought that 5x8 was [any number]. Really it is 40?!". While studying, in general, mnemonic hooks pose a foundation for further notions to become solid. Then, the whole of them become available micro-tools for reasoning.
- jimhefferon 5y ago
  I'm a mathematician. When I was in grade school they told us to memorize up to twelve. But I figured I could skip the evens, because doubling is easy, so I would just memorize the odds. One is trivial, three and five are simple, as is eleven. There is an easy algorithm for mine. So I memorized seven and called it done. When I think of the thousands of multiplications I've done since then, it's clear I was a dope and my teachers were perfectly right.

roenxi 5y ago

The mathematicians are probably wrong. Mathematicians will have above average ability with arithmatics, but they're going to be meeting people who memorise pi to 50 decimal places or happen to calculate the sum of small cubic numbers for fun to pass the time and are really good at arithmetic. What the mathematicians are probably cluing in to is the fact that around half of mathematicians are below median arithmetic ability in their immidiate academic community.

gjulianm 5y ago
> but they're going to be meeting people who memorise pi to 50 decimal places or happen to calculate the sum of small cubic numbers for fun to pass the time and are really good at arithmetic. Not really. The "above average ability" depends on the population: if you compare mathematicians with other college educated people, I'd guess they'd be at the bottom among the STEM fields. It wasn't weird to see people (or myself) having the occasional "wait, what's 5 times 7". And it shouldn't be surprising if people knew that 99% of the arithmetic operations done in math degrees are things like "2+1" or "2·3".
- lupire 5y ago
  It's unsurprising that abstract mathematicians are worse at engineering math than engineers, and vice versa for abstract math.
watwut 5y ago
> Mathematicians will have above average ability with arithmatics They dont. My family has multiple ma mathematicians in it and as a kid I spent a lot of time with their colleagues on activities. Many do regularly huge mistakes in basic arithmetic like multiplication or addition. Some of them do "memorise pi to 50 decimal places" or learn some other "stunt" for fun of it or in order to impress people. But they all treat it more of as a stunt then something meaningful. It just does not matter for work of mathematician whether you are good with arithmetic. So they dont care about becoming good at it. They just joke about it when someone makes mistake yet again.

jonathanstrange 5y ago

I doubt that the premise is true. Self-reporting is not a reliable indicator of actual performance in this case. It seems plausible that an empirical study would find mathematicians way above the average in elementary arithmetic, though possibly trumped by waiters and cashiers who often have to calculate without aid. Of course, without an actual study this is just speculation.

anoplus 5y ago

I think this is a crucial message for young students who feel inferior to that human calculator classmate.

harshreality 5y ago

Contest-style rapid numeric calculation is a special case of "math". Many kids in math clubs focus on both — a significant part of contest math is word problems that have to be interpreted correctly and then calculated correctly, under time pressure — but calculation has little to do with higher math other than being able to validate symbolic results. Fast calculation is about drilling and learning tricks. People can get pretty accurate and fast at simple arithmetic as long as numbers fit (or they've learned tricks to chunk them) into their working memories. If there's no inherent motivation or necessity to maintain those skills after school, they'll decay. As the article points out, accountants and engineers are likely to be better at being human calculators. I'd guess accountants first, because engineers do more complex calculations and it'd be much more efficient to rely on computers for most of that. Accounting is focused almost entirely on arithmetic that's possible to be really good at without computers, and less on developing complex formulas where it's simpler to write them out on a computer and then let the computer plug in values and solve. For simpler math, inputting and transcribing numbers from a calculator or computer could end up being the limiting factor. The other aspect to being good at arithmetic is not being particularly good or fast at doing the exact calculation, but rather at estimating what the results should be, so that if the computer gives them the wrong answer, they know almost immediately that they typed something wrong.

immmmmm 5y ago

i learned multiplication table up to 10 time 10 during my phd, while doing 100+ pages long tensor/spinor calculations. at some point it looked more effective learning 6x7 by heart that using a calculator.

rich_sasha 5y ago

I think it’s also that mathematicians rarely care about the answer, more about the process. Figuring out the volume of a complex shape with size scale x? Yes please! Missed a factor of pi/2? Meh who cares? Multiplying two numbers? Oh look one is twice the other one, so it’s a perfect square times 2. Got the squaring wrong? Meh who cares. Then even if you do care, it’s hard to shake old habits. I can’t imagine an accountant saying “ooh here’s an interesting method for multiplying times the tax rate of 13.75%. Got the counting wrong? Meh”.

anthony_r 5y ago

Because arithmetic is completely solved and boring, duh. There was a time when it was at least a little bit interesting, and many mathematicians were actually quite good at it.

ogogmad 5y ago
There are clever techniques for doing multiplication like: Logarithm tables, prosthaphaeresis ("trigonometric logarithm tables"), quarter-square tables, abacuses. More recently (that is, within the last 60 years) faster than O(n^2) algorithms have been found as well, with a time complexity of O(n log n) having been achieved. These last algorithms range from being impractical to do by hand, to being outright galactic.
- jart 5y ago
  I was just about to post this. Arithmetic starts going to the moon once you're dealing with larger than 64-bit numbers. Stuff like Karatsuba's algorithm or you can read all the fourier transform convolution hacks libraries like mpdecimal use. Arithmetic is also very dominant in any sort of low-level programming. It's just that it isn't the same kind of arithmetic that math is used to dealing with, or even likes dealing with, since it's usually over a field that mixes boolean logic with arithmetic. It actually ended up being a security issue because malware authors would find ways to obfuscate their programs using types of math that haven't traditionally been studied, so math tools would be completely powerless to make sense of them. So definitely not a solved problem.
- kragen 5y ago
  I didn't know about prosthaphaeresis! Thank you! Richard Guy developed a single-scale nomogram based on elliptic curves in 01953: https://www.jstor.org/stable/3609499 https://www.jstor.org/stable/3609499 His explanation is wonderfully simple; quoting the beginning: "Since the equation x³ + ax + b = 0 has zero for the sum of its roots, the x-coordinates of the three intersections of the line y = mx + c and the curve y = x³ + px + q add to zero." It may be entertaining to attempt to derive the rest of the nomogram from that sentence and the use of logarithms before consulting the (one-page) paper. A nice advantage of Guy's contrivance over slide rules is its facility with squares and square roots. On a conventional Oughtred slide rule you can easily enough read off the square root of a number on the A or B scales by reading across the hairline to the D or C scales, respectively; but if your square had been computed on C or D, you are out of luck. Guy's nomogram has some similar limitations, but you can in general easily take the square root of any point on it.

yobbo 5y ago

The reason is that arithmetic is a muscle memory that atrophies without use, and no one outside of school benefits from doing arithmetic by hand. The same is true for algebra and calculus. Mathematicians who teach keep their memories fresh, but no one can pass calculus exams without practising.

stared 5y ago

I am waiting for a follow up: "Why are accountants so bad at proving theorems?"

lmilcin 5y ago

The simple reason is that what you think is math is actually not math at all. When I started studying theoretical math, on my first day, I was told to completely forget what I have learned in school because "it is not math". And then when we talked with our professors about them giving lectures for other students (studying electrical engineering or physics, etc.) we would hear from them something like "Yeah, these guys think math is hard but they don't actually study math". In short -- adding or multiplying things, applying numbers to formulae -- isn't math. Actual mathematicians do not need to calculate a lot of stuff in their heads (though estimating things is sometimes helpful) and don't need to remember formulae (although if you spend any time doing actual math you will learn a lot of formulae). And if they need to they are just as likely to pull out a calculator or Google as any other person. And funny thing is -- before I went to study math I have attended trade school. There, besides a lot of useful topics like economics, accounting, law, touchtyping, etc., we had one semester of actual arithmetic. Which was actually about calculating stuff in your head, fast. We would spend ENTIRE time learning tricks to calculate things faster. And the exams would consist solely of sheets of paper with columns of things to calculate (multiply these three six-digit numbers, etc.) which we had to do in memory.

hdivider 5y ago

Forget arithmetic; I remember conversations with exceptionally capable academic mathematicians who in many cases couldn't count without making mistakes. The likely reason: every number triggers a symphony of mathematical results and complicated ideas in their minds, from both memory of association as well as logic itself, and by necessity their minds also conjure up new concepts every now and then. All this added mathematical machinery interferes with the actual counting process at hand. In an extremely interdependent field like mathematics, maybe the more you know, the harder simple operations become, because our short term memory inevitably gets occupied and interrupted with all the more complicated stuff.

mbeex 5y ago
Sometimes a cigar Is just a cigar. I'm a mathematician, I love numbers. But believe me, many do not. And even in a considerably insistent way, they define themselves literally about it.

Koshkin 5y ago

Arnold may have partially explained it in https://www.math.fsu.edu/~wxm/Arnold.htm https://www.math.fsu.edu/~wxm/Arnold.htm

Someone 5y ago

How can you write such an article without mentioning the Grothendieck prime? https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf https://www.ams.org/notices/200410/fea-grothendieck-part2.pd...: One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.” But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. “He doesn’t think concretely.” Consider by contrast the Indian mathematician Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. “He really never worked on examples,” Mumford observed. “I only understand things through examples and then gradually make them more abstract. I don’t think it helped Grothendieck in the least to look at an example.

danidiaz 5y ago
Maybe Grothendieck, like Avicenna's conception of God, only knew particulars "in as much as they are universal". Grothendieck once flunked an exam due to—in his own words— "une erreur idiote de calcul numérique".
davidivadavid 5y ago
For those who can read French, probably as good a place as any to mention Grothendieck's journal Récoltes et semailles recently got published by Gallimard: https://www.gallimard.fr/Catalogue/GALLIMARD/Tel/Recoltes-et-Semailles-I-II https://www.gallimard.fr/Catalogue/GALLIMARD/Tel/Recoltes-et...

mcv 5y ago

I believe it. I remember from my student days, a couple of M&CS students were playing some game, and afterwards, the mathematician managed to fill an entire A4 sheet trying to add up the scores.

mi_lk 5y ago

why are (some) computer scientists so bad at software engineering?

tpoacher 5y ago

What a great example of the Bulverism fallacy! Love it!

quux 5y ago

This rings true to me. I'm a good software engineer, decent at "real math" and close to hopeless at arithmetic to a level that has had me wondering if I suffer from some version of dyscalculia. This is very confusing to friends and family who assume I should be some kind of savant with numbers until I explain "oh no, in fact the first practical program I wrote as a kid was one to do all my second or third grade math homework for me."

charlieyu1 5y ago

You need mental energy for arithmetic. Mostly gone when you are old enough to be called mathematican

gordaco 5y ago

That's funny. I have a degree in maths, which I guess qualifies me as a mathematician, although I've always worked as a software developer. So, the thing is that I'm not a good mathematician, but I happen to be good at arithmetic. By this I mean that I'm good with mental math (of the "square a 4-digit number in ten seconds or less" type; I'm not nearly as good as the savants out there who perform operations with many more digits, and much more quickly), but also that I like playing with numbers and I've came up with a ton of silly "theorems" [1] (I'm not sure if they even deserve that name) that are mostly based on basic modular arithmetics, so any actual mathematician might find them amusing but nothing more, while a layperson is often amazed. So, mental arithmetic can be useful to make people believe that you are smarter than you actually are :) . I'm not fond of doing this, by the way. But it's a thing that happens. [1] Here goes an example. Take a number that is a multiple of 73, that has exactly seven digits, and that has a zero somewhere in the middle. Say, 73*75391 = 5503543. Then you can exchange whatever goes before and after the zero, and the result is also a multiple of 73: 3543055/73 = 48535. For added WTF, I'd like to mention that it also works with 137: 137*8621 = 1181077, and then, 7701181/137=56213. The proof is surprisingly simple, but you need to know what to look for.

openknot 5y ago
A great book for this is "Secrets of Mental Math" by Benjamin and Shermer [0]. I remember a feeling of fun when I memorized the tricks many years ago, but unfortunately I lost the digital flash card deck for reviewing them, so I've forgotten them now. I should recreate it. [0] Goodreads link: https://www.goodreads.com/book/show/83585.Secrets_of_Mental_Math https://www.goodreads.com/book/show/83585.Secrets_of_Mental_...
- ziml77 5y ago
  I came up with my own shortcuts for mental math back when I was in middle school. But since then whenever I've needed to do anything more than a simple calculation I've just reached for a calculator and have basically lost the ability to do the longer work in my head. While it would have been nice to retain that ability without continued practice, pulling out my phone's calculator is simply faster and won't make an error like I can easily in my head when trying to remember the all the intermediate numbers I'm calculating.

thatjoeoverthr 5y ago

Why would anyone be good at arithmetic? Who does their own arithmetic? I understand that before smartphones it was less common to have a calculator in your literal pocket all the time, but you’d have one at work. You’d have one doing your taxes. Even you child would have one at the bottom of the toy box or left on the floor somewhere. That was the state of things for decades. I recently taught my daughter long division. Home schooling; it’s a requirement. I have to be honest, so I can’t tell her it’s important. She wants to know why it’s in the requirements. My best guess is that it was a job skill in the 1970s and that the education system has a lot of bureaucratic inertia.

erehweb 5y ago
While you certainly can calculate everything easily on a calculator, I think there's a value to being able to do your own arithmetic easily, in that this transfers over to good estimation skills and having a sense for when you typed the wrong thing into the calculator. Not something I have a proof of, though.
- BeFlatXIII 5y ago
  My teachers used to call that intuition "number sense".
kragen 5y ago
I did long division on paper yesterday, to convert swimming-pool evaporation rates given as millimeters per day to nanometers per second. Probably a skill I use every week or two. It's true that I could do it faster with a calculator. Perhaps a more practical example was that the day before yesterday my father told me that the recent collapse of an ice shelf off Antarctica was likely to raise sea levels by 27 inches in the next three to five years by debuttressing [what turned out to be] the Thwaites Glacier, so possibly the seaside camping spot he was enjoying that day would be under a foot of water in a few years. I immediately protested that this could not be correct; he must have misunderstood the research, because it was the wrong order of magnitude for such a short time period. And in fact it was the wrong order of magnitude, and the article he had read was deliberately sensationalized by juxtaposing sea-level rises that might occur over the next 80 years with events that will happen over the next three to five years. So his campsite will be fine. Didn't need mental long division for that, though.

calebm 5y ago

I do math art (https://gods.art https://gods.art) and Machine Learning, but I pull out my phone calculator to tips, and my most hated class in school ever was 5th grade math (long division).

dwater 5y ago

Arithmetic (mental math) is a skill that must be practiced like juggling. I used to be a high school math teacher and spent a few hours a day working problems on the board. I got to the point where I could work through stats problems with 3 decimal places about as fast as the students could do them with calculators, and I didn't need to write out my work (although I did). Now 5 years after leaving I prefer to reach for a calculator when adding or subtracting 2 numbers, just to make sure I don't make a mistake.

IncRnd 5y ago
> Why Are Mathematicians So Bad at Arithmetic? Why are Programmers So Bad at Programming Bug-Free?
- sumtechguy 5y ago
  Because we spend 90% of our time in meetings?
  - deleted 5y ago
    [deleted]
kragen 5y ago
Watching math professors working problems on the blackboard I am constantly amazed at how rapid they are. They have the training advantage that when they make a mistake, which is not uncommon, someone in the class will immediately point it out.
- savingsPossible 5y ago
  Also, we do them often. Some problems we use every year (CS teacher here, but I assume the same applies)
CoastalCoder 5y ago
I'm curious how much of that is attributable to aging.

deleted 5y ago

[deleted]

usrbinbash 5y ago

For the same reason why my reply to the question: "Hey, can you fix my printer" has always been: "No, I cannot." Just because some things are very losely related, doesn't mean the skills between the two are transferable.

spywaregorilla 5y ago
You don't think you could troubleshoot an average printer problem?
- ninkendo 5y ago
  If the person asking me to help them couldn't figure it out, why would I have a better chance?
  - spywaregorilla 5y ago
    Because they presumably asked you because they think you can do it.
- usrbinbash 5y ago
  No, I don't, because "an average printer problem" usually translates to "I bought these ink/toner cartridges from one website, and the sledge they go into from another one, and I managed to wedge them into the printer somehow even though now the hatch no longer closes properly and it makes funny noises when I start it, but the light is slighly more orange than last time, so that's a good sign, but it cannot fetch paper from the tray now, could you have a look at it? Because you're so good with the tech stuff..." Sorry, but my proficiency in software engineering doesn't exactly qualify me for handling things like hatches, hinges, tiny gears, levers, springs and plastic boxes that don't fit well together.

dynamic_sausage 5y ago

Not all mathematicians are bad at arithmetic. Both Euler and Gauss were brilliant calculators. Another comment mentions Ramanujan. In more recent history, Arnold in his exams would give problems with plenty of arithmetic estimates, that had to be performed orally and be within 10% of the exact answer. In a surprising turn of events, people studying mathematics are a large group, and some of them are indeed incapable of factoring 57.

wrycoder 5y ago
51 looks kinda prime, too.
- mdp2021 5y ago
  Well, theoretical studies teach you about navigating, managing and creating complex structures; life teaches you to distrust and verify all appearances.
__MatrixMan__ 5y ago
The question in the article title sounds to me like: > Why are people from the USA bad at navigating the New York subway? And you're right to point out: > People from New York aren't. If people are surprised by the idea that many mathematicians are bad at arithmetic, then I'm guessing they also think that arithmetic is taught first because it's fundamentally foundational, rather than something to do with Diophantus having lived before Erdős.

umvi 5y ago

> When I began to teach 3D vectors two years ago, I realized I first had to teach it to myself, because I’d never actually learned it. My college courses skipped straight to “n-dimensional vectors.” This sums up why I disliked higher level math classes in college so much. We never actually did anything _useful_ with the math, we never actually applied it to real life, we always just rapidly advanced to the general case ("n-dimensions"), took a test, then moved onto the next topic.

dash2 5y ago
That's just why some people like it. My favourite review on Amazon, of Rudin's Principles of Mathematical Analysis (https://www.amazon.com/gp/customer-reviews/R23MC2PCAJYHCB/ref=cm_cr_getr_d_rvw_ttl?ie=UTF8&ASIN=0070856133 https://www.amazon.com/gp/customer-reviews/R23MC2PCAJYHCB/re...): > It is not possible to overstate how good this book is. I tried to give it uncountably many stars but they only have five. Five is an insult. I'm sorry Dr. Rudin.... > "The material is not motivated." Not motivated? Judas just stick a dagger in my heart. This material needs no motivation. Just do it. Faith will come. He's teaching you analysis. Not selling you a used car. By the time you are ready to read this book you should not need motivation from the author as to why you need to know analysis. You should just feel a burning in you chest that can only be quenched by arguments involving an arbitrary sequence {x_n} that converges to x in X. >... if you'r a student and find the book too hard? Try harder. That's the point. If you did not crave intellectual work why are you sitting in an analysis course? Dig in. It will make you a better person. Trust me. > Or you could just change your major back to engineering. It's more money and the books always have lots of nice pictures.
- wrycoder 5y ago
  Bourbaki themself wrote a review on Amazon? {x-n}

herodotus 5y ago

Stanislaw Ulam (from his book Adventures of a Mathematician): "There are three types of mathematicians. Those that can count and those that can not."

mathteddybear 5y ago

But is there a perception that they are? I mean, in my home country, the stereotypes about mathematicians usually involve them being out-of-touch with the material world, so to speak.

aught 5y ago

arithmetic is a subset of mathematics but its a part that gets in the way of understanding you cant prove things abstractly using numbers for the most part, you can test cases in a very glib way: arithmetic: 1,2,3,… i bet you i can count really high. Arithmetic is integers and while those are cool they are ordered mathematics: what kind of objects behave this way can i prove there are finitely many or infinity many. The field of complex numbers is not ordered very different there hasn’t been a universal mathematician for a very long time and you must choose for your own sanity and productivity what you’re gonna spend your energy on are you going to calculate then don’t go into “modern” abstract mathematics you have to choose what you’re priorities are going to be and everything else has to take a backseat

asow92 5y ago

Does anyone else feel like we should be teaching programming in math classes and implementing proofs instead of writing out arithmetic?

allo37 5y ago

It's funny, in grade school we used to have "speed tests" where you had to add, subtract, multiply numbers as quickly as possible. I used to always do terribly, easily one of the slowest in the class. Then I remember we got into high school and started doing more abstract math. The kids who were amazing at doing math quickly seemed to struggle with this, but I did just fine. I'm not a mathematician or anything, but this article at least validates my belief that doing arithmetic fast in your head and doing more analytical math involve two completely different parts of your brain.

nelgaard 5y ago

Well, not mathematicians. But I once was a physics student. We had a professor which was usually brilliant. But we had a few classes involving arithmetic: Dimensional analysis or practical examples. He would scorn students that took out their calculator and say that any decent physicist could work it out within a few percents margin. Then he would work it out on the blackboard, and every single time he would be wrong by orders of magnitude and we all tried our best not to laugh.

JoeAltmaier 5y ago

Mensa members - 25% can't do math, 10% can't do arithmetic. From a 'Mensa puzzle-a-day' book with answers in the back and percentages of Mensa members getting them right.

tzs 5y ago

Relevant Asimov: https://urbigenous.net/library/power.html https://urbigenous.net/library/power.html