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When will I ever use math?

189 points by mrspeaker 15y ago

grn 15y ago
I don't think that the comparison with music or sports is correct. If I had to play an instrument I would ask for a motivation because I don't enjoy playing. Similarly someone who doesn't enjoy maths asks for a reason to study it. When you present maths to someone who doesn't like it on its own then the problem is to find a balance between abstraction and applications. When maths is presented too abstractly then it looks useless. When it's presented too concretely then it looses its essence and may seem trivial.
khyryk 15y ago
> This, to me, is mathematics. Playing, confirming, questioning — even in my real life. It gave me a much sadder answer for people when they ask me “when am I ever going to use this”. This isn't exclusive to mathematics. I'm sure there are thousands of blog posts lamenting the lack of philosophy, comparative literature, computer science, etc. instruction.
msluyter 15y ago
The analogy between band and math is problematic. Band has various payoffs that math doesn't: getting attention from peers, the inherent joy in playing music, peer bonding via football games, band trips and whatnot. (Not that math doesn't have "inherent joy" -- it just seems more solitary, more cerebral, and less socially glorified than music.) There's no doubt that our math education destroys curiousity, and if we could teach math in a non-utilitarian way, as a sort of artistic endeavor, that would be amazing, but... is it even possible? Has it ever been tried? Whenever I think about this, I think about season 4 of The Wire.
- m_for_monkey 15y ago
  Really utilitarian math education would be good. The problem is that it's not even that. It's just test-oriented and boring. See this twelve minute video: http://www.ted.com/talks/lang/en/dan_meyer_math_curriculum_makeover.html http://www.ted.com/talks/lang/en/dan_meyer_math_curriculum_m...
- clarebear 15y ago
  I always thought that band was "cooler" than math because some people make out on band buses during trips. I've never seen anyone make out on a math trip.
- slindsey 15y ago
  I always go to Vi Hart (http://vihart.com/doodling/ http://vihart.com/doodling/) when thinking about how we should teach math.
- screwt 15y ago
  Re "the inherent joy in playing music" - isn't that the whole point of the article? When it's not reduced to mindless rote learning, there can be an inherent joy in doing math.
- xyzzyz 15y ago
  I don't think that math is fundamentally different than band with regard to things you mentioned. Best mathematicians certainly get lots of attention from peer mathematicians. The equivalent of band trips are summer schools, where also lots of peer bonding happen. Inherent joy? Why, that's the whole point of doing math for me.
- mechanical_fish 15y ago
  Music can be exactly as solitary and cerebral as math. That aspect of music doesn't get the same press, is all. If you play three chords on a tall stage people know you're in a band; if you sit in your home working out a Bach fugue nobody needs to know. I have a slightly silly book about birdwatching. It has a section which talks about birding competitions - "Big Days", they call them - and the final two sentences stick in my head, always: Don't go away from this thinking that birding is an endless succession of fabbydoo games or fun, fun, fun without a moment's rest. Quite the opposite. Birding is mostly about looking at birds. It is no use to pretend otherwise. A useful motto. Birding is very popular, of course, even in the go-go all-action United States. Other popular activities include knitting, gardening, hiking, sudoku, crosswords, reading, fantasy football, Angry Birds, writing comments on message boards, and, ahem, hacking. All of them solitary, cerebral, and socially unglorified. (Though I guess fantasy football is arguable: You can probably spend an entire evening over beer talking with your friends about the performance of their fantasy football teams. For all I know it's even popular in high school. I knew several people in high school who were reliable authorities on every active major-league baseball player...) People have a warped view of other people's lives in general, and particularly the lives of high school students. I suspect that high school kids enjoy quiet, solitary activities as much as anyone else: In other words, more than you notice. The quiet hobbies are just unobtrusive, so they don't get a lot of press and they don't show up in movies or TV except around the edges. Speaking for myself, I think I stayed away from band in school because it was full of people and attention. I gravitated toward the quiet sources of pleasure and meaning. Of course, I was blessed with a math club mentor who knew what "recreational mathematics" was...
  - nickpinkston 15y ago
    I think matrix math could actually be presented in a Sudoku-like format - for a Gaussian Elimination or some such - and that'd actually be fun for the Sudoku crowd to play. It's really pretty similar skills involved. Sudoku is probably just a special case matrix problem...
- ckpwong 15y ago
  I beg to differ on your point of math being inherently non-social. In high school, I actively participated--and later led--my school's math league team. Every Friday, we were either home or away for a match with another school. My school wasn't particularly known as a math hothouse (unlike other schools with gifted programs), but we managed to get pretty far in the playoffs for the years I was there, finishing 3rd in the district once even. Back then, I also actively participated in math and science contests, which eventually led me to be invited to a week-long math seminar. During that week, we had daily team competitions and other activities that were fun, social, and mind boggling at the same time. And it doesn't hurt on that one faithful June morning too many years ago, I also met the person whom eventually became my husband. wink
edw519 15y ago
Asking "When will I ever use math?" is like jogging and asking, "When will I ever use these calf muscles?" (The answer to both is "all the time", but that's not the point.) I was a math major who did independent research in Elementary Number Theory and decided to switch paths and become a computer programmer (many years ago). It's true, I haven't encountered many sigmas, deltas, and derivative signs in all those years, but there's absolutely no doubt in my mind that I'm exercising the same mental muscles built with math. OP mentions “wondering, playing, amusing yourself with your imagination.” Hell, build something. Assembling ones and zeros to help real people solve real problems is every bit as wonderful, playful, and amusing as anything I ever did with pure mathematics. And probably even more rewarding...I've discovered that it's much more likely to see a customer do a happy dance with software that never existed before I built it than proving Fermat's Last Theorem or figuring out what Galois was up to on that long last night.
- bluekeybox 15y ago
  > OP mentions “wondering, playing, amusing yourself with your imagination.” Hell, build something. Mathematics is like AI. As soon as a company/whoever builds upon one of the advances in the field and people en masse start using a practical result that comes out of it, it stops being called mathematics/AI. When we hear the word "mathematician" we almost right away imagine an absent-minded professor not contributing anything immediately useful to the real world. People are basically arguing about language, not realizing that they are pawns of a subtle phenomenon that the name of a discipline taught in school refers not so much to knowledge based on and derived from that discipline in the world at large, but to the actual act of teaching that discipline to children and young adults, and sometimes to performing academic-model-funded (meaning charity-like funded) research. It's a bit sad because this trick the language plays on us probably devalues in the eyes of young people something that is actually a useful/practical skill. Kids may say to themselves, "Why do I need this? I don't want to be a schoolteacher," and they will be both right and wrong at the same time, not realizing how many high-paying jobs from engineering to banks to Wall Street require the mental skill they chose not to spend time developing.
- timwiseman 15y ago
  Very well said. Though it is worth noting the distinctions between different types of math. I found my studies of theoretical math in college enormous fruitful just as I found jogging beneficial. But I thought doing numerous arithmetic problems in middle school to be of minimal value and the rote memorization of things like multiplication tables to be worthless. In short, much like exercise, studying math should be done in a way that is pushing your personal limits at least a little.
Jarred 15y ago
I suspect when students ask, "When will I use this?", they don't see any practical or abstract uses of what the teacher is teaching. In other words, it isn't expanding their mind or changing how they think about things. I've yet to have a math teacher that does this well, but I've also yet to have a good math teacher. Maybe there's a correlation.
- georgieporgie 15y ago
  I keep mentioning that, in my opinion, non-college mathematics teachers generally only know enough math to get through the end of the material they're teaching in any given semester. I don't think they're capable of teaching the material from multiple angles, which seems necessary in order to instill a fundamental grasp of the material.
flom 15y ago
The problem with the analogy between music and math is the free-will aspect. Everyone is FORCED to take math, whereas most people are NOT forced to play an instrument (at least in the US). Everyone knew a couple of math wizzes who usually were not the one's asking "why do I need to learn this?" These kids would probably do math even if they weren't forced to, and indeed, many of them go on to pursue a higher education in mathematics, completely voluntarily. On the other hand, many kids whose parents force them to play an instrument often complain and ask "why do I need to play an instrument?" tl;dr: If you force someone to do something, and you don't want to make them resent the thing you're forcing them to do, you should explain to them why you're forcing them to do it, i.e., why it's in their best interest, whether it's math, music, learning a language, etc.
ef4 15y ago
If you didn't take the author's advice and read [Lockhart's Lament](http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf), go do it. It's worth it.
- draggnar 15y ago
  2nded... It is the most influential thing I have ever read. I used to hate math in school and the perspective of math as art completely changed the way I think about it.
jgrahamc 15y ago
One of the simplest uses of math was shown to me by a carpenter who made a triangle from three pieces of wood with sides 24", 32" and 40". Because of this his triangle had a right angle in the corner and he could use it to check that things (such as large areas of tiling) were square. Good old Pythagoras: 24^2 + 32^2 = 40^2. Because the sides were long he had a nice big right angle to work with.
- bryanlarsen 15y ago
  Yes, I remember my uncle showing me this when we were doing some roofing. He then refused to believe me when I figured out a few other ratios that would also do the same thing.
  - ajross 15y ago
    Amusing, but this is where engineering thought differs: obviously your rediscovery of the 5:12:13 right triangle or whatever was precocious and showed a deeper mastery of the subject. That said: your advice sucked. The 3:4:5 triangle is a better choice for obvious reasons (smaller numbers) and not so obvious ones (less sensitivity to measurement error due to larger internal angles). The critically important distinction there is precisely that between, say, Haskell and Ruby. :)
    - derleth 15y ago
      Except both Haskell and Ruby are useful.
    - bryanlarsen 15y ago
      Actually I couldn't even get him to agree that a 6:8:10 triangle was equivalent to a 3:4:5 triangle.
    - madhadron 15y ago
      > The critically important distinction there is precisely that between, say, Haskell and Ruby. :) Absolutely. Why bother with all that unnecessary complexity in Ruby?
gxs 15y ago
Football players don't lift weights on the field - yet they lift weights to gain strength and conditioning to prepare for what occurs on the field. I was a math major in college. I don't use the actual math I learned, but 4 years of solving really hard math problems at Cal honed my problem solving skills and helped me develop a type of stamina to try my hand at them for long periods of time. My grades weren't the best, and having math Olympiads in your classes sometimes makes things harder than they should be. That said, I treasure the experience. I learned to push myself in a way I hadn't before. I learned the value of being rigorous, and even the value of getting creative to solve problems. I learned that even after 4 hours of staring at a problem, I should keep at it because I may get that ah-ha moment at the fifth or sixth hour. So do I use math everyday? Not really. Do I use the ability to solve problems, to abstract my knowledge in one area and apply it another, to carry through long logical thoughts everyday? You bet your ass I do.
m_for_monkey 15y ago
The band kids and the football kids never ask their teachers and coaches, “when will I ever use this”. Because they are playing the flute and they are playing football. They enjoy it now and that's what counts, they don't even think about the future. And yet they come into my math class and raise their hand half-way through my demonstration of the mean value theorem to ask me when they will ever use this. Because the "mean value theorem" sounds like boring shit and their only hope is that it may be useful in the future. If you teach them programming to solve their physics homework and make it a game using math, they won't ask. Never.
- TeMPOraL 15y ago
  > If you teach them programming to solve their physics homework and make it a game using math, they won't ask. True. That's actually how I ended up as a programmer - math in school was boring, trying to make a video game was not. I finally learned trigonometry only when I was trying to figure out how to rotate an object in 2D space for my game. Also, there was a point in time when I used a "formula for distance/vector length in 2D space", but I had absolutely no idea what that "Pythagoras' theorem" is useful for.
  - cellis 15y ago
    Game programming will more quickly take you down the math rabbit hole than than any other kind of programming. It is always painfully clear that you should know better math when you run into a simple problem like "find a solution to hit this moving target", or something more complex like "figure out how the inverse kinematics of animal's bones work". For the first problem you could use anything from tight to algebra to calculus to solve it. For the second, you might easily find yourself knee deep in a PDF giving you a "remedial treatment of jacobian matrices"
kalid 15y ago
A huge problem with math is we end up teaching mathematical vocabulary, not mathematical fluency. It's like high-school language classes: everyone memorizes vocab lists, stutters out canned phrases, and forgets it all later. I'd prefer to speak fluently with a 3-year old's vocabulary than artificially with a high-schooler's. Similarly, I'd prefer students leave high school fluent in basic algebra, vs. trying to force-march people through algebra 2, trig, calculus, etc. when it's clear they'll just hate the subject afterwards. (Some students will read ahead, great. The others, since they actually enjoyed math, will pick up the other stuff later). Asking "When will I use this?" reveals that we don't understand a major goal of math education: fluency with powerful mental models, not just factoids you can directly apply.
- learc83 15y ago
  Exactly. In my experience tutoring 3 younger siblings, the problems they've had with trig and calculus are caused by a lack of mastery of basic algebra. I think everyone would be much better off if they left high school with a mastery of basic algebra and left trig and calculus for College (for most kids).
jderick 15y ago
I think that a lot of the math we learn in middle and high school is not that useful. For example, when was the last time I used the quadratic equation, or had to calculate a derivative using the chain rule, or had to do a geometric proof of any kind. Personally I think learning to program is far more useful than any of those skills and yet it is usually presented as an 'elective' course in most schools. Not to say that I don't appreciate math, but if we look at cost vs benefit, I think our current curriculum could be updated somewhat. Maybe some math classes could be offered as 'electives'. Of course, there were other less useful classes I was required to take as well.
- TeMPOraL 15y ago
  > when was the last time I used the quadratic equation Actually, quadratic equation might be one of the most important things in high school maths - lots of practical problems, especially involving optimization, tend to be reduced to (or approximated by) quadratic equation.
jl6 15y ago
This question should be answered with a challenge. "You won't use math, but your boss will."
maratd 15y ago
I'll leave external benefits stemming from mathematics for others to discuss. When will you use the actual math you're learning? Never. Because you'll forget all of it within short order and when you actually need to use it, you'll be forced to re-learn it. Re-learning it will be much easier though. Kind of like remembering how to ride a bicycle. Anyway, what are the times when you'll need math? When you're trying to solve interesting problems. You will never use math if you're doing routine programming work. However, if you need to create an algorithm that detects clients within a radius of 1 mile of your location, you'll need math. If you need to rate those clients on a curved basis, you'll need math. Not skull-fracturing math, but still math. Many, many other examples. So if you're pulling data from a database and displaying it, no math. If you're actually creating that data or heavily modifying it, math. I don't think anything past calculus is necessary unless you're doing some very specialized work, but up to that point is an absolute must for any computer scientist.
podopie 15y ago
I pushed this comment out to my peers for a read first, but thought I'd share here as well. I've been in the author's shoes as both an English teacher and band director (at the same time), and disagree wholeheartedly. As others pointed out, he's comparing hard skills (math) and soft skills (gained from anything, but in this particular case football and band). No kid asks when band or football is going to be useful in their life because they already have a premise around it: start from the bottom, and you have four years to become a leader. Math doesn't provide this opportunity, because the moment you get a passing grade in a math course, you move on to the next class. There's no leadership here. No opportunity to lead that class you passed with what you now know. Nothing shifts. On another note, you do gain group work skills and peer bonding, like in other said activities. The calendar thing pisses me off, like him, but for other reasons. Primarily, this isn't because people don't know math. It's because they don't want to do it. We're currently in an era where it's easier to share information--good and bad--than for us to figure it out on our own. The problem here isn't that no one knows math, it's that "share" and "be a sheep" is much higher on everyone's bucket list than "do something by myself and learn from it." This is especially with kids. Instead of frustration, however, he's provided with a the perfect warmup problem. Ask kids to figure out if the answer is true or not using what they know about math, five minutes pass, and you show them how to handle it. You make two points now: math is useful, and don't always believe everything that gets shared around the internet.
Tycho 15y ago
Yeah but maths isn't fun.
- InclinedPlane 15y ago
  Math is quite fun, and exciting. But often it is taught in schools in a very poor manner which destroys any of the fun aspects of it. Read, say, Cryptonomicon or Diamond Age and tell me math isn't fun.
wheels 15y ago
This is passionate, noble and wrong. Or at least a false-dichotomy. This is a defense of pure mathematics. Pure mathematics can certainly be a thing of beauty and that elegance is the draw which pulls in most mathematicians. But applied mathematics are also a powerful tool. One needn't love the elegance of pure mathematics to appreciate the utility of applied mathematics. I mostly like applied mathematics, though I appreciate pure mathematics. I like physics and applied computer science. Exploration into them wouldn't be possible were it not for advanced mathematics, but I usually only learn new mathematical concepts when it's demanded by the application that I'm studying. That's not the "wrong" way to appreciate mathematics and the implication is that I've almost always already answered, "Where am I ever going to use this?" before I learn add new mathematics to my toolkit.
- demian 15y ago
  Almost every problem that involves material resources and time can be modeled and solved using math. The strech people go around to avoid using applied mathematics, either by choice or ignorance, is astonishing.
  - jacquesm 15y ago
    One part of this is that computers are now so fast that you can get the answer to fairly complicated questions for large amounts of data without getting anywhere close to the optimal analytical solution. The need to optimize and the associated knowledge is not quite as much of a problem as it was in the recent past. This leads to a hidden form of bloat, programs written in a terribly inefficient way that still perform adequately in isolation but that fail to compose in a useful way because that quickly slows things down to the point where it no longer produces an answer in acceptable time. That probably falls under ignorance in your enumeration but it may be a sub-category labelled 'appears unnecessary'. There ought to be a an energy label for algorithms :)
    - rcfox 15y ago
      > There ought to be a an energy label for algorithms Isn't that what we use asymptotic analysis for?
Dn_Ab 15y ago
As a fervent math addict whose enjoyment reaches into my choice of programming language (functional) and who would be delighted to be gifted a text on differential forms, I think this question deserves to be asked. Math teaching is being carried along with a thousand year momentum and while the current curriculum made sense when many jobs involved building catapults, bridges, ships or cathedrals and jobs as a carpenter or mason were more numerous, they make little sense now. Notice also that most of these subjects were set at a time before education was necessary so that if you went into say a gymnasium; odds were you wanted to be a teacher, academic or engineer. So topics like trigonometry, geometry, calculus and higher algebra (matrices, analytic geometry) made sense. But these days, the vast majority of people do not need these subjects. On top of that there is a great crime. The most pertinent topics to modern living are given short thrift. Subjects like understanding basic statistics (including mean, mode, median, stdev, and variance), probability (including expected value), basic decision theory and estimation. All of these would have far more use to every day life and could be fully taught in the context of how they would help in real life (media, gamblers fallacy, money management etc). Advanced topics would be things like distinguishing conditional and joint probabilities, counting (combinatorics), graphs and networks, exponentiation and logarithms, common plots (logistic, exponential, parabolic), rate of change, and the relationship between a circle and triangle (must be taught with animations). These things actually still have use to many people. There is also the question of should math be taught at early years at all? A 12 year old can probably compress their previous 7 year math eduaction to 1. Maybe just numbers, (Z,+) or (Z,*)? I don't know but I think the question of if math education starts too early deserves to be looked at. The current hatred is in part due to a cycle of teachers who hated the subject having to force learn it in college and then having to teach it by force in addition to other subjects they may be stronger in. Instead let the child's curiosity guide them. So they would arrive not by force and a bunch of unmotivated subjects but by curiosity. To augment the lack of math classes there will be game classes to teach reasoning. Not just video games but also card, dice and board games - with the caveat that the game must be PSPACE complete. Just let the kids play and compete. Maybe they will learn the same type of reasoning that will be useful to learning about chains, posets, groups, first order logic or probability. The more determined may even go read about the topics. For video games the game must allow scripting. I think such a policy would just about eliminate thoughts of the pointlessnsess of math. Kids are not dumb, they will do impressive things if it interests them. Adults make this mistake of underestimating kids all the time e.g. whenever they say things like "whaoh that was done by a 12 year old?!"
dmvaldman 15y ago
This is a pretty easy question to answer, and calendar arithmetic is not how you do it. If you want to do something, you don't need much math. If you want to do it WELL, you do. The second you want to optimize something, you need math. Whether you're figuring out the analytics of an A/B test (stats!), or finding the best inputs for optimal outputs (set a derivative equal to 0 anyone?), or making an algorithm more efficient by lowering its asymptotic complexity. You can do stuff. Math just makes it better. Like salt on bland food. Full disclosure: I'm defending my PhD in math in 2 months! My opinions may be biased.
- madhadron 15y ago
  > Whether you're figuring out the analytics of an A/B test (stats!) Sorry, off topic, and not personally directed at you, but I'm getting so tired of everyone pretending that A/B testing is something fancy as opposed to a willful ignorance of the past hundred years of work in experimental design. Will you all please go look up orthogonal arrays and linear models?
commieneko 15y ago
I always tell my media technology students that everyone should learn to sketch and learn to play a musical instrument. You don't really do this in order to be able to draw something to hang in a gallery, or to perform in front of others, though that may be a side benefit. You do this in order to learn to see and to hear better. No doubt this is useful too, but the real reason is to better appreciate and experience the world around you.
stiff 15y ago
Just save your time and read V. I. Arnolds "On teaching mathematics" instead: http://pauli.uni-muenster.de/~munsteg/arnold.html http://pauli.uni-muenster.de/~munsteg/arnold.html He said everything I could possibly want to say as a reply here but probably better then I ever will be able to put it: It is only possible to understand the commutativity of multiplication by counting and re-counting soldiers by ranks and files or by calculating the area of a rectangle in the two ways. Any attempt to do without this interference by physics and reality into mathematics is sectarianism and isolationism which destroy the image of mathematics as a useful human activity in the eyes of all sensible people.
unexpected 15y ago
It's only a little bit ironic that his calendar for July 2012 is wrong.
- tjr 15y ago
  I kept staring at the calendar trying to figure out if his point was that people were so uninformed about mathematics that they don't know what day of the month it is...
  - deleted 15y ago
    [deleted]
- thebigshane 15y ago
  From the article: "In order to confirm that July 1 advances by one day in a non-leap year and two days in a leap year I had to look at the actual calendar. There I discovered that the premise of the email was wrong. July 1st doesn’t fall on a Friday this year."
orbitingpluto 15y ago
When someone sent me the '5Fri, 5Sat, 5Sun only every 823 years' email I sent a quick refutation and explained that there are just a couple variations of the calendar. It went something like this: The first day of the year has 7 seven choices. It's either a leap year or it isn't. Also 823 is a prime number. Can you now figure out why this isn't true? (You can also prove it by looking at the calendar when you double click on the time in Windows.) The person did not want to be enlightened and I was deemed a buzzkill. The lesson I learned is to be careful when educating someone when it may take away that person's 'awe and wonder'. That is why atheists should avoid trying to reason away the faith of the religious.
- zasz 15y ago
  It isn't about "not wanting to be enlightened." That person wanted to share a fun fact--they were trying to be social. And you shot them down and essentially called them stupid.
  - orbitingpluto 15y ago
    "Essentially called them stupid?" I shared some "fun-facts" back and offered them a chance to figure it out. That's social. If the email was fire-and-forget, that's not social. If we are all predisposed to take unconsidered facts as an insult to our intelligence and not as a prelude to a discussion, then that is a whole other educational issue. Also please accept my apologies if you think the word enlighten confers a condescending tone. I was going for 'greater knowledge/understanding'.
    - waqf 15y ago
      I guess they would have preferred if you'd forwarded some fun facts which didn't contradict theirs. Something like "91 is the only prime number that isn't blue", perhaps.
  - waqf 15y ago
    It seems to me that in that case they did, indeed, not want to be enlightened. (Of course, not wanting is relative.)
drostie 15y ago
I really like to put it this way: "Of the several professional mathematicians I have known, only one of them could calculate a 15% tip in her head." Now, mind you, all of them know that, in order to get the right overall tip, every person can just calculate the tip on what they themselves ordered and pay that -- and it will magically sum to the right value. They might also know that if you had to tip self-consistently -- that is, if you also had to pay a 15% tip on your tip, and a 15% tip on your tip on your tip, and so on, that this process converges and is essentially the same as just paying an effective tip. (They might even be able to tell you that the effective tip is 15%/0.85, if they're still reasonably young.) Those are the sorts of things they're good at. I know some who will talk your ears off about the convergence of an involution series in a noncommutative algebra and the problems of just finding a nice notation which makes the problem not look ugly, because the idea is really just so simple once you skip past the messy derivation to the intuitive result. Computing the actual tip? Not so much. Heck, that effective tip? That's 3/17ths, if you really churn the mental gears! Who has time to divide 3 by 17?! That's what I have a calculator for. Except, well, I didn't bring a calculator because we never use them -- but that's what the computer in my office is for.
- vacri 15y ago
  I really don't understand your point. Calculating a 15% tip is monstrously simple to do in your head. When I visited the US, I was able to do it from the first meal onward, for meals solo or alone. Dropping the last digit and adding half again is so brain-numbingly simple, though I must admit I did dine at one stage with some native college students who pulled out a calculator to figure out their part of the tip. It's not clear in what you're writing if you mean "when presented with a bill, how much to tip" or "given the final payment, how much of it was tip", or something else.
  - drostie 15y ago
    I mean "when presented with a bill, how much to tip." It's just not the sort of thing which mathematicians are ever expected to do. There is no math journal where you can publish the tips you calculated. It's not their job, there are no theorems to be proven there, etc., etc. (You're actually doing it a little more complicated than it has to be because it sounds like you're spending a little memory remembering the number you took 10% of. Take half, add it to the original, which is presumably still right in front of you, then drop the digit after.) I learned a lot of mental calculation because my background is in applied physics, where you're expected to reason about the size of things etc. (A good example question might be, "how far do you think an air molecule can go before it bumps into another air molecule?") So, just for example, to convert Celsius to Fahrenheit you multiply by 2, subtract 10%, and add 32. It is exact. So 25°C → 50 → 45 → 77°F. To convert Fahrenheit to Celsius you subtract 32, divide by 2, add 10%, then add 1% if you really feel like it; it is approximate. So 52°F → 20 → 10 → 11 → 11.11°C. Those sorts of things I will do in my head when people give me a number in one or the other temperature. Tipping is especially nice when compared to the fact that in New York State there is an 8% sales tax which is not added to any of the prices on stuff at the store -- calculate a tip and halve it. [Naive reasonings on air: small upper bounds can be given by the fact that it has to travel easily through the small passageways in your inner ear, but my favorite calculation is to take (kinematic viscosity) / (speed of sound), both of which are things that an applied physics geek should roughly know.]
kappaknight 15y ago
Using a thin font + small font + gray on white font = hard to read. There's a better math joke in there somewhere...
WalterBright 15y ago
I encounter many people who do not see the point in learning math. They're the same people who get taken for a ride regularly when they finance a purchase, deal with contractors, plan their investments, get rooked on their credit card fees, etc. And they rarely realize what has happened to them. It's expensive to not know math.
gaoshan 15y ago
When you have to help your kids with their homework :)
DarkStarX1 15y ago
Math geeks always see it this way. It's the same for any geek and his favorite subject. What's sad is that he should have studied harder in his English classes.
ajratner 15y ago
The grouping of theoretical, 'QED' style math with music and football is interesting to think about. I think football and math go together and can be seen as inverse processes wrt to music. Both football and theoretical math have you start with arbitrary rules or principles and then build up a system, add extrapolated layers of complexity on top of that. The top layers recreate the world building up from that core set of assumptions. Music on the other hand can be seen, at its most elegant, as taking the complexity of the world and reducing it or rather tying it together, coalescing it into patterns, rhythms, and other things that approach the simplicity and fundamental nature of what one starts out with math, or at least the earliest lemmas of a mathematical system. I think both are intensely pleasurable activities in their own way because they let you trace this path from fundamentals to complexity and back. Math and football as challenges that have you climb up the mountain of complexity, but that still remain close enough to the base to be simple and absolute and beautiful in these ways; and music as an initially complex and tumultuous thing that gets rid of just enough entropy to be simpler but not fake.
krollew 15y ago
Maths are sometimes useful for some people. It's matter of what part of maths we are talking about. For example I used to use some geometry and statistics/probability calculus. Of course I use algebra almost everyday. Rest of maths may be great entertainment for now. :)

189 points by mrspeaker 15y ago

grn 15y ago

I don't think that the comparison with music or sports is correct. If I had to play an instrument I would ask for a motivation because I don't enjoy playing. Similarly someone who doesn't enjoy maths asks for a reason to study it. When you present maths to someone who doesn't like it on its own then the problem is to find a balance between abstraction and applications. When maths is presented too abstractly then it looks useless. When it's presented too concretely then it looses its essence and may seem trivial.

khyryk 15y ago

> This, to me, is mathematics. Playing, confirming, questioning — even in my real life. It gave me a much sadder answer for people when they ask me “when am I ever going to use this”. This isn't exclusive to mathematics. I'm sure there are thousands of blog posts lamenting the lack of philosophy, comparative literature, computer science, etc. instruction.

msluyter 15y ago

The analogy between band and math is problematic. Band has various payoffs that math doesn't: getting attention from peers, the inherent joy in playing music, peer bonding via football games, band trips and whatnot. (Not that math doesn't have "inherent joy" -- it just seems more solitary, more cerebral, and less socially glorified than music.) There's no doubt that our math education destroys curiousity, and if we could teach math in a non-utilitarian way, as a sort of artistic endeavor, that would be amazing, but... is it even possible? Has it ever been tried? Whenever I think about this, I think about season 4 of The Wire.

m_for_monkey 15y ago
Really utilitarian math education would be good. The problem is that it's not even that. It's just test-oriented and boring. See this twelve minute video: http://www.ted.com/talks/lang/en/dan_meyer_math_curriculum_makeover.html http://www.ted.com/talks/lang/en/dan_meyer_math_curriculum_m...
clarebear 15y ago
I always thought that band was "cooler" than math because some people make out on band buses during trips. I've never seen anyone make out on a math trip.
slindsey 15y ago
I always go to Vi Hart (http://vihart.com/doodling/ http://vihart.com/doodling/) when thinking about how we should teach math.
screwt 15y ago
Re "the inherent joy in playing music" - isn't that the whole point of the article? When it's not reduced to mindless rote learning, there can be an inherent joy in doing math.
xyzzyz 15y ago
I don't think that math is fundamentally different than band with regard to things you mentioned. Best mathematicians certainly get lots of attention from peer mathematicians. The equivalent of band trips are summer schools, where also lots of peer bonding happen. Inherent joy? Why, that's the whole point of doing math for me.
mechanical_fish 15y ago
Music can be exactly as solitary and cerebral as math. That aspect of music doesn't get the same press, is all. If you play three chords on a tall stage people know you're in a band; if you sit in your home working out a Bach fugue nobody needs to know. I have a slightly silly book about birdwatching. It has a section which talks about birding competitions - "Big Days", they call them - and the final two sentences stick in my head, always: Don't go away from this thinking that birding is an endless succession of fabbydoo games or fun, fun, fun without a moment's rest. Quite the opposite. Birding is mostly about looking at birds. It is no use to pretend otherwise. A useful motto. Birding is very popular, of course, even in the go-go all-action United States. Other popular activities include knitting, gardening, hiking, sudoku, crosswords, reading, fantasy football, Angry Birds, writing comments on message boards, and, ahem, hacking. All of them solitary, cerebral, and socially unglorified. (Though I guess fantasy football is arguable: You can probably spend an entire evening over beer talking with your friends about the performance of their fantasy football teams. For all I know it's even popular in high school. I knew several people in high school who were reliable authorities on every active major-league baseball player...) People have a warped view of other people's lives in general, and particularly the lives of high school students. I suspect that high school kids enjoy quiet, solitary activities as much as anyone else: In other words, more than you notice. The quiet hobbies are just unobtrusive, so they don't get a lot of press and they don't show up in movies or TV except around the edges. Speaking for myself, I think I stayed away from band in school because it was full of people and attention. I gravitated toward the quiet sources of pleasure and meaning. Of course, I was blessed with a math club mentor who knew what "recreational mathematics" was...
- nickpinkston 15y ago
  I think matrix math could actually be presented in a Sudoku-like format - for a Gaussian Elimination or some such - and that'd actually be fun for the Sudoku crowd to play. It's really pretty similar skills involved. Sudoku is probably just a special case matrix problem...
ckpwong 15y ago
I beg to differ on your point of math being inherently non-social. In high school, I actively participated--and later led--my school's math league team. Every Friday, we were either home or away for a match with another school. My school wasn't particularly known as a math hothouse (unlike other schools with gifted programs), but we managed to get pretty far in the playoffs for the years I was there, finishing 3rd in the district once even. Back then, I also actively participated in math and science contests, which eventually led me to be invited to a week-long math seminar. During that week, we had daily team competitions and other activities that were fun, social, and mind boggling at the same time. And it doesn't hurt on that one faithful June morning too many years ago, I also met the person whom eventually became my husband. wink

edw519 15y ago

Asking "When will I ever use math?" is like jogging and asking, "When will I ever use these calf muscles?" (The answer to both is "all the time", but that's not the point.) I was a math major who did independent research in Elementary Number Theory and decided to switch paths and become a computer programmer (many years ago). It's true, I haven't encountered many sigmas, deltas, and derivative signs in all those years, but there's absolutely no doubt in my mind that I'm exercising the same mental muscles built with math. OP mentions “wondering, playing, amusing yourself with your imagination.” Hell, build something. Assembling ones and zeros to help real people solve real problems is every bit as wonderful, playful, and amusing as anything I ever did with pure mathematics. And probably even more rewarding...I've discovered that it's much more likely to see a customer do a happy dance with software that never existed before I built it than proving Fermat's Last Theorem or figuring out what Galois was up to on that long last night.

bluekeybox 15y ago
> OP mentions “wondering, playing, amusing yourself with your imagination.” Hell, build something. Mathematics is like AI. As soon as a company/whoever builds upon one of the advances in the field and people en masse start using a practical result that comes out of it, it stops being called mathematics/AI. When we hear the word "mathematician" we almost right away imagine an absent-minded professor not contributing anything immediately useful to the real world. People are basically arguing about language, not realizing that they are pawns of a subtle phenomenon that the name of a discipline taught in school refers not so much to knowledge based on and derived from that discipline in the world at large, but to the actual act of teaching that discipline to children and young adults, and sometimes to performing academic-model-funded (meaning charity-like funded) research. It's a bit sad because this trick the language plays on us probably devalues in the eyes of young people something that is actually a useful/practical skill. Kids may say to themselves, "Why do I need this? I don't want to be a schoolteacher," and they will be both right and wrong at the same time, not realizing how many high-paying jobs from engineering to banks to Wall Street require the mental skill they chose not to spend time developing.
timwiseman 15y ago
Very well said. Though it is worth noting the distinctions between different types of math. I found my studies of theoretical math in college enormous fruitful just as I found jogging beneficial. But I thought doing numerous arithmetic problems in middle school to be of minimal value and the rote memorization of things like multiplication tables to be worthless. In short, much like exercise, studying math should be done in a way that is pushing your personal limits at least a little.

Jarred 15y ago

I suspect when students ask, "When will I use this?", they don't see any practical or abstract uses of what the teacher is teaching. In other words, it isn't expanding their mind or changing how they think about things. I've yet to have a math teacher that does this well, but I've also yet to have a good math teacher. Maybe there's a correlation.

georgieporgie 15y ago
I keep mentioning that, in my opinion, non-college mathematics teachers generally only know enough math to get through the end of the material they're teaching in any given semester. I don't think they're capable of teaching the material from multiple angles, which seems necessary in order to instill a fundamental grasp of the material.

flom 15y ago

The problem with the analogy between music and math is the free-will aspect. Everyone is FORCED to take math, whereas most people are NOT forced to play an instrument (at least in the US). Everyone knew a couple of math wizzes who usually were not the one's asking "why do I need to learn this?" These kids would probably do math even if they weren't forced to, and indeed, many of them go on to pursue a higher education in mathematics, completely voluntarily. On the other hand, many kids whose parents force them to play an instrument often complain and ask "why do I need to play an instrument?" tl;dr: If you force someone to do something, and you don't want to make them resent the thing you're forcing them to do, you should explain to them why you're forcing them to do it, i.e., why it's in their best interest, whether it's math, music, learning a language, etc.

ef4 15y ago

If you didn't take the author's advice and read [Lockhart's Lament](http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf), go do it. It's worth it.

draggnar 15y ago
2nded... It is the most influential thing I have ever read. I used to hate math in school and the perspective of math as art completely changed the way I think about it.

jgrahamc 15y ago

One of the simplest uses of math was shown to me by a carpenter who made a triangle from three pieces of wood with sides 24", 32" and 40". Because of this his triangle had a right angle in the corner and he could use it to check that things (such as large areas of tiling) were square. Good old Pythagoras: 24^2 + 32^2 = 40^2. Because the sides were long he had a nice big right angle to work with.

bryanlarsen 15y ago
Yes, I remember my uncle showing me this when we were doing some roofing. He then refused to believe me when I figured out a few other ratios that would also do the same thing.
- ajross 15y ago
  Amusing, but this is where engineering thought differs: obviously your rediscovery of the 5:12:13 right triangle or whatever was precocious and showed a deeper mastery of the subject. That said: your advice sucked. The 3:4:5 triangle is a better choice for obvious reasons (smaller numbers) and not so obvious ones (less sensitivity to measurement error due to larger internal angles). The critically important distinction there is precisely that between, say, Haskell and Ruby. :)
  - derleth 15y ago
    Except both Haskell and Ruby are useful.
  - bryanlarsen 15y ago
    Actually I couldn't even get him to agree that a 6:8:10 triangle was equivalent to a 3:4:5 triangle.
  - madhadron 15y ago
    > The critically important distinction there is precisely that between, say, Haskell and Ruby. :) Absolutely. Why bother with all that unnecessary complexity in Ruby?

gxs 15y ago

Football players don't lift weights on the field - yet they lift weights to gain strength and conditioning to prepare for what occurs on the field. I was a math major in college. I don't use the actual math I learned, but 4 years of solving really hard math problems at Cal honed my problem solving skills and helped me develop a type of stamina to try my hand at them for long periods of time. My grades weren't the best, and having math Olympiads in your classes sometimes makes things harder than they should be. That said, I treasure the experience. I learned to push myself in a way I hadn't before. I learned the value of being rigorous, and even the value of getting creative to solve problems. I learned that even after 4 hours of staring at a problem, I should keep at it because I may get that ah-ha moment at the fifth or sixth hour. So do I use math everyday? Not really. Do I use the ability to solve problems, to abstract my knowledge in one area and apply it another, to carry through long logical thoughts everyday? You bet your ass I do.

m_for_monkey 15y ago

The band kids and the football kids never ask their teachers and coaches, “when will I ever use this”. Because they are playing the flute and they are playing football. They enjoy it now and that's what counts, they don't even think about the future. And yet they come into my math class and raise their hand half-way through my demonstration of the mean value theorem to ask me when they will ever use this. Because the "mean value theorem" sounds like boring shit and their only hope is that it may be useful in the future. If you teach them programming to solve their physics homework and make it a game using math, they won't ask. Never.

TeMPOraL 15y ago
> If you teach them programming to solve their physics homework and make it a game using math, they won't ask. True. That's actually how I ended up as a programmer - math in school was boring, trying to make a video game was not. I finally learned trigonometry only when I was trying to figure out how to rotate an object in 2D space for my game. Also, there was a point in time when I used a "formula for distance/vector length in 2D space", but I had absolutely no idea what that "Pythagoras' theorem" is useful for.
- cellis 15y ago
  Game programming will more quickly take you down the math rabbit hole than than any other kind of programming. It is always painfully clear that you should know better math when you run into a simple problem like "find a solution to hit this moving target", or something more complex like "figure out how the inverse kinematics of animal's bones work". For the first problem you could use anything from tight to algebra to calculus to solve it. For the second, you might easily find yourself knee deep in a PDF giving you a "remedial treatment of jacobian matrices"

kalid 15y ago

A huge problem with math is we end up teaching mathematical vocabulary, not mathematical fluency. It's like high-school language classes: everyone memorizes vocab lists, stutters out canned phrases, and forgets it all later. I'd prefer to speak fluently with a 3-year old's vocabulary than artificially with a high-schooler's. Similarly, I'd prefer students leave high school fluent in basic algebra, vs. trying to force-march people through algebra 2, trig, calculus, etc. when it's clear they'll just hate the subject afterwards. (Some students will read ahead, great. The others, since they actually enjoyed math, will pick up the other stuff later). Asking "When will I use this?" reveals that we don't understand a major goal of math education: fluency with powerful mental models, not just factoids you can directly apply.

learc83 15y ago
Exactly. In my experience tutoring 3 younger siblings, the problems they've had with trig and calculus are caused by a lack of mastery of basic algebra. I think everyone would be much better off if they left high school with a mastery of basic algebra and left trig and calculus for College (for most kids).

jderick 15y ago

I think that a lot of the math we learn in middle and high school is not that useful. For example, when was the last time I used the quadratic equation, or had to calculate a derivative using the chain rule, or had to do a geometric proof of any kind. Personally I think learning to program is far more useful than any of those skills and yet it is usually presented as an 'elective' course in most schools. Not to say that I don't appreciate math, but if we look at cost vs benefit, I think our current curriculum could be updated somewhat. Maybe some math classes could be offered as 'electives'. Of course, there were other less useful classes I was required to take as well.

TeMPOraL 15y ago
> when was the last time I used the quadratic equation Actually, quadratic equation might be one of the most important things in high school maths - lots of practical problems, especially involving optimization, tend to be reduced to (or approximated by) quadratic equation.

jl6 15y ago

This question should be answered with a challenge. "You won't use math, but your boss will."

maratd 15y ago

I'll leave external benefits stemming from mathematics for others to discuss. When will you use the actual math you're learning? Never. Because you'll forget all of it within short order and when you actually need to use it, you'll be forced to re-learn it. Re-learning it will be much easier though. Kind of like remembering how to ride a bicycle. Anyway, what are the times when you'll need math? When you're trying to solve interesting problems. You will never use math if you're doing routine programming work. However, if you need to create an algorithm that detects clients within a radius of 1 mile of your location, you'll need math. If you need to rate those clients on a curved basis, you'll need math. Not skull-fracturing math, but still math. Many, many other examples. So if you're pulling data from a database and displaying it, no math. If you're actually creating that data or heavily modifying it, math. I don't think anything past calculus is necessary unless you're doing some very specialized work, but up to that point is an absolute must for any computer scientist.

podopie 15y ago

I pushed this comment out to my peers for a read first, but thought I'd share here as well. I've been in the author's shoes as both an English teacher and band director (at the same time), and disagree wholeheartedly. As others pointed out, he's comparing hard skills (math) and soft skills (gained from anything, but in this particular case football and band). No kid asks when band or football is going to be useful in their life because they already have a premise around it: start from the bottom, and you have four years to become a leader. Math doesn't provide this opportunity, because the moment you get a passing grade in a math course, you move on to the next class. There's no leadership here. No opportunity to lead that class you passed with what you now know. Nothing shifts. On another note, you do gain group work skills and peer bonding, like in other said activities. The calendar thing pisses me off, like him, but for other reasons. Primarily, this isn't because people don't know math. It's because they don't want to do it. We're currently in an era where it's easier to share information--good and bad--than for us to figure it out on our own. The problem here isn't that no one knows math, it's that "share" and "be a sheep" is much higher on everyone's bucket list than "do something by myself and learn from it." This is especially with kids. Instead of frustration, however, he's provided with a the perfect warmup problem. Ask kids to figure out if the answer is true or not using what they know about math, five minutes pass, and you show them how to handle it. You make two points now: math is useful, and don't always believe everything that gets shared around the internet.

Tycho 15y ago

Yeah but maths isn't fun.

InclinedPlane 15y ago
Math is quite fun, and exciting. But often it is taught in schools in a very poor manner which destroys any of the fun aspects of it. Read, say, Cryptonomicon or Diamond Age and tell me math isn't fun.

wheels 15y ago

This is passionate, noble and wrong. Or at least a false-dichotomy. This is a defense of pure mathematics. Pure mathematics can certainly be a thing of beauty and that elegance is the draw which pulls in most mathematicians. But applied mathematics are also a powerful tool. One needn't love the elegance of pure mathematics to appreciate the utility of applied mathematics. I mostly like applied mathematics, though I appreciate pure mathematics. I like physics and applied computer science. Exploration into them wouldn't be possible were it not for advanced mathematics, but I usually only learn new mathematical concepts when it's demanded by the application that I'm studying. That's not the "wrong" way to appreciate mathematics and the implication is that I've almost always already answered, "Where am I ever going to use this?" before I learn add new mathematics to my toolkit.

demian 15y ago
Almost every problem that involves material resources and time can be modeled and solved using math. The strech people go around to avoid using applied mathematics, either by choice or ignorance, is astonishing.
- jacquesm 15y ago
  One part of this is that computers are now so fast that you can get the answer to fairly complicated questions for large amounts of data without getting anywhere close to the optimal analytical solution. The need to optimize and the associated knowledge is not quite as much of a problem as it was in the recent past. This leads to a hidden form of bloat, programs written in a terribly inefficient way that still perform adequately in isolation but that fail to compose in a useful way because that quickly slows things down to the point where it no longer produces an answer in acceptable time. That probably falls under ignorance in your enumeration but it may be a sub-category labelled 'appears unnecessary'. There ought to be a an energy label for algorithms :)
  - rcfox 15y ago
    > There ought to be a an energy label for algorithms Isn't that what we use asymptotic analysis for?

Dn_Ab 15y ago

As a fervent math addict whose enjoyment reaches into my choice of programming language (functional) and who would be delighted to be gifted a text on differential forms, I think this question deserves to be asked. Math teaching is being carried along with a thousand year momentum and while the current curriculum made sense when many jobs involved building catapults, bridges, ships or cathedrals and jobs as a carpenter or mason were more numerous, they make little sense now. Notice also that most of these subjects were set at a time before education was necessary so that if you went into say a gymnasium; odds were you wanted to be a teacher, academic or engineer. So topics like trigonometry, geometry, calculus and higher algebra (matrices, analytic geometry) made sense. But these days, the vast majority of people do not need these subjects. On top of that there is a great crime. The most pertinent topics to modern living are given short thrift. Subjects like understanding basic statistics (including mean, mode, median, stdev, and variance), probability (including expected value), basic decision theory and estimation. All of these would have far more use to every day life and could be fully taught in the context of how they would help in real life (media, gamblers fallacy, money management etc). Advanced topics would be things like distinguishing conditional and joint probabilities, counting (combinatorics), graphs and networks, exponentiation and logarithms, common plots (logistic, exponential, parabolic), rate of change, and the relationship between a circle and triangle (must be taught with animations). These things actually still have use to many people. There is also the question of should math be taught at early years at all? A 12 year old can probably compress their previous 7 year math eduaction to 1. Maybe just numbers, (Z,+) or (Z,*)? I don't know but I think the question of if math education starts too early deserves to be looked at. The current hatred is in part due to a cycle of teachers who hated the subject having to force learn it in college and then having to teach it by force in addition to other subjects they may be stronger in. Instead let the child's curiosity guide them. So they would arrive not by force and a bunch of unmotivated subjects but by curiosity. To augment the lack of math classes there will be game classes to teach reasoning. Not just video games but also card, dice and board games - with the caveat that the game must be PSPACE complete. Just let the kids play and compete. Maybe they will learn the same type of reasoning that will be useful to learning about chains, posets, groups, first order logic or probability. The more determined may even go read about the topics. For video games the game must allow scripting. I think such a policy would just about eliminate thoughts of the pointlessnsess of math. Kids are not dumb, they will do impressive things if it interests them. Adults make this mistake of underestimating kids all the time e.g. whenever they say things like "whaoh that was done by a 12 year old?!"

dmvaldman 15y ago

This is a pretty easy question to answer, and calendar arithmetic is not how you do it. If you want to do something, you don't need much math. If you want to do it WELL, you do. The second you want to optimize something, you need math. Whether you're figuring out the analytics of an A/B test (stats!), or finding the best inputs for optimal outputs (set a derivative equal to 0 anyone?), or making an algorithm more efficient by lowering its asymptotic complexity. You can do stuff. Math just makes it better. Like salt on bland food. Full disclosure: I'm defending my PhD in math in 2 months! My opinions may be biased.

madhadron 15y ago
> Whether you're figuring out the analytics of an A/B test (stats!) Sorry, off topic, and not personally directed at you, but I'm getting so tired of everyone pretending that A/B testing is something fancy as opposed to a willful ignorance of the past hundred years of work in experimental design. Will you all please go look up orthogonal arrays and linear models?

commieneko 15y ago

I always tell my media technology students that everyone should learn to sketch and learn to play a musical instrument. You don't really do this in order to be able to draw something to hang in a gallery, or to perform in front of others, though that may be a side benefit. You do this in order to learn to see and to hear better. No doubt this is useful too, but the real reason is to better appreciate and experience the world around you.

stiff 15y ago

Just save your time and read V. I. Arnolds "On teaching mathematics" instead: http://pauli.uni-muenster.de/~munsteg/arnold.html http://pauli.uni-muenster.de/~munsteg/arnold.html He said everything I could possibly want to say as a reply here but probably better then I ever will be able to put it: It is only possible to understand the commutativity of multiplication by counting and re-counting soldiers by ranks and files or by calculating the area of a rectangle in the two ways. Any attempt to do without this interference by physics and reality into mathematics is sectarianism and isolationism which destroy the image of mathematics as a useful human activity in the eyes of all sensible people.

unexpected 15y ago

It's only a little bit ironic that his calendar for July 2012 is wrong.

tjr 15y ago
I kept staring at the calendar trying to figure out if his point was that people were so uninformed about mathematics that they don't know what day of the month it is...
- deleted 15y ago
  [deleted]
thebigshane 15y ago
From the article: "In order to confirm that July 1 advances by one day in a non-leap year and two days in a leap year I had to look at the actual calendar. There I discovered that the premise of the email was wrong. July 1st doesn’t fall on a Friday this year."

orbitingpluto 15y ago

When someone sent me the '5Fri, 5Sat, 5Sun only every 823 years' email I sent a quick refutation and explained that there are just a couple variations of the calendar. It went something like this: The first day of the year has 7 seven choices. It's either a leap year or it isn't. Also 823 is a prime number. Can you now figure out why this isn't true? (You can also prove it by looking at the calendar when you double click on the time in Windows.) The person did not want to be enlightened and I was deemed a buzzkill. The lesson I learned is to be careful when educating someone when it may take away that person's 'awe and wonder'. That is why atheists should avoid trying to reason away the faith of the religious.

zasz 15y ago
It isn't about "not wanting to be enlightened." That person wanted to share a fun fact--they were trying to be social. And you shot them down and essentially called them stupid.
- orbitingpluto 15y ago
  "Essentially called them stupid?" I shared some "fun-facts" back and offered them a chance to figure it out. That's social. If the email was fire-and-forget, that's not social. If we are all predisposed to take unconsidered facts as an insult to our intelligence and not as a prelude to a discussion, then that is a whole other educational issue. Also please accept my apologies if you think the word enlighten confers a condescending tone. I was going for 'greater knowledge/understanding'.
  - waqf 15y ago
    I guess they would have preferred if you'd forwarded some fun facts which didn't contradict theirs. Something like "91 is the only prime number that isn't blue", perhaps.
- waqf 15y ago
  It seems to me that in that case they did, indeed, not want to be enlightened. (Of course, not wanting is relative.)

drostie 15y ago

I really like to put it this way: "Of the several professional mathematicians I have known, only one of them could calculate a 15% tip in her head." Now, mind you, all of them know that, in order to get the right overall tip, every person can just calculate the tip on what they themselves ordered and pay that -- and it will magically sum to the right value. They might also know that if you had to tip self-consistently -- that is, if you also had to pay a 15% tip on your tip, and a 15% tip on your tip on your tip, and so on, that this process converges and is essentially the same as just paying an effective tip. (They might even be able to tell you that the effective tip is 15%/0.85, if they're still reasonably young.) Those are the sorts of things they're good at. I know some who will talk your ears off about the convergence of an involution series in a noncommutative algebra and the problems of just finding a nice notation which makes the problem not look ugly, because the idea is really just so simple once you skip past the messy derivation to the intuitive result. Computing the actual tip? Not so much. Heck, that effective tip? That's 3/17ths, if you really churn the mental gears! Who has time to divide 3 by 17?! That's what I have a calculator for. Except, well, I didn't bring a calculator because we never use them -- but that's what the computer in my office is for.

vacri 15y ago
I really don't understand your point. Calculating a 15% tip is monstrously simple to do in your head. When I visited the US, I was able to do it from the first meal onward, for meals solo or alone. Dropping the last digit and adding half again is so brain-numbingly simple, though I must admit I did dine at one stage with some native college students who pulled out a calculator to figure out their part of the tip. It's not clear in what you're writing if you mean "when presented with a bill, how much to tip" or "given the final payment, how much of it was tip", or something else.
- drostie 15y ago
  I mean "when presented with a bill, how much to tip." It's just not the sort of thing which mathematicians are ever expected to do. There is no math journal where you can publish the tips you calculated. It's not their job, there are no theorems to be proven there, etc., etc. (You're actually doing it a little more complicated than it has to be because it sounds like you're spending a little memory remembering the number you took 10% of. Take half, add it to the original, which is presumably still right in front of you, then drop the digit after.) I learned a lot of mental calculation because my background is in applied physics, where you're expected to reason about the size of things etc. (A good example question might be, "how far do you think an air molecule can go before it bumps into another air molecule?") So, just for example, to convert Celsius to Fahrenheit you multiply by 2, subtract 10%, and add 32. It is exact. So 25°C → 50 → 45 → 77°F. To convert Fahrenheit to Celsius you subtract 32, divide by 2, add 10%, then add 1% if you really feel like it; it is approximate. So 52°F → 20 → 10 → 11 → 11.11°C. Those sorts of things I will do in my head when people give me a number in one or the other temperature. Tipping is especially nice when compared to the fact that in New York State there is an 8% sales tax which is not added to any of the prices on stuff at the store -- calculate a tip and halve it. [Naive reasonings on air: small upper bounds can be given by the fact that it has to travel easily through the small passageways in your inner ear, but my favorite calculation is to take (kinematic viscosity) / (speed of sound), both of which are things that an applied physics geek should roughly know.]

kappaknight 15y ago

Using a thin font + small font + gray on white font = hard to read. There's a better math joke in there somewhere...

WalterBright 15y ago

I encounter many people who do not see the point in learning math. They're the same people who get taken for a ride regularly when they finance a purchase, deal with contractors, plan their investments, get rooked on their credit card fees, etc. And they rarely realize what has happened to them. It's expensive to not know math.

gaoshan 15y ago

When you have to help your kids with their homework :)

DarkStarX1 15y ago

Math geeks always see it this way. It's the same for any geek and his favorite subject. What's sad is that he should have studied harder in his English classes.

ajratner 15y ago

The grouping of theoretical, 'QED' style math with music and football is interesting to think about. I think football and math go together and can be seen as inverse processes wrt to music. Both football and theoretical math have you start with arbitrary rules or principles and then build up a system, add extrapolated layers of complexity on top of that. The top layers recreate the world building up from that core set of assumptions. Music on the other hand can be seen, at its most elegant, as taking the complexity of the world and reducing it or rather tying it together, coalescing it into patterns, rhythms, and other things that approach the simplicity and fundamental nature of what one starts out with math, or at least the earliest lemmas of a mathematical system. I think both are intensely pleasurable activities in their own way because they let you trace this path from fundamentals to complexity and back. Math and football as challenges that have you climb up the mountain of complexity, but that still remain close enough to the base to be simple and absolute and beautiful in these ways; and music as an initially complex and tumultuous thing that gets rid of just enough entropy to be simpler but not fake.

krollew 15y ago

Maths are sometimes useful for some people. It's matter of what part of maths we are talking about. For example I used to use some geometry and statistics/probability calculus. Of course I use algebra almost everyday. Rest of maths may be great entertainment for now. :)