7 ms·

Great Scientist ≠ Good at Math

55 points by tokenadult 14y ago

michaell2 14y ago
there is math, and then there is math. In Russia they have a saying "beat a rabbit long enough and it will eventually learn to take derivatives, but integrals are another matter". For many people areas involving spatial reasoning like college physics for engineers is that "another matter", while (simple) integrals are still no biggie. As for the original article, the implication that somebody having trouble with basic algebra can be "great scientist" sounds dubious to say the least. Like I said, there is math, and then there is math... there is stuff that anybody claiming any meaningful level of intelligence should be able to handle.
- kiba 14y ago
  there is math, and then there is math. In Russia they have a saying "beat a rabbit long enough and it will eventually learn to take derivatives, but integrals are another matter". A rabbit will be woefully unprepared to learn integrals if it forgot derivatives before it starts learning integral.
  - jleader 14y ago
    One moderately popular college calculus textbook (by Prof. Apostol of Caltech) introduces integrals before derivatives.
- gruseom 14y ago
  In Russia they have a saying "beat a rabbit long enough and it will eventually learn to take derivatives, but integrals are another matter". Something about that is quintessentially Russian.
- thaumasiotes 14y ago
  I find that saying bizarre. In high school, I found derivatives significantly more difficult to learn than I did integrals. Then, in multivariable calc, I found derivatives significantly more difficult, again. Integrals follow your intuition in a way that derivatives just don't.
  - semaphorism 14y ago
    Tell that to a rabbit.
  - shrughes 14y ago
    What. Derivatives are a very straightforward algorithm. Integrals aren't.
  - dsrguru 14y ago
    Derivatives are formulaic. Integrals, like proofs, require thinking backwards, i.e. creativity and/or luck. For the vast majority of people, cultivating that intuition is a lot harder than plugging numbers into formulas...
    - zerr 14y ago
      Formally speaking, solving integrals requires brute force. It is only after many such brute force samples your starting to get an intuition. But I won't call this creativity.
  - Q6T46nT668w6i3m 14y ago
    Do you have this backward (computing a derivative is algorithmic, computing an integral is analytic)?
  - claudius 14y ago
    I would guess that this depends on the things you usually integrate and those one differentiates – as the former only has (simple) algorithms for very simple cases, whereas the latter has very general algorithms, differentiation exercises in school tend to use more complex examples than integration exercises. However, given a ‘random’ expression, integration will be much more difficult than differentiation.
- nknighthb 14y ago
  > there is stuff that anybody claiming any meaningful level of intelligence should be able to handle Well, you've just called many dyslexics stupid. Does your assertion extend to basic arithmetic? Because if so, you've just called everyone with dyscalculia and/or acalculia stupid, and that group includes a lot of autism-spectrum engineers.
kaptain 14y ago
My manager once asked me to finish out a statistical problem to better analyze the results I was getting from my code changes that were intended to speed up an API. I looked at the whiteboard for about 5 seconds and grinned: "Who needs math? That's what computers are for!" Then I went to lunch. Of course I went back and finished the analysis after lunch.
kiba 14y ago
Math isn't that hard to learn, it's just that it requires lot of tutoring and lot of thinking. The reason why people today don't possess that much mathematical knowledge is that they don't maintain their knowledge of mathematics. So, when it comes to learning calculus or other advanced mathematics, you have a swiss cheese foundation. That swiss cheese foundation simply means you didn't mastered the previous required materials. So it's hard to learn. I did the really elementary to high school materials in the past two years on and off. Math concepts didn't really get harder to learn. They're easy or hard to learn at time, but there's no difficulty ramp to speak of. Then what happens afterward is that you start forgetting about how to do things like logarithmic operation, how to simplify trig identities, and so on after a week or two, or sometime days. So you need to continuously review them everyday or do enough real world problems that you know how to do them for life. The skills and knowledge that we master requires daily maintenance, or otherwise you lose your ability to do them. It's just like fitness. A person who stop long distance running for a while will no longer be able to run as long.
- Xcelerate 14y ago
  > Math isn't that hard to learn [...] calculus or other advanced mathematics Most people's concept of what "math" is, isn't advanced math. Advanced math is incredibly complex. (I honestly kind of chuckle when people tell me they are "really good at math".) Read Wiles' proof of Fermat's Last Theorem (http://www.cs.berkeley.edu/~anindya/fermat.pdf http://www.cs.berkeley.edu/~anindya/fermat.pdf), or Godel's incompleteness theorem and tell me if you understand any of that. Math much easier than his proof, yet vastly more difficult than calculus, is used in many areas of physics and chemistry. And I think it is this kind of math to which the original article was referring. People like to quip that Einstein wasn't good at math, because he had mathematicians helping him with his work. What they don't understand is that Einstein's skills in math blows everyone else's out of the water; it's just that they weren't up to the level of an actual mathematician.
  - kiba 14y ago
    it's just that they weren't up to the level of an actual mathematician. I guess what I am doing and learning is really elementary. But I like to think my point about having foundational knowledge and the willingness to practice everyday still stand. I know what I am doing and learning isn't what mathematican really do day to day. They make up new stuff, prove things, and solve problems in creative ways. I just commit to memory or practice steps on how to solve exercise sets, although the way I do is way smarter and time efficient than what people do when I was in high school. I don't know if all that practice will eventually pay off in some way, but I know that I just really hate forgetting stuff that I learned in high school math class. ( Yes, I really do "incredibly boring" math homework everyday despite finishing high school three years ago)
Permit 14y ago
E.O. Wilson did an excellent TED talk on this exact subject called "Advice to young scientists". I'd recommend watching it as it's one of my favorite talks. http://www.ted.com/talks/e_o_wilson_advice_to_young_scientists.html http://www.ted.com/talks/e_o_wilson_advice_to_young_scientis...
Myrmornis 14y ago
E O Wilson is a great biologist and author. However, this article is completely wrong. In particular, this > Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. is embarrassingly incorrect. For one example of why this is wrong, and sticking to E O Wilson's field, consider statistics. No biologist can publish anything nowadays without including some statistical analysis in their paper. So there's a pretty simple choice: either publish statistical stuff you don't understand, or learn enough math to achieve a basic understanding. Integrating probability densities, maximum likelihood estimators, etc etc, you certainly need calculus, and linear algebra will be very helpful too. As a second example, what about theoretical biology? How is a student going to have a hope of understanding theoretical models in behavioral ecology or population genetics without some mathematical training? What E O Wilson is saying is straight out of the bad old days which ended in the 1990s. Back then, at least in the UK, it was much more common to think that students studying biology didn't need math. Those days are over. Everyone recognizes that the statistical, computational, and theoretical parts of biology are essential for students to come to grips with. I'm a little sad to publicly criticize an old biologist who has made great contributions but no young scientist should read that article and come away with the impression that it's anything other than embarrassingly out of touch.
- kiba 14y ago
  Wilson said that he simply rely on statisticians as collaborator. Of course, what if you can't find a statistician to help you do your paper?
  - tezka 14y ago
    you use R?
  - saraid216 14y ago
    Stop living in an academic silo?
- anigbrowl 14y ago
  But he's not denying that everyone needs basic fluency - indeed, he recounts the embarrassing necessity of learning calculus in early middle age in order to master his own field. He's saying that exceptional fluency is only required in a few fields. You're arguing with a straw man.
stiff 14y ago
Just compare what has been achieved in science in, say, 2000 years before the invention of calculus, with just the 100 years after its invention. As almost always, the author is extrapolating what is true in his field (biology) to "the world as the whole". Biology hasn't historically often used mathematics because it was and to a large extent still is a descriptive science. With molecular biology now being the hottest stream in biology the need for mathematics is much stronger than before even in this discipline. Instead of denying the obvious, it would be better to think of ways to not scare people away from mathematics - he makes it seem like some people simply do not have the mathematical ability and there is nothing to do about it except finding a field that doesn't need it.
- deleted 14y ago
  [deleted]
beloch 14y ago
Wilson's point is not that math/stats aren't necessary for most research. They are. He admits it. Instead, he argues that there is an ample supply of math/stats researchers to collaborate with, so you can get by in science being mathematically illiterate. I disagree. As a grad student, I did work in experimental quantum physics. Emphasis on experimental. There were only a handful of places on Earth where theorists could go to test the sort of stuff we could do in the lab. In a very specific corner of scientific knowledge, we were the choke point. We collaborated with theorists from all over the world. Many of them could do things on paper that I could barely understand. I had to understand them to test them though, and they helped me greatly. I'd be rather disappointed in Wilson if he was happy to test theories he couldn't understand! I think the message shouldn't be that "there are people to do math/stats for you if you want to do science". Perhaps you could get by that way, and perhaps Wilson has been able to con people into thinking he's good when he's testing things he doesn't understand. That takes a completely different skillset than math/stats I suppose, but I don't find it admirable. Perhaps a better message is that you don't have to be a hardcore theorist to contribute to scientific research. You need to be able to understand what you're doing, but you don't need to be a genius who covers every surface around him in incomprehensible symbols while gibbering to himself gleefully. (Yes, these people do exist, and they are sometimes awesome to have around.) Theorists are just one kind of scientist. Experimentalists are every bit as important, but their skill set is different. Theorists can wave their hands and make assumptions when solving problems. Experimentalists have to think things through very pedantically because assumptions usually bite them in the ass. Theorists can tackle a different problem every day and move between wildly disparate fields on a whim. Experimenalists have to stick with one problem for months or years at a time. Experimental work involves a lot of craft and patience. So no, you don't need to be a mathematical genius to be a scientist, but I wouldn't want to be an experimentalist who can't understand what he's doing!
- asafira 14y ago
  I think the fact of the matter is simply this: at some point in one's career in physics, when you make a decision between being an experimentalist and theorist, you don't spend nearly as much time focusing on the theory. I don't think it's wrong, but it's just natural that at some point you won't be as fluent with the theory as theorists. I was writing out how I don't agree with the author, but then I took in the bigger picture and realized that indeed I do think that a lot of the experimentalists in the field have either forgotten or just aren't that great at their math skills. I think this shows most in classes, where it's easy for them to get tripped up over details. That being said, most of the time it's just simple things. I think there is still clearly a higher bar (in general) in physics than in other sciences (i.e., biology) as far as math goes, and it's far too much of a stretch to say you don't need to know math well to do well. We aren't talking about algebraic topology here, I think Wilson is commenting even on just multivariable calc and linear algebra. Quantum Mechanics without linear algebra? At the very least, it would be very hard to learn (if at all). If anyone from non-physics fields has some comments, I would be interested to hear.
poof131 14y ago
I agree with the article, I think? <TLDR> The only difference between math and English, or any other language, is a degree of precision. In math, the symbols and connotations are more refined, but the results are still interpreted. There is no absolute truth. Mathematical truth is still defined by agreement among leading scholars that something is correct. Physical truth in the sciences also depends upon agreement. In the ephemeral world of communication, words and their meanings are relevant only to our own perception. We can try to better agree upon the starting ground, the definitions, but definitions still depend upon the flimsy symbols and what they signify in each person’s mind. There is no perfect line. I enjoy math as a dilettante communicator. And while math can greatly enhance the precision of our communications, it can also be used to deceive. My non-schizoid self agrees that the probability of pulling the “Ace of Spades” from a deck of cards is 1 in 52, but this depends upon our understanding of the definitions, our belief that the logic of probability is reasonable, and our intuition that the results agree with the world we perceive. My skeptic self, however, disbelieves that the esoteric formulas of macroeconomics accurately predict the world around us. How much "advanced math" is being conducted at banks, universities, and government institutions in pursuit of the illusory goal of modeling the economy? This math serves the purpose of providing the illusion of understanding, appropriate for politicians justifying desired actions, bankers selling products, and economics professors advancing careers. In my perception of reality, this math too often blows up when events it describes as one in a trillion come to fruition on a much more frequent basis. While I believe understanding math can prove beneficial to any endeavor that is trying to more precisely communicate a perception of the world, that mathematical understanding does not trump the necessity of generating agreement upon the definitions and the results. With little math but plenty of logic, Darwin was able to generate an insight into the world with which many people agree (including myself). Yet with plenty of math and very little logic, many areas of "science" travel down rabbit hole after rabbit hole where the community coalesces in complicated group think, with insights that fail to agree with most peoples' perception of reality, but results that are nonetheless justified as correct based upon the "math." In the end, math is a method of communication, often more precise than other languages, but still transitory in its ability to convey meaning and generate agreement. It is a helpful tool but not an indispensable instrument to science. But I guess this all depends upon the definition of science. </QED>
erichocean 14y ago
In my opinion, the problem with math is actual mathematical notation, which is, frankly, terrible. Ridiculously bad. Especially given the advances that have been made in CS in that regard. Early programming languages created by mathematicians? They were terrible (for the most part). Then CS people started formalizing stuff, grammars were invented, and finally, the situation began to improve in the late 60s. But not math. Nope, it's the same archaic, imprecise, terrible notation that's been around for centuries. AFAIK there's nothing in math comparable to the development of programming languages in CS. It simply doesn't improve. Imagine if the first language ever created in CS was also the last. That's math. In CS, we've kept inventing new, better programming languages and conceptual foundations. Not math. There, they have a bad foundation, but they just keep building up and up and up, each paper even more hand-wavy and imprecise than the next. It's to the point where things that are actually trivial mathematical concepts to understand are damn near impossible to learn by actually reading a math paper about the topic -- all because of the notation, implied rules, etc. IN my experience, mathematical objects and concepts are simple, at the same level of difficulty as, say, quicksort or an AVL tree. All of math is that way. What's hard about math is the notation, not the concepts or mathematical objects that are presented. And because the notation is so bad, it's very hard for people to make use of math in an À la carte manner. You either spend years of drudgery with little payoff, or you don't use math at all. Contrast that with open source software (the CS equivalent, I would argue, to reading math papers), which is easy to use, because, hey, consistent notation, no hidden rules, no assumed set of knowledge or information. Everything has a definition. There is an answer for everything in the source code itself. Math papers are the opposite, including the math articles on Wikipedia. Math is damn near unusable for that reason by anyone but mathematicians who can intuit the implicit rules, notational deviations, etc. after a lifetime of study. It doesn't have to be this way.
- tome 14y ago
  Could you give some examples? [EDIT: unlike the other replies I don't actually disagree with the parent, I just want some examples!]
  - erichocean 14y ago
rodrigoavie 14y ago
Last year I entered CS school and found myself embarrassingly weak at Math. I've been studying really hard since them and I don't really believe I'll be a very good Computer Scientist if I do not learn Math (Linear Algebra, Discrete Math, Graph Theory, Game Theory, Calculus, Statistics).

55 points by tokenadult 14y ago

there is math, and then there is math. In Russia they have a saying "beat a rabbit long enough and it will eventually learn to take derivatives, but integrals are another matter". For many people areas involving spatial reasoning like college physics for engineers is that "another matter", while (simple) integrals are still no biggie. As for the original article, the implication that somebody having trouble with basic algebra can be "great scientist" sounds dubious to say the least. Like I said, there is math, and then there is math... there is stuff that anybody claiming any meaningful level of intelligence should be able to handle.

kiba 14y ago
there is math, and then there is math. In Russia they have a saying "beat a rabbit long enough and it will eventually learn to take derivatives, but integrals are another matter". A rabbit will be woefully unprepared to learn integrals if it forgot derivatives before it starts learning integral.
- jleader 14y ago
  One moderately popular college calculus textbook (by Prof. Apostol of Caltech) introduces integrals before derivatives.
gruseom 14y ago
In Russia they have a saying "beat a rabbit long enough and it will eventually learn to take derivatives, but integrals are another matter". Something about that is quintessentially Russian.
thaumasiotes 14y ago
I find that saying bizarre. In high school, I found derivatives significantly more difficult to learn than I did integrals. Then, in multivariable calc, I found derivatives significantly more difficult, again. Integrals follow your intuition in a way that derivatives just don't.
- semaphorism 14y ago
  Tell that to a rabbit.
- shrughes 14y ago
  What. Derivatives are a very straightforward algorithm. Integrals aren't.
- dsrguru 14y ago
  Derivatives are formulaic. Integrals, like proofs, require thinking backwards, i.e. creativity and/or luck. For the vast majority of people, cultivating that intuition is a lot harder than plugging numbers into formulas...
  - zerr 14y ago
    Formally speaking, solving integrals requires brute force. It is only after many such brute force samples your starting to get an intuition. But I won't call this creativity.
- Q6T46nT668w6i3m 14y ago
  Do you have this backward (computing a derivative is algorithmic, computing an integral is analytic)?
- claudius 14y ago
  I would guess that this depends on the things you usually integrate and those one differentiates – as the former only has (simple) algorithms for very simple cases, whereas the latter has very general algorithms, differentiation exercises in school tend to use more complex examples than integration exercises. However, given a ‘random’ expression, integration will be much more difficult than differentiation.
nknighthb 14y ago
> there is stuff that anybody claiming any meaningful level of intelligence should be able to handle Well, you've just called many dyslexics stupid. Does your assertion extend to basic arithmetic? Because if so, you've just called everyone with dyscalculia and/or acalculia stupid, and that group includes a lot of autism-spectrum engineers.

kaptain 14y ago

My manager once asked me to finish out a statistical problem to better analyze the results I was getting from my code changes that were intended to speed up an API. I looked at the whiteboard for about 5 seconds and grinned: "Who needs math? That's what computers are for!" Then I went to lunch. Of course I went back and finished the analysis after lunch.

kiba 14y ago

Math isn't that hard to learn, it's just that it requires lot of tutoring and lot of thinking. The reason why people today don't possess that much mathematical knowledge is that they don't maintain their knowledge of mathematics. So, when it comes to learning calculus or other advanced mathematics, you have a swiss cheese foundation. That swiss cheese foundation simply means you didn't mastered the previous required materials. So it's hard to learn. I did the really elementary to high school materials in the past two years on and off. Math concepts didn't really get harder to learn. They're easy or hard to learn at time, but there's no difficulty ramp to speak of. Then what happens afterward is that you start forgetting about how to do things like logarithmic operation, how to simplify trig identities, and so on after a week or two, or sometime days. So you need to continuously review them everyday or do enough real world problems that you know how to do them for life. The skills and knowledge that we master requires daily maintenance, or otherwise you lose your ability to do them. It's just like fitness. A person who stop long distance running for a while will no longer be able to run as long.

Xcelerate 14y ago
> Math isn't that hard to learn [...] calculus or other advanced mathematics Most people's concept of what "math" is, isn't advanced math. Advanced math is incredibly complex. (I honestly kind of chuckle when people tell me they are "really good at math".) Read Wiles' proof of Fermat's Last Theorem (http://www.cs.berkeley.edu/~anindya/fermat.pdf http://www.cs.berkeley.edu/~anindya/fermat.pdf), or Godel's incompleteness theorem and tell me if you understand any of that. Math much easier than his proof, yet vastly more difficult than calculus, is used in many areas of physics and chemistry. And I think it is this kind of math to which the original article was referring. People like to quip that Einstein wasn't good at math, because he had mathematicians helping him with his work. What they don't understand is that Einstein's skills in math blows everyone else's out of the water; it's just that they weren't up to the level of an actual mathematician.
- kiba 14y ago
  it's just that they weren't up to the level of an actual mathematician. I guess what I am doing and learning is really elementary. But I like to think my point about having foundational knowledge and the willingness to practice everyday still stand. I know what I am doing and learning isn't what mathematican really do day to day. They make up new stuff, prove things, and solve problems in creative ways. I just commit to memory or practice steps on how to solve exercise sets, although the way I do is way smarter and time efficient than what people do when I was in high school. I don't know if all that practice will eventually pay off in some way, but I know that I just really hate forgetting stuff that I learned in high school math class. ( Yes, I really do "incredibly boring" math homework everyday despite finishing high school three years ago)

Permit 14y ago

E.O. Wilson did an excellent TED talk on this exact subject called "Advice to young scientists". I'd recommend watching it as it's one of my favorite talks. http://www.ted.com/talks/e_o_wilson_advice_to_young_scientists.html http://www.ted.com/talks/e_o_wilson_advice_to_young_scientis...

Myrmornis 14y ago

E O Wilson is a great biologist and author. However, this article is completely wrong. In particular, this > Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. is embarrassingly incorrect. For one example of why this is wrong, and sticking to E O Wilson's field, consider statistics. No biologist can publish anything nowadays without including some statistical analysis in their paper. So there's a pretty simple choice: either publish statistical stuff you don't understand, or learn enough math to achieve a basic understanding. Integrating probability densities, maximum likelihood estimators, etc etc, you certainly need calculus, and linear algebra will be very helpful too. As a second example, what about theoretical biology? How is a student going to have a hope of understanding theoretical models in behavioral ecology or population genetics without some mathematical training? What E O Wilson is saying is straight out of the bad old days which ended in the 1990s. Back then, at least in the UK, it was much more common to think that students studying biology didn't need math. Those days are over. Everyone recognizes that the statistical, computational, and theoretical parts of biology are essential for students to come to grips with. I'm a little sad to publicly criticize an old biologist who has made great contributions but no young scientist should read that article and come away with the impression that it's anything other than embarrassingly out of touch.

kiba 14y ago
Wilson said that he simply rely on statisticians as collaborator. Of course, what if you can't find a statistician to help you do your paper?
- tezka 14y ago
  you use R?
- saraid216 14y ago
  Stop living in an academic silo?
anigbrowl 14y ago
But he's not denying that everyone needs basic fluency - indeed, he recounts the embarrassing necessity of learning calculus in early middle age in order to master his own field. He's saying that exceptional fluency is only required in a few fields. You're arguing with a straw man.

stiff 14y ago

Just compare what has been achieved in science in, say, 2000 years before the invention of calculus, with just the 100 years after its invention. As almost always, the author is extrapolating what is true in his field (biology) to "the world as the whole". Biology hasn't historically often used mathematics because it was and to a large extent still is a descriptive science. With molecular biology now being the hottest stream in biology the need for mathematics is much stronger than before even in this discipline. Instead of denying the obvious, it would be better to think of ways to not scare people away from mathematics - he makes it seem like some people simply do not have the mathematical ability and there is nothing to do about it except finding a field that doesn't need it.

deleted 14y ago
[deleted]

beloch 14y ago

Wilson's point is not that math/stats aren't necessary for most research. They are. He admits it. Instead, he argues that there is an ample supply of math/stats researchers to collaborate with, so you can get by in science being mathematically illiterate. I disagree. As a grad student, I did work in experimental quantum physics. Emphasis on experimental. There were only a handful of places on Earth where theorists could go to test the sort of stuff we could do in the lab. In a very specific corner of scientific knowledge, we were the choke point. We collaborated with theorists from all over the world. Many of them could do things on paper that I could barely understand. I had to understand them to test them though, and they helped me greatly. I'd be rather disappointed in Wilson if he was happy to test theories he couldn't understand! I think the message shouldn't be that "there are people to do math/stats for you if you want to do science". Perhaps you could get by that way, and perhaps Wilson has been able to con people into thinking he's good when he's testing things he doesn't understand. That takes a completely different skillset than math/stats I suppose, but I don't find it admirable. Perhaps a better message is that you don't have to be a hardcore theorist to contribute to scientific research. You need to be able to understand what you're doing, but you don't need to be a genius who covers every surface around him in incomprehensible symbols while gibbering to himself gleefully. (Yes, these people do exist, and they are sometimes awesome to have around.) Theorists are just one kind of scientist. Experimentalists are every bit as important, but their skill set is different. Theorists can wave their hands and make assumptions when solving problems. Experimentalists have to think things through very pedantically because assumptions usually bite them in the ass. Theorists can tackle a different problem every day and move between wildly disparate fields on a whim. Experimenalists have to stick with one problem for months or years at a time. Experimental work involves a lot of craft and patience. So no, you don't need to be a mathematical genius to be a scientist, but I wouldn't want to be an experimentalist who can't understand what he's doing!

asafira 14y ago
I think the fact of the matter is simply this: at some point in one's career in physics, when you make a decision between being an experimentalist and theorist, you don't spend nearly as much time focusing on the theory. I don't think it's wrong, but it's just natural that at some point you won't be as fluent with the theory as theorists. I was writing out how I don't agree with the author, but then I took in the bigger picture and realized that indeed I do think that a lot of the experimentalists in the field have either forgotten or just aren't that great at their math skills. I think this shows most in classes, where it's easy for them to get tripped up over details. That being said, most of the time it's just simple things. I think there is still clearly a higher bar (in general) in physics than in other sciences (i.e., biology) as far as math goes, and it's far too much of a stretch to say you don't need to know math well to do well. We aren't talking about algebraic topology here, I think Wilson is commenting even on just multivariable calc and linear algebra. Quantum Mechanics without linear algebra? At the very least, it would be very hard to learn (if at all). If anyone from non-physics fields has some comments, I would be interested to hear.

poof131 14y ago

I agree with the article, I think? <TLDR> The only difference between math and English, or any other language, is a degree of precision. In math, the symbols and connotations are more refined, but the results are still interpreted. There is no absolute truth. Mathematical truth is still defined by agreement among leading scholars that something is correct. Physical truth in the sciences also depends upon agreement. In the ephemeral world of communication, words and their meanings are relevant only to our own perception. We can try to better agree upon the starting ground, the definitions, but definitions still depend upon the flimsy symbols and what they signify in each person’s mind. There is no perfect line. I enjoy math as a dilettante communicator. And while math can greatly enhance the precision of our communications, it can also be used to deceive. My non-schizoid self agrees that the probability of pulling the “Ace of Spades” from a deck of cards is 1 in 52, but this depends upon our understanding of the definitions, our belief that the logic of probability is reasonable, and our intuition that the results agree with the world we perceive. My skeptic self, however, disbelieves that the esoteric formulas of macroeconomics accurately predict the world around us. How much "advanced math" is being conducted at banks, universities, and government institutions in pursuit of the illusory goal of modeling the economy? This math serves the purpose of providing the illusion of understanding, appropriate for politicians justifying desired actions, bankers selling products, and economics professors advancing careers. In my perception of reality, this math too often blows up when events it describes as one in a trillion come to fruition on a much more frequent basis. While I believe understanding math can prove beneficial to any endeavor that is trying to more precisely communicate a perception of the world, that mathematical understanding does not trump the necessity of generating agreement upon the definitions and the results. With little math but plenty of logic, Darwin was able to generate an insight into the world with which many people agree (including myself). Yet with plenty of math and very little logic, many areas of "science" travel down rabbit hole after rabbit hole where the community coalesces in complicated group think, with insights that fail to agree with most peoples' perception of reality, but results that are nonetheless justified as correct based upon the "math." In the end, math is a method of communication, often more precise than other languages, but still transitory in its ability to convey meaning and generate agreement. It is a helpful tool but not an indispensable instrument to science. But I guess this all depends upon the definition of science. </QED>

erichocean 14y ago

In my opinion, the problem with math is actual mathematical notation, which is, frankly, terrible. Ridiculously bad. Especially given the advances that have been made in CS in that regard. Early programming languages created by mathematicians? They were terrible (for the most part). Then CS people started formalizing stuff, grammars were invented, and finally, the situation began to improve in the late 60s. But not math. Nope, it's the same archaic, imprecise, terrible notation that's been around for centuries. AFAIK there's nothing in math comparable to the development of programming languages in CS. It simply doesn't improve. Imagine if the first language ever created in CS was also the last. That's math. In CS, we've kept inventing new, better programming languages and conceptual foundations. Not math. There, they have a bad foundation, but they just keep building up and up and up, each paper even more hand-wavy and imprecise than the next. It's to the point where things that are actually trivial mathematical concepts to understand are damn near impossible to learn by actually reading a math paper about the topic -- all because of the notation, implied rules, etc. IN my experience, mathematical objects and concepts are simple, at the same level of difficulty as, say, quicksort or an AVL tree. All of math is that way. What's hard about math is the notation, not the concepts or mathematical objects that are presented. And because the notation is so bad, it's very hard for people to make use of math in an À la carte manner. You either spend years of drudgery with little payoff, or you don't use math at all. Contrast that with open source software (the CS equivalent, I would argue, to reading math papers), which is easy to use, because, hey, consistent notation, no hidden rules, no assumed set of knowledge or information. Everything has a definition. There is an answer for everything in the source code itself. Math papers are the opposite, including the math articles on Wikipedia. Math is damn near unusable for that reason by anyone but mathematicians who can intuit the implicit rules, notational deviations, etc. after a lifetime of study. It doesn't have to be this way.

tome 14y ago
Could you give some examples? [EDIT: unlike the other replies I don't actually disagree with the parent, I just want some examples!]
- erichocean 14y ago

rodrigoavie 14y ago

Last year I entered CS school and found myself embarrassingly weak at Math. I've been studying really hard since them and I don't really believe I'll be a very good Computer Scientist if I do not learn Math (Linear Algebra, Discrete Math, Graph Theory, Game Theory, Calculus, Statistics).