6 ms·

"What I fight against most in some sense, [when talking to the public,] is the kind of message, for example as put out by the film Good Will Hunting, that there

by Jun8 10y ago

"What I fight against most in some sense, [when talking to the public,] is the kind of message, for example as put out by the film Good Will Hunting, that there is something you're born with and either you have it or you don't. That's really not the experience of mathematicians. We all find it difficult, it's not that we're any different from someone who struggles with maths problems in third grade. It's really the same process. We're just prepared to handle that struggle on a much larger scale and we've built up resistance to those setbacks." I disagree. I understand the purpose of this statement, i.e. not to discourage people, etc. but clearly there are differences between Terry Tao, Wiles, Feynman, and many others and your typical PhD in these fields. This is like saying anyone can become Phelps with practice (although pinpointing his unique advantages can be complicated: https://www.scientificamerican.com/article/what-makes-michael-phelps-so-good1/ https://www.scientificamerican.com/article/what-makes-michae...). Not everybody can be above average! And of course, there are the rare cases such as Ramanujan. I think a better explanation is the one that Stephen gives in On Writing: "I don’t believe writers can be made, either by circumstances or by selfwill (although I did believe those things once). The equipment comes with the original package. Yet it is by no means unusual equipment; I believe large numbers of people have at least some talent as writers and storytellers, and that those talents can be strengthened and sharpened."

Isamu 10y ago
I disagree with your disagreement. When people say that there is not so much something special about themselves but that the work they put in enabled their success, they are not claiming the reverse is true: that hard work results in success. They are saying that success is the result of hard work. Not that hard work results in success.
- metaphorm 10y ago
  I'm not clear what distinction you're making. It's a bit of a truism (to the point of it being a cliche) for a successful person to say "I'm successful because I worked hard." Of course that isn't an identical statement with "hard work results in success." Nor should anyone with a fluent grasp of language conflate the two statements. So what are you disagreeing with, really? That's what I'm not clear about. Successful people, for diplomatic reasons, emphasize their work ethic instead of their talent. Certainly they have both. Did anyone claim differently?
  - pc86 10y ago
    Everyone I know with a PhD has asserted that it is 99% about being willing to slog through the years required to get the work done. That seems to suggest that the only difference (or most of the difference) between an average person and someone with a PhD is that the PhD just... took the time to get a PhD.
    - metaphorm 10y ago
      that's what they assert when discussing it in polite company. perhaps there's a difference between what people say to others and what is really true?
      - krapht 10y ago
        Then I'll say it anonymously as a former graduate student who left academia? For getting a PhD at any tier 2 or lower school, it is sufficient to work hard and be reasonably intelligent.
        metaphorm 10y ago
        getting a PhD is just a credential. that's a pretty weak measure of success. I was referring to public statements made by "famously successful" people.
        laichzeit0 10y ago
        Take every non-trivial side project you ever worked on and calculate the percentage you completed. Not half ass completed, but actually completed completed. Like you commented everything, wrote documentation, put it on Github, have decent test coverage, etc. Or how many Coursera courses did you sign up (with the real intent of actually finishing) vs how many did you _actually_ finish, doing all the homework, getting a really good grade? Employers look for people with degrees because it's very good estimate for "this person can finish shit" for this very reason. To say PhD is "just a credential" and has no predictive capabilities in terms of being "successful" I think is being disingenuous.
- BurningFrog 10y ago
  It seems obvious to me that success at the highest levels is the result of hard work and talent and luck.
gohrt 10y ago
Almost everyone can do some kind of math. For the same amount of discipline and effort, some people can prove Fermat's Last Theorem, and some people can prove Fermat's Little Theorem. And everyone can coast. Some people can get as far as Calculus without really trying, and some people can only get to basic arithmetic without really trying. But no one can just wander up to a whiteboard and solve a unproven theorem from intuition alone.
- meowface 10y ago
  >But no one can just wander up to a whiteboard and solve a unproven theorem from intuition alone. ...except von Neumann. But most would agree he really did have something special about him. (Especially if you include his frequent desires to nuke Russia.)
kxyvr 10y ago
As a disclaimer, I've a Ph.D. in mathematics and work professionally as a mathematician. That said, this sentiment is something that I'm very sensitive to. I've a problem with your phrasing because I feel it implies that to be a successful mathematician someone needs to operate at the level of someone like Andrew Wiles or Terry Tao. More generally, the question to me is whether mathematics should be treated differently than any other field like engineering, law, or cooking. To me, the answer is no. I believe that becoming a professional mathematician is primarily about hard work and long hours. Of course, natural talent helps, but it helps in every field. Very specifically, even if someone is not born with some kind of natural talent for math, with sufficient training I believe that most people can be successful professionally as well as provide new results that aid everyone in the field. And, again, I don't believe that this is any different than any other field. With enough training, someone who can figure out a way to burn a bowl of cereal can become a wonderful cook. They may not become Julia Childs, but they don't need to be. Further, they can create new dishes that everyone can enjoy and benefit from. Again, the core of my point is that most people I interact with believe that mathematics is special from all other fields. It's something that I strongly disagree with. I believe that this sentiment discourages people from entering the field. On a personal level, I find it alienating because it creates an artificial social separation. In any case, I'm glad people are talking about this and, certainly, these are just my thoughts.
- b_emery 10y ago
  > Very specifically, even if someone is not born with some kind of natural talent for math, with sufficient training I believe that most people can be successful professionally as well as provide new results that aid everyone in the field. You sum it up very well - I completely agree. I might not have the genes to be Einstein, but I can be a professional scientist. A very important point that is often missed.
  - sn9 10y ago
    And to turn it around, you might actually have the genes to be the best. But if you never put in the thousands of hours of quality work necessary to brush up against that genetic ceiling, you'll never know. I find that this is case in >99.9% of the people who say they don't have the genes for something.
joe_the_user 10y ago
This is like saying anyone can become Phelps with practice. Aside from the objections that others have made, that the main point is being a professional mathematician and not a unique genius, I would mention that "greatness" in mathematics (and other professional fields) isn't comparable being the best in an arena sport (or even in a mental sport like chess or go). The greatness of each great mathematician can be different - it's not solving some particular assigned problem all mathematicians face, it's choosing which problems to tackle, it's finding effective ways to frame problems, it's choosing who to associate with and get ideas from and give ideas to, it's teaching with extraordinary clarity or challenging your students in a unique way or whatever. The "unique genius" perspective closes-off the need of each mathematician to find the pursuit which them best. And your Stephen quote is equally unfortunate. The world is more evolving out of the view of there being singular writers moving more towards a place which welcomes those who effective use their particular gifts in whatever kinds of writing and storytelling suits them.
gxs 10y ago
You might be misinterpreting what he's saying. He's not saying if you work hard and practice you can be Phelps. What he's saying is that if you work hard and practice you can become a very good swimmer, even if not world class. You jumped to that conclusion on your own - studying math hard doesn't mean you'll end up an Andrew Wiles, it means you too can gain an understanding of mathematics. Not all mathematicians are celebrity scholars, there are plenty of average mathematicians that are moving the field forward inch by inch.

by Jun8 10y ago

Isamu 10y ago

I disagree with your disagreement. When people say that there is not so much something special about themselves but that the work they put in enabled their success, they are not claiming the reverse is true: that hard work results in success. They are saying that success is the result of hard work. Not that hard work results in success.

metaphorm 10y ago
I'm not clear what distinction you're making. It's a bit of a truism (to the point of it being a cliche) for a successful person to say "I'm successful because I worked hard." Of course that isn't an identical statement with "hard work results in success." Nor should anyone with a fluent grasp of language conflate the two statements. So what are you disagreeing with, really? That's what I'm not clear about. Successful people, for diplomatic reasons, emphasize their work ethic instead of their talent. Certainly they have both. Did anyone claim differently?
- pc86 10y ago
  Everyone I know with a PhD has asserted that it is 99% about being willing to slog through the years required to get the work done. That seems to suggest that the only difference (or most of the difference) between an average person and someone with a PhD is that the PhD just... took the time to get a PhD.
  - metaphorm 10y ago
    that's what they assert when discussing it in polite company. perhaps there's a difference between what people say to others and what is really true?
    - krapht 10y ago
      Then I'll say it anonymously as a former graduate student who left academia? For getting a PhD at any tier 2 or lower school, it is sufficient to work hard and be reasonably intelligent.
      - metaphorm 10y ago
        getting a PhD is just a credential. that's a pretty weak measure of success. I was referring to public statements made by "famously successful" people.
        laichzeit0 10y ago
        Take every non-trivial side project you ever worked on and calculate the percentage you completed. Not half ass completed, but actually completed completed. Like you commented everything, wrote documentation, put it on Github, have decent test coverage, etc. Or how many Coursera courses did you sign up (with the real intent of actually finishing) vs how many did you _actually_ finish, doing all the homework, getting a really good grade? Employers look for people with degrees because it's very good estimate for "this person can finish shit" for this very reason. To say PhD is "just a credential" and has no predictive capabilities in terms of being "successful" I think is being disingenuous.
BurningFrog 10y ago
It seems obvious to me that success at the highest levels is the result of hard work and talent and luck.

gohrt 10y ago

Almost everyone can do some kind of math. For the same amount of discipline and effort, some people can prove Fermat's Last Theorem, and some people can prove Fermat's Little Theorem. And everyone can coast. Some people can get as far as Calculus without really trying, and some people can only get to basic arithmetic without really trying. But no one can just wander up to a whiteboard and solve a unproven theorem from intuition alone.

meowface 10y ago
>But no one can just wander up to a whiteboard and solve a unproven theorem from intuition alone. ...except von Neumann. But most would agree he really did have something special about him. (Especially if you include his frequent desires to nuke Russia.)

kxyvr 10y ago

As a disclaimer, I've a Ph.D. in mathematics and work professionally as a mathematician. That said, this sentiment is something that I'm very sensitive to. I've a problem with your phrasing because I feel it implies that to be a successful mathematician someone needs to operate at the level of someone like Andrew Wiles or Terry Tao. More generally, the question to me is whether mathematics should be treated differently than any other field like engineering, law, or cooking. To me, the answer is no. I believe that becoming a professional mathematician is primarily about hard work and long hours. Of course, natural talent helps, but it helps in every field. Very specifically, even if someone is not born with some kind of natural talent for math, with sufficient training I believe that most people can be successful professionally as well as provide new results that aid everyone in the field. And, again, I don't believe that this is any different than any other field. With enough training, someone who can figure out a way to burn a bowl of cereal can become a wonderful cook. They may not become Julia Childs, but they don't need to be. Further, they can create new dishes that everyone can enjoy and benefit from. Again, the core of my point is that most people I interact with believe that mathematics is special from all other fields. It's something that I strongly disagree with. I believe that this sentiment discourages people from entering the field. On a personal level, I find it alienating because it creates an artificial social separation. In any case, I'm glad people are talking about this and, certainly, these are just my thoughts.

b_emery 10y ago
> Very specifically, even if someone is not born with some kind of natural talent for math, with sufficient training I believe that most people can be successful professionally as well as provide new results that aid everyone in the field. You sum it up very well - I completely agree. I might not have the genes to be Einstein, but I can be a professional scientist. A very important point that is often missed.
- sn9 10y ago
  And to turn it around, you might actually have the genes to be the best. But if you never put in the thousands of hours of quality work necessary to brush up against that genetic ceiling, you'll never know. I find that this is case in >99.9% of the people who say they don't have the genes for something.

joe_the_user 10y ago

This is like saying anyone can become Phelps with practice. Aside from the objections that others have made, that the main point is being a professional mathematician and not a unique genius, I would mention that "greatness" in mathematics (and other professional fields) isn't comparable being the best in an arena sport (or even in a mental sport like chess or go). The greatness of each great mathematician can be different - it's not solving some particular assigned problem all mathematicians face, it's choosing which problems to tackle, it's finding effective ways to frame problems, it's choosing who to associate with and get ideas from and give ideas to, it's teaching with extraordinary clarity or challenging your students in a unique way or whatever. The "unique genius" perspective closes-off the need of each mathematician to find the pursuit which them best. And your Stephen quote is equally unfortunate. The world is more evolving out of the view of there being singular writers moving more towards a place which welcomes those who effective use their particular gifts in whatever kinds of writing and storytelling suits them.

gxs 10y ago

You might be misinterpreting what he's saying. He's not saying if you work hard and practice you can be Phelps. What he's saying is that if you work hard and practice you can become a very good swimmer, even if not world class. You jumped to that conclusion on your own - studying math hard doesn't mean you'll end up an Andrew Wiles, it means you too can gain an understanding of mathematics. Not all mathematicians are celebrity scholars, there are plenty of average mathematicians that are moving the field forward inch by inch.