Are mathematicians born not made?

[homeomorphic]

An 18 year old doing a PhD? wow, I am envious of people who get this far ahead. Are you at one of the top 10 US graduate schools in Math?

We had 2 people under 20 in our program the whole time I have been here (6 years). It's a big program. Over a hundred students. No, it's not top 10. Top 25, maybe.

 

[Group_Complex]

Hmmm, even Putnam competition winners do not go straight to Grad School.

Do these people just get mathematics better than the rest of us?

 

[wisvuze]

Hmmm, even Putnam competition winners do not go straight to Grad School.

Do these people just get mathematics better than the rest of us?

Putnam mathematics is not quite the same as "real mathematics".

And you should read this:


http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

 

[Group_Complex]

Putnam mathematics is not quite the same as "real mathematics".

And you should read this:


http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

I have read that. There seems to be quite an overlap between the two. Those who succeed in the Putnam always go on to succeed in mathematics (If they choose to continue in the field).

 

[Mépris]

Perhaps. I bet there are successful mathematicians who have not participated in any math competitions, let alone, enjoyed them.

 

[Group_Complex]

Mepris, I agree. However, I do not believe I make up for my lack of Putnam ability in the "real" areas of pure mathematics.

 

[deRham]

Even if mathematicians are born, they have to do a lot of work and struggle to do something great. Everyone struggles at his/her own level. Point is: will the struggle be worth it for you?

 

[deRham]

Also, I do not believe there is a well-defined top 10 in mathematics programs, although maybe there is possibly a top 3 or 4, depending on how one measures stuff.

 

[homeomorphic]

Hmmm, even Putnam competition winners do not go straight to Grad School.

Do these people just get mathematics better than the rest of us?

Of course not. As I said, one of them seems to have flunked out. Just did stuff at an earlier age. Graduated high school 4 years early. Wasn't any better at math than everyone else here. You shouldn't read too much into a mere chronological advantage. Some of them are no different than anyone else, except that they did everything at an earlier age. It's just a mere time-shift. Nothing special, per se.

 

[homeomorphic]

Mepris, I agree. However, I do not believe I make up for my lack of Putnam ability in the "real" areas of pure mathematics.

One of my profs in undergrad was considered the best mathematician in the department (though it wasn't exactly Harvard, most people there had degrees from big name places). He said he didn't do very well on the Putnam.

 

[RoshanBBQ]

This is just a bit much. If you like mathematics, then go on with your degree. If you don't like mathematics, don't go on with your degree. It's as simple as that. And to reference a part of the conversation from before, I once asked a professor of mine how he solved unsolved problems. He said he thought about it for years.

And the 99% figure is most likely not about modestly but truth. Think about how many thoughts a person can have in a day on a subject. If even 50% of his thought were correct, he would contribute such an enormous amount to whatever field in which he was that he would be regarded as the greatest thinker of all time (not just in his field). As an example, have you ever seen an image of the notebook full of equations Einstein wrote down, all going on false or imperfect thoughts?

http://thevintagestandard.com/?p=1296

Like that. What would be the use of an erasable blackboard if 99% of his thoughts were right? He would instead be writing in pen in his final version with such an accuracy.

 

[Dembadon]

Hello.
It concerns me, that I may lack the creativity to pursue my interests in Pure Mathematics. I do not believe I am any more intelligent than average, Yet for some reasong I love the deductive method and beauties I find in Mathematics.

I was reading a short article http://journalstar.com/news/local/math-whiz-gives-lecture-at-unl/article_aacec19e-e75d-5537-9742-92efc517b3a7.html In which Michael Atiyah (Who I look up to very much as a mathematician) claims that Mathematicians are born rather than made. This dissapointed me greatly and for a few days I was considering giving up my goal of becoming a pure mathematician.

The reason I do not believe I am creative in mathematics is that I cannot prove theorems presented In textbooks, without reading the proof in the text (Real and Complex analysis). This has led to a reduced confidece in my mathematical abilities, which was already quite low due to poor performances in mathematical competitios and olympiads.

I am not striving to be a fields medalist or ground breaking mathematician (those were once my immature goals), but rather to contribute to research somehow, and present at least one creative proof in pure mathematics (It does not need to be a "proof from the book"). I really admire Raoul Bott, and would like to work in a field such as his, but I am unsure how to do this, if I lack creativity and insight at the undergraduate level.

I can understand all parts of the mathematics I study (Real Analysis, Complex Analysis, Abstract Algebra) with enough head banging, but I can rarely do the harder exercises without looking at the solutions, seeking aid, or re-reading the text.

Any advice?

All mathematicians are made. Even the people who learn and understand new mathematical concepts faster than others need to work at becoming proficient. They were not born with the ability to prove or create new theorems, they had to go to school and/or work at it just like everyone else. Therefore, they are made.

I don't think it is helpful for you to worry about what you will or will not be able to contribute to mathematical knowledge. If you have a passion for it, then pursue it with all you've got. See where it takes you.

 

[alexmahone]

Hello.
It concerns me, that I may lack the creativity to pursue my interests in Pure Mathematics. I do not believe I am any more intelligent than average, Yet for some reasong I love the deductive method and beauties I find in Mathematics.

I was reading a short article http://journalstar.com/news/local/math-whiz-gives-lecture-at-unl/article_aacec19e-e75d-5537-9742-92efc517b3a7.html In which Michael Atiyah (Who I look up to very much as a mathematician) claims that Mathematicians are born rather than made. This dissapointed me greatly and for a few days I was considering giving up my goal of becoming a pure mathematician.

The reason I do not believe I am creative in mathematics is that I cannot prove theorems presented In textbooks, without reading the proof in the text (Real and Complex analysis). This has led to a reduced confidece in my mathematical abilities, which was already quite low due to poor performances in mathematical competitios and olympiads.

I am not striving to be a fields medalist or ground breaking mathematician (those were once my immature goals), but rather to contribute to research somehow, and present at least one creative proof in pure mathematics (It does not need to be a "proof from the book"). I really admire Raoul Bott, and would like to work in a field such as his, but I am unsure how to do this, if I lack creativity and insight at the undergraduate level.

I can understand all parts of the mathematics I study (Real Analysis, Complex Analysis, Abstract Algebra) with enough head banging, but I can rarely do the harder exercises without looking at the solutions, seeking aid, or re-reading the text.

Any advice?

You Can Count On This: Math Ability Is Inborn, New Research Suggests

 

[homeomorphic]

Talk about overzealous on that last link. I didn't read that carefully, but it's pretty skimpy on the evidence to make such a grandiose claim as "Math ability is inborn".

It's much more complicated than such a simplistic statement could ever address. I'm not contesting the finding that some sort of number sense has a genetic basis, but rather that that finding has an incredibly limited scope in addressing the issue at hand.

To mention just one complicating factor, out of potentially billions of things I could bring up, my strength in math and in general, is visual/spatial reasoning ability. That has very little to do with "number sense", as far as I can tell.

 

[alexmahone]

I'm not contesting the finding that some sort of number sense has a genetic basis, but rather that that finding has an incredibly limited scope in addressing the issue at hand.

To mention just one complicating factor, out of potentially billions of things I could bring up, my strength in math and in general, is visual/spatial reasoning ability. That has very little to do with "number sense", as far as I can tell.

Surely visuospatial ability is genetic as well.

 

[homeomorphic]

Surely visuospatial ability is genetic as well.

That's far from obvious.

In fact, it's obviously true that just about any ability is NOT genetic, in the sense that it can be improved through practice.

The phrase practice makes perfect is a lie.

PERFECT practice makes perfect.

Practice is worthless, unless it's good practice, and in many case, people don't have a clue to practice well, so a great deal of their efforts are wasted.

 

[homeomorphic]

Let's put it this way. Suppose I had just become an artist after high school, according to my original plan and never did any math, other than arithmetic since high school. Would my math ability be anywhere in the ballpark of what it is now?

OBVIOUSLY NOT!

It would scarcely be 1% of what it is now.

Therefore the statement "math ability is genetic" is preposterous beyond belief, and not only that, but OBVIOUSLY, obviously, obviously so.

 

[RoshanBBQ]

You Can Count On This: Math Ability Is Inborn, New Research Suggests

That test is not directly related to this thread, because we don't know the OP's number sense or the statistics of number sense among "accomplished" mathematicians against which to compare him even if we had his performance.

I recall watching some show or video introducing the idea of the number sense test. The speaker in the show was a mathematician, and he only scored average against adults (though he blew the child's score out of the water). I know this isn't as meaningful as it could be, because I don't recall the show or the speaker.

Let's put it this way. Suppose I had just become an artist after high school, according to my original plan and never did any math, other than arithmetic since high school. Would my math ability be anywhere in the ballpark of what it is now?

OBVIOUSLY NOT!

It would scarcely be 1% of what it is now.

Therefore the statement "math ability is genetic" is preposterous beyond belief, and not only that, but OBVIOUSLY, obviously, obviously so.

That's just a false counterexample. Obviously, by math ability, people are talking about the ability to become mathematical. It doesn't have to do with the amount of mathematical knowledge you have relative to your life choices. What if I took all the best math geniuses in the world and put them in the cave age from birth? They would all suck at math, but that is just obvious. It doesn't show anything about whether their inborn skills attributed to their mathematical ability.To an extent, every intellectual task is a bit based on birth. The simple example of mental retardation preventing entirely the pursuit in any intellectual field demonstrates this fact. But its effect is not binary, it is a continuum. It's sort of like when night turns into day. If you are blazing with the light of the sun, maybe you have a good chance at intellectual work. If you are dark as void, well, it will be impossible for you to do so. But if you are somewhere in between, it is dubious to determine whether you can contribute to knowledge. Most people getting their Ph.D. in mathematics are certainly in this dubious state or the bright state. So there is no reason to crush your dreams simply because you find yourself to be in an unsure situation. The answer is not within our grasp. The only way to find out is for your to work out your mathematical career and observe it after the fact.

 

[alexmahone]

In fact, it's obviously true that just about any ability is NOT genetic, in the sense that it can be improved through practice.

Practice can help you improve, but only to an extent. Someone who isn't born with an innate ability for mathematics could be trained to become adept at basic mathematics, but it is preposterous to say that he could one day become another Gauss. Likewise, if Gauss received no mathematical training, he may never have become a mathematician at all! So, both nature and nurture play roles in deciding how good you are at maths.

 

[RoshanBBQ]

Practice can help you improve, but only to an extent. Someone who isn't born with an innate ability for mathematics could be trained to become adept at basic mathematics, but it is preposterous to say that he could one day become another Gauss. Likewise, if Gauss received no mathematical training, he may never have become a mathematician at all! So, both nature and nurture play roles in deciding how good you are at maths.

It looks like you're dealing in extremes, though. Does the OP want to figure out whether he can become an absolutely famous mathematician due to his immense, ingenious contributions? I don't think he ever stated that was what troubled his mind. He, in fact, stated his trouble comes from whether he has the ability to contribute novel ideas. Coming up with novel ideas needn't be grand enough to bring him to the levels of Gauss, so it makes no sense to mislead the OP by mentioning his inability to become the next Gauss.

 

[alexmahone]

It looks like you're dealing in extremes, though. Does the OP want to become an absolutely famous mathematician due to his immense, ingenious contributions? I don't think he ever stated that was what troubled his mind. He, in fact, stated his trouble comes from whether he has the ability to contribute novel ideas. This task needn't be grand enough to bring him to the levels of Gauss, so it makes no sense to mislead the OP by mentioning his inability to become the next Gauss.

Regardless of whether the OP wants to become the next Gauss, my point was clear: both nature and nurture play important roles in deciding how good you are at mathematics. That is the harsh truth.

 

[homeomorphic]

Obviously, by math ability, people are talking about the ability to become mathematical.

Yes, and that's exactly why it's NOT a false counter-example. You're talking semantics here, and it's precisely the semantics that I am objecting to.

 

[homeomorphic]

Regardless of whether the OP wants to become the next Gauss, my point was clear: both nature and nurture play important roles in deciding how good you are at mathematics. That is the harsh truth.

But there is no content to that claim. Everyone already knows that nature and nature play a role. The question is exactly what role they play and my point was just that it's not a simple thing. We don't have all the answers. And one little study doesn't add too much to that.

I could bring studies that show the role of nurture. For example, the recent trends in mastery-based learning reveal that some students are lagging behind in performance, simply because they have gaps in their knowledge. When the gaps are filled in, they can improve dramatically. So, we shouldn't just jump to the conclusion that they are inherently bad at math. The good news is that probably everyone is a little bit better at math than they think. Unless they have an inflated sense of their abilities or something.

 

[homeomorphic]

When you say "math ability", it should mean your ability to tackle a new subject in math.

And that improves with practice. If you give me a low-level math course, the contents of which I am ignorant of, I can outperform 95% of the undergraduates by putting in about 1% of the effort that they are putting in (the key being that I don't actually have to know the material in question). On the other hand, when I was in their position, before studying math, I'd still probably be one of the better students, but I would just be one of the pack. So, it seems rather silly to me not to call that "math ability". It's not just knowledge. It's skills that transfer to any new subject.

So, I find that title rather irresponsible. People will draw the wrong conclusions from it.

 

[Group_Complex]

It looks like you're dealing in extremes, though. Does the OP want to figure out whether he can become an absolutely famous mathematician due to his immense, ingenious contributions? I don't think he ever stated that was what troubled his mind. He, in fact, stated his trouble comes from whether he has the ability to contribute novel ideas. Coming up with novel ideas needn't be grand enough to bring him to the levels of Gauss, so it makes no sense to mislead the OP by mentioning his inability to become the next Gauss.

I once dreamed of reaching the levels of Gauss, Euler and Newton but I attribute that now to youthful arrogance. Still it troubles me to think that I would become a mathematician who contributes nothing.

 

[sweetpotato]

I once dreamed of reaching the levels of Gauss, Euler and Newton but I attribute that now to youthful arrogance. Still it troubles me to think that I would become a mathematician who contributes nothing.

If you are of at average to above average intelligence, and of above average motivation, you will most likely successfully complete a mathematics degree.

No one can determine if you will contribute anything meaningful to mathematics or not until your mathematics career is over. I mean, 10 years from now you may not have contributed anything you consider meaningful, but in 11 years you may well have.

Sometimes it's simply a matter of luck, of researching the right mathematical question/issue at the right time and the right place.

Like others have said, it makes no sense to compare yourself to mathematical prodigies. Say one mathematician came up with a meaningful contribution when they were 20, and another when they were 40. Who cares that the 2nd mathematician discovered his/her contribution later in life.

 

[RoshanBBQ]

Regardless of whether the OP wants to become the next Gauss, my point was clear: both nature and nurture play important roles in deciding how good you are at mathematics. That is the harsh truth.

The OP sets the theme of the thread with his question. It would be a shame if he interpreted your divergence from his question as an answer to it.

 

[Group_Complex]

The OP sets the theme of the thread with his question. It would be a shame if he interpreted your divergence from his question as an answer to it.

Roshan, I do not think his point detracted too much. For part of my concern is the constant comparisons I make between myself and great mathematicians and scientists and what they achieved at a certain age.
I think part of this was instigated by my reading of Bell's "Men of Mathematics" at a younger age, which provides many accounts of the precocious nature of these great men.
That being said, I also compare myself to more modern mathematicians, who win prizes for instance, and find my accomplishments at my age lacking in comparison to theirs at a similar age.

 

[Steely Dan]

It is probably better to find inspiration from these people than to find disappointment. What these people prove is that there are many ways of contributing to the field of mathematics, and that your contribution is often not well correlated with how well you do in your undergraduate and graduate coursework.

 

[deRham]

All mathematicians are made. Even the people who learn and understand new mathematical concepts faster than others need to work at becoming proficient. They were not born with the ability to prove or create new theorems, they had to go to school and/or work at it just like everyone else. Therefore, they are made.

Quoted out of hearty agreement. It always takes a lot of hard work and interest, because there is an ocean to face when you think about it.

 

[Skrew]

I ponderd this as well, I am pretty good at mathematics but I don't think I could come up with or prove most of the significant theorems on my own and I sometimes mis things that are obvious once a solution or proof is found(but I make sure I add the idea or concept that I overlooked to my memmory for future use). I have a tendency to overcomplicate things.

Perhaps this is a rationalization but to my understanding most Ph'D graduates contribute one minor but new thing to a field of study. It's not like they developed all of mathematics from scratch and even if one could it would be horribly inefficent to do so. Mathematics like every other subject is a result of thousands of years of development with each new development made being rather small when compared to the current subject as a whole now.

 

[DoomBringer2]

I was born and raised in India, went to a private school and faced extreme hardship in Grade 6, my math teacher gave me a 2/100 on an exam then proceeded to humiliate me in front of the class with 50+ people. After that I never cared for math... I took all the dumbass math courses while in high school in Canada and was rather unhappy about it. But my brain kept telling me to take math, learn math MATH MATH!I felt inadequate without it...in community college I was getting good grades but still I really wanted to learn more math.

My interest in math spiked when I took a statistics course while at college, I found it very interesting and fun! Fast-forward a few years, last year I finally took the step and signed up for grade 10 university math course in October 2011, finished in February 2012 and got 95%. I had so much fun learning the material and going through all the units. And just yesterday I finished all the units for grade 11 functions, my average is 90% ATM but I haven't written the exam yet. I can't wait to get started on advance functions and then move on to calculus & vectors.

Moral of the story is, don't let failure stop you. You got to work hard and devote a lot of hours to become good at math. But yes, some people are naturally good at mathematics, that's for sure.

 

[RoshanBBQ]

I was born and raised in India, went to a private school and faced extreme hardship in Grade 6, my math teacher gave me a 2/100 on an exam then proceeded to humiliate me in front of the class with 50+ people. After that I never cared for math... I took all the dumbass math courses while in high school in Canada and was rather unhappy about it. But my brain kept telling me to take math, learn math MATH MATH!I felt inadequate without it...in community college I was getting good grades but still I really wanted to learn more math.

My interest in math spiked when I took a statistics course while at college, I found it very interesting and fun! Fast-forward a few years, last year I finally took the step and signed up for grade 10 university math course in October 2011, finished in February 2012 and got 95%. I had so much fun learning the material and going through all the units. And just yesterday I finished all the units for grade 11 functions, my average is 90% ATM but I haven't written the exam yet. I can't wait to get started on advance functions and then move on to calculus & vectors.

Moral of the story is, don't let failure stop you. You got to work hard and devote a lot of hours to become good at math. But yes, some people are naturally good at mathematics, that's for sure.

This seems to be a repeated concept in the discussion here, that if you go to school for math, you can learn math. But I still stand by my opinion that the OP wants to know whether he can contribute to math, not learn it. He actually stated he learns fine in his coursework. His main question is "If I struggle at redoing basic proofs, does that indicate I will not be able to discover unique truths in math?"

 

[DoomBringer2]

Sorry, I didn't read the op. I was just going by the title heading. My apologies

 

[mathwonk]

I think it is hard to predict in advance who can do original math. My dad introduced me to comic books, then felt guilty about it and berated me for enjoying them. The point? I think the kind of rampant creativity in those old comics is related to my visual creativity in math! I never became convinced I could do math until I had actually done some. So even if mathematicians are born, we can't which ones were born to it until they finish their careers. So the answer to this rhetorical question won't help you decide what to do with your life. Choose based on the love, I say. (But it helps to have a high tolerance for poverty, rejection, and frustration).