Are mathematicians born not made?

[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).

 

[alexmahone]

But it helps to have a high tolerance for poverty

You got that right!

 

[deRham]

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.

Even if a textbook is in a "basic" course, that often just means the material is old and foundational to a lot more. It doesn't mean that producing it from scratch is any easier.

For example, even if calculus is "basic", I would say developing all of single variable calculus from scratch seems more daunting to me than developing multivariable calculus after single. So I wouldn't worry too much about not being able to prove theorems in Rudin without ever seeing the proofs.

Now after you have learned a lot of analysis, I'd say you should try your hand at figuring out ideas more on your own...

Also mathwonk's post is extremely spot on in my experience.

 

[mathwonk]

alexmahone: have you heard the one about the difference between a PhD in mathematics and a large pizza?
[ a large pizza can feed a family of four.]

 

[chiro]

I tend to think that people forget how knowledge is attained, how it's organized, and it's incremented.

When you are around people that have dedicated large chunks of their lives to something, then talking to them for ten minutes, an hour, or a day could give you more understanding than you would get if you just went your own way.

If you look at all the 'greats', you'll realize that their experiences as children and adults shaped not only their character, but their ideas.

As an example people talk about Gauss coming up with the prime conjecture before he was 18, but what people don't often know is that he was actually staring at log tables for a particular task he had to do and from that could see a pattern.

Another example is with the Gaussian distribution when we decided to measure the number of steps taken to get to school: he did this and realized that the distribution had the pattern that things were clustered highly around the mean and decayed fast as you got further out.

We look at people like Von Neumann as greats and he certainly did some great work, but again although Von Neumann was very smart, he was born into a wealthy family who got access to language training and got the best mathematics education in one of the best gymnasiums for where he was born. He worked under mathematicians like Hilbert and worked with people like Turing as well. Also imagine the effect of the Manhattan project in which you bring all these genius minds together and look at the result.

The point is that things are incremental and that there are processes that go behind these things and I get the feeling that a lot of people seem to forget this and characterize a kind of creativity as something that is not attainable by anyone else and that is not only very misleading (I would say false), but it's very detrimental to the young minds because it reinforces a very skewed and negative perception of what genius really is and everything else that surrounds not only creativity itself, but the pretext for such creativity.

 

[nucl34rgg]

Also, another major issue with students today is the "go big or go home" attitude. If you aren't a genius like the historical legends, you can likely still make a contribution with hard work and dedication. There is an element of natural talent (as in everything) that is required, but I believe most of the better students in math, engineering, or the quantitative sciences have this minimal level of talent. Obviously, the more talent one has, the less one would need to struggle to attain the same level of proficiency. The talent itself however is not sufficient to create a mathematician.

 

[chiro]

Also, another major issue with students today is the "go big or go home" attitude. If you aren't a genius like the historical legends, you can likely still make a contribution with hard work and dedication. There is an element of natural talent (as in everything) that is required, but I believe most of the better students in math, engineering, or the quantitative sciences have this minimal level of talent. Obviously, the more talent one has, the less one would need to struggle to attain the same level of proficiency. The talent itself however is not sufficient to create a mathematician.

This is a great point and personally I think it deserves serious discussion in all areas of the world both for parents, educators, politicians and policy makers.

The way people are taught in high school is that making mistakes is bad and this is causing a huge detrimental distortion in the minds of many people no matter what their talent or intelligence quotient (or some other measure) is.

The result of this is the kind of thing you have described as 'go big or go home' in that many young people don't realize that mistakes and risk is a natural part of life and because their perception of failure is so distorted, they just don't want to bear the pain of screwing up or being wrong and this is really a huge social issue that needs to be addressed.

I have seen it personally inside high school on practicum and in university where people crack very easily the minute they are put under some kind of stress. In the high school, it was very hard for me to watch one teacher just make the class so ridiculously easy and giving an overwhelming amount of praise for nothing, that I really wasn't surprised that this phenomena you have described in mathematics (I was doing a practicum for mathematics teaching btw) is so widespread.

Once the youth realize that these so called 'legends' or 'gods of math' were just other human beings and that often most things are done in a climate of uncertainty where many things just don't work, then they will get over this obstacle that they have to be superhuman in order to succeed.

In fact twofish-quant has said this kind of thing a few times in that he realized that 'if they could do it, then I could as well'.

If I had to say one thing to the youth it would be to realize that all you see is a polished trophy and the final result: you don't see all the activity behind the scenes to get to that final result. When you read a math paper that is claimed to be a work of genius, you don't see all the failed attempts to solve the problem. You don't see the collaboration with other people helping to solve that problem. You don't see all the research that has been undertaken where many many books written and contributed by many many people have been read and analyzed. You don't see all the influences that particular person has had from their upbringing, family, educators, and even other family, friends, and acquaintances.

Once they realize these things, risk won't be a dirty word and neither will failure.

 

[nucl34rgg]

The way people are taught in high school is that making mistakes is bad and this is causing a huge detrimental distortion in the minds of many people no matter what their talent or intelligence quotient (or some other measure) is.

I fully agree with you. People often forget the important role that failure and subsequent perseverance has played in pretty much every human pursuit.