Are mathematicians born not made?

[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.