Traits of a Fields Medalist: Pursuing Excellence in Mathematics

[RickTheBrick12]

I want to preface this by saying the question is a little tongue in cheek, I don't personally think that pursuing fame and glory is a good reason at all to be pursuing a career in mathematics. However, I would like to know what people here feel are the sort of traits that mathematicians who produce the caliber of work that would earn a fields medal. Just to provide some background as to why I'm asking this question I'll say a little about myself. Personally I'm still in my last few months of high school, really passionate about mathematics but never any good at the competitions and stuff that get you national recognition like the imo selection exams. Hell I never even made it past the AMC lol, that sort of thing just doesn't interest someone as noncompetitive as me. Despite this I made it into a pretty good university for undergrad and plan on studying math with the intention of getting a PhD afterwards. I'd like to one day produce really great work because I love mathematics but honestly I just want to spend my life doing what I love.

 

[ZapperZ]

This is as rational as asking for the characteristics of people who have won the Nobel Prize.

You are ignoring one very important aspect of many of the discoveries that have won these people such prizes - pure, unadulterated serendipity! They were doing something, and out comes something unexpected. They were smart and knowledgeable enough to know where the "boundary of the box" of knowledge was at that time to realize that this thing they found was clearly outside of that box. The discovery of superconductivity was one such example (there are many others).

You can't train, nor study, for such thing to happen. You just have to be at the right place and at the right time, and smart enough to be aware of it.

Zz.

 

[HuskyNamedNala]

This is true. You can be the smartest most determined person in the world...but if you are unlucky (as in the wrong time or place) then...well things might not work out.

 

[QuantumCurt]

Winning various middle school/high school math competitions says very little about how one will perform as a mathematician, or even about how one will perform as a math major in college. Upper level math is an entirely different ball game.

 

[Loop]

While skill and proficiency are crucial, it is also important to maintain a certain level of creativity. To make breakthroughs in certain fields it is important to use imagination and to have the willingness to push the bounds of what is known. Also, I would start looking up certain aspects of higher level mathematics that interest you. For example, I only got interested in physics when I was younger when I first started reading about quantum mechanics. I didn't understand many of the equations at the time, but I appreciated the concepts and became fascinated with everything about quantum & particle physics. For mathematics, I would recommend reading "Fermat's Last Theorem" written by Simon Singh (if you have not already) which is relatively easy to read and comprehend while at the same time captivating about mathematical proof.

 

[QuantumCurt]

The BBC documentary about Andrew Wiles and his proof of Fermat's Last Theorem is wonderful too. It serves as a wonderful counterpoint to the assumptions made by many that mathematics is a dry and emotionless field. At one point Wiles is reduced to tears upon finding that there was a mistake in his original proof.