Early Career in Math: Why Peak Before 30?

[Silviu]

I read several articles saying that most mathematicians have the peak of their career before 30 and after that they don't do much significant work. Although this is a simplification of the reality, the truth is that in math many people do major breakthroughs before 30, a lot more than in other fields of science. I was wondering what is the cause of it? On one hand I would expect that with age you get more experience and you have more directions in which you can go when trying to solve a problem so more chances to succeed. On the other hand mathematics is older than any other science, so one would expect that you need a much longer time to reach the modern knowledge, compared to other sciences, before doing any breakthrough. So why is the reality so different from the expectations?

 

[Borek]

Creativity vs experience. You gain the latter, you lose the former.

 

[fresh_42]

I read several articles ... ...the truth is that in math many people do major breakthroughs before 30, a lot more than in other fields of science...So why is the reality so different from the expectations?

Do you have ANY references, preferably scientific studies, or other sources which support your claims, or are we just wildly guessing, claim and argue about nonsense? There are so many vague terms in your statements "breakthrough, truth(!), modern knowledge, expectations" that it cannot be discussed seriously. We do no politics here. And whose expectations were you talking about?

Please send me relevant sources which we can discuss per PM, and I like to add, that the statistical basis of any such studies alone will very likely be worth a debate already, let alone conclusions, esp. yours! Until then I recommend to read the vita of Leonhard Euler or Andrew Wiles.

Thread closed.

 

[jedishrfu]

There are several factors here that affect this stereotypical notion:

1) The Fields medal is given out to folks under 40 once every 4 years who those have done outstanding mathematical research.

Older folks need not apply. There is no Nobel Medal for Math. However there is the Nobel Medal for Economics that some mathematicians receive most notably John Nash (1994). And there's the Abel prize and the Wolf prize among others annually for mathematicians of any age.

https://en.wikipedia.org/wiki/List_of_Nobel_Memorial_Prize_laureates_in_Economics​

2) Younger folks are willing to buck trends and are encouraged to explore new fields because it won't affect their career initially.

The act of getting a PhD and writing a dissertation reinforces this doctoral responsibility.​

3) We learn from our mistakes and as we age we make less of them with material we have worked with for many years.

Sometimes our mistakes and our subsequent analysis lead us to something truly grand and other times lead us to misery. Einstein ran into both outcomes while developing General Relativity along with the fear that Hilbert might beat him to the solution.​

Have there been discoveries by folks over 40? Yes

From Quanta magazine:

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of geometry, probability theory and statistics that had eluded top experts for decades.

https://www.quantamagazine.org/statistician-proves-gaussian-correlation-inequality-20170328/