6 ms·

While extremely talented, I am not surprised to find this coming from a teen. Major mathematical discoveries often have come from those in their mid 20’s with t

by bradly 1y ago

While extremely talented, I am not surprised to find this coming from a teen. Major mathematical discoveries often have come from those in their mid 20’s with the greater discoveries being skewed towards the younger 20s and teens. I think this because pure mathematics is just so creative.

fhdkweig 1y ago
The Fields Medal has a cutoff age of 40 years old.
- jebarker 1y ago
  My understanding is that that’s more about encouraging younger mathematicians rather than an expectation that older ones won’t produce anything worthy.
  - ameliaquining 1y ago
    Sort of. It's complicated and there was politics involved. https://web.archive.org/web/20210324121533/https://www.nature.com/articles/d41586-018-00513-8 https://web.archive.org/web/20210324121533/https://www.natur...
    - jebarker 1y ago
      Thanks for sharing, it's much more complicated than I believed.
TechnicalVault 1y ago
It doesn't help what we've designed a rather silly academic system where principal investigators are forced to spend a good deal of their time thinking where they'll be applying for their next grant. We also optimise the system for short term thinking rather than long games. There are some exceptions in research institutes but I think young people are the ones who have the clearest minds because of it.
- Qem 1y ago
  I wonder how many years on average people can dedicate themselves to think deep about research problems, before they must stop thinking and start managing, or quit the race.
  - thelock85 1y ago
    You could replace “research” with nearly any term not undergirded by a direct profit motive (eg civics, politics, education, community health, urban planning). Or maybe it’s just (and you may be saying this) that one can only dedicate themselves up until a clear profit opportunity appears.
  - burning_hamster 1y ago
    Natural sciences: about 3 years at best. You finish your degree, and start your PhD. The first year, you are busy learning techniques and getting caught up with the relevant literature. You are far too concentrated on learning new things to get any thinking done. In your second year of your PhD, you are getting better. You can do most things without thinking about them. This frees up your brain to think about other things. However, your grasp of the wider literature is still lacking, so you use that brainspace to optimise your current experiments (as you should). In your third year of your PhD, you are starting to write things up: either your thesis, or your first (big) paper. You read a lot more, you know a lot more. The deep thinking can commence. Your first postdoc is probably your most productive time: you know what you are doing; you know the state of the literature and which parts are reliable and which aren't; you have a clear idea of what problems need solving. You are starting to write your first grant applications, but you only need one for yourself and not several to cover the needs of a full lab. You don't have any kids at home. This is a good time to solve some big problems. It lasts about 2-3 years. At the start of your second postdoc, you panic. The big problem was harder than you thought and you don't have enough high-impact papers to be competitive in job applications for a principal investigator (PI) role. You start churning out low-value fillers and collaborating with everyone and their hamster to get your name on as many papers as possible. The rest of the time is taken up by applying for grants and PI positions. You don't even make it to the interview stage. You start pondering about life outside of academia. The big problems are forgotten.
jebarker 1y ago
Whenever I hear this claim about younger mathematicians I wonder if it still holds true (or really did historically). For example, Andrew Wiles proved Fermat’s Last Theorem in his 40s and there are numerous examples of productive older mathematicians. But also I think the claim skews towards big flashy problems rather than the work of building mathematical frameworks, finding structural insights and finding connections between disparate areas (which requires broad experience rather than just young intensity).
- Qem 1y ago
  > there are numerous examples of productive older mathematicians Curious about the extreme cases. Did any centenarians ever managed to come with an outstanding original math result? If it didn't happen before, I hope to see it happening in the next decades, given current demographic trends.
  - sebmellen 1y ago
    Erdős? I’m sure the Ritalin helped.
  - CurtMonash 1y ago
    I was told that a book published in honor of Oscar Zariski's 80th birthday included a paper by Oscar Zariski, either proving or at least making progress on a longstanding conjecture by Oscar Zariski. I was in the relevant department at the time (Harvard math), but I wasn't much of an algebraic geometer, so I took that at face value without probing for details.
- LunaSea 1y ago
  Wiles started working on it at 33 so it took some time to finish it but the base ideas were already in place in his early thirties.
  - jebarker 1y ago
    That seems like a pretty weak argument. I don’t think he was just filling in easy details for the next decade plus. Also, even 33 is quite a bit older than the commonly claimed early 20s needed for great mathematical work.
codedokode 1y ago
Probably it is because the first solved problem seems like fun, but solving problems daily as a job quickly become boring?
loeber 1y ago
I think this hasn't been true in a long, long time. The most recent example of major contributions coming from someone in their 20s would be Evariste Galois around the time of the French Revolution. Teens? No way, not really ever.
- kevinventullo 1y ago
  Peter Scholze received his Fields Medal at 30 for work he carried out through his 20’s. However he is not the youngest recipient: J.P. Serre received his Fields medal at 27.
  - getnormality 1y ago
    Before we get too excited about the Fields Medal as an indicator for age of great mathematical achievements, let's remember that it's only awarded to people under 40 for work done earlier, potentially many years earlier.
aaron695 1y ago
[dead]
Qem 1y ago
https://en.m.wikipedia.org/wiki/Shoshin https://en.m.wikipedia.org/wiki/Shoshin https://en.m.wikipedia.org/wiki/Einstellung_effect https://en.m.wikipedia.org/wiki/Einstellung_effect

by bradly 1y ago

fhdkweig 1y ago

The Fields Medal has a cutoff age of 40 years old.

jebarker 1y ago
My understanding is that that’s more about encouraging younger mathematicians rather than an expectation that older ones won’t produce anything worthy.
- ameliaquining 1y ago
  Sort of. It's complicated and there was politics involved. https://web.archive.org/web/20210324121533/https://www.nature.com/articles/d41586-018-00513-8 https://web.archive.org/web/20210324121533/https://www.natur...
  - jebarker 1y ago
    Thanks for sharing, it's much more complicated than I believed.

TechnicalVault 1y ago

It doesn't help what we've designed a rather silly academic system where principal investigators are forced to spend a good deal of their time thinking where they'll be applying for their next grant. We also optimise the system for short term thinking rather than long games. There are some exceptions in research institutes but I think young people are the ones who have the clearest minds because of it.

Qem 1y ago
I wonder how many years on average people can dedicate themselves to think deep about research problems, before they must stop thinking and start managing, or quit the race.
- thelock85 1y ago
  You could replace “research” with nearly any term not undergirded by a direct profit motive (eg civics, politics, education, community health, urban planning). Or maybe it’s just (and you may be saying this) that one can only dedicate themselves up until a clear profit opportunity appears.
- burning_hamster 1y ago
  Natural sciences: about 3 years at best. You finish your degree, and start your PhD. The first year, you are busy learning techniques and getting caught up with the relevant literature. You are far too concentrated on learning new things to get any thinking done. In your second year of your PhD, you are getting better. You can do most things without thinking about them. This frees up your brain to think about other things. However, your grasp of the wider literature is still lacking, so you use that brainspace to optimise your current experiments (as you should). In your third year of your PhD, you are starting to write things up: either your thesis, or your first (big) paper. You read a lot more, you know a lot more. The deep thinking can commence. Your first postdoc is probably your most productive time: you know what you are doing; you know the state of the literature and which parts are reliable and which aren't; you have a clear idea of what problems need solving. You are starting to write your first grant applications, but you only need one for yourself and not several to cover the needs of a full lab. You don't have any kids at home. This is a good time to solve some big problems. It lasts about 2-3 years. At the start of your second postdoc, you panic. The big problem was harder than you thought and you don't have enough high-impact papers to be competitive in job applications for a principal investigator (PI) role. You start churning out low-value fillers and collaborating with everyone and their hamster to get your name on as many papers as possible. The rest of the time is taken up by applying for grants and PI positions. You don't even make it to the interview stage. You start pondering about life outside of academia. The big problems are forgotten.

jebarker 1y ago

Whenever I hear this claim about younger mathematicians I wonder if it still holds true (or really did historically). For example, Andrew Wiles proved Fermat’s Last Theorem in his 40s and there are numerous examples of productive older mathematicians. But also I think the claim skews towards big flashy problems rather than the work of building mathematical frameworks, finding structural insights and finding connections between disparate areas (which requires broad experience rather than just young intensity).

Qem 1y ago
> there are numerous examples of productive older mathematicians Curious about the extreme cases. Did any centenarians ever managed to come with an outstanding original math result? If it didn't happen before, I hope to see it happening in the next decades, given current demographic trends.
- sebmellen 1y ago
  Erdős? I’m sure the Ritalin helped.
- CurtMonash 1y ago
  I was told that a book published in honor of Oscar Zariski's 80th birthday included a paper by Oscar Zariski, either proving or at least making progress on a longstanding conjecture by Oscar Zariski. I was in the relevant department at the time (Harvard math), but I wasn't much of an algebraic geometer, so I took that at face value without probing for details.
LunaSea 1y ago
Wiles started working on it at 33 so it took some time to finish it but the base ideas were already in place in his early thirties.
- jebarker 1y ago
  That seems like a pretty weak argument. I don’t think he was just filling in easy details for the next decade plus. Also, even 33 is quite a bit older than the commonly claimed early 20s needed for great mathematical work.

codedokode 1y ago

Probably it is because the first solved problem seems like fun, but solving problems daily as a job quickly become boring?

loeber 1y ago

I think this hasn't been true in a long, long time. The most recent example of major contributions coming from someone in their 20s would be Evariste Galois around the time of the French Revolution. Teens? No way, not really ever.

kevinventullo 1y ago
Peter Scholze received his Fields Medal at 30 for work he carried out through his 20’s. However he is not the youngest recipient: J.P. Serre received his Fields medal at 27.
- getnormality 1y ago
  Before we get too excited about the Fields Medal as an indicator for age of great mathematical achievements, let's remember that it's only awarded to people under 40 for work done earlier, potentially many years earlier.

aaron695 1y ago

[dead]

Qem 1y ago

https://en.m.wikipedia.org/wiki/Shoshin https://en.m.wikipedia.org/wiki/Shoshin https://en.m.wikipedia.org/wiki/Einstellung_effect https://en.m.wikipedia.org/wiki/Einstellung_effect