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Hardy's comment about math being a "young man's game" has bothered me since I read his "Course of Pure Mathematics" about 10 years ago. I'm sure there's at lea

Hardy's comment about math being a "young man's game" has bothered me since I read his "Course of Pure Mathematics" about 10 years ago. I'm sure there's at least a bit of truth to the statement that mathematical discovery is, in general, easier for younger minds, but it seems to be an unnecessary and harmful trope to propagate. Either you still have it, or you don't. Why does the Fields Medal care about age? If a 60 year old proves the Riemann Hypothesis, why is he or she ineligible? This happened notably with Andrew Wiles. He (indirectly) proved Fermat's Last Theorem and was rewarded a "special plaque" instead of the Fields Medal for the crime of waiting until after his 40th trip around the sun to work on it. There's also the issue of economic pressure. We expect our young minds to solve "real problems" and to want to make a lot of money doing it. Pure mathematicians get to "hide" in academia when times are good and are often on the street when they aren't so good. In the absence of a focus on supporting the arts (including math) through patronage etc it is just hard for young people to get in the field. Older people have more time. Let them create without lowered expectations. For a deeply beautiful subject with a lot of very smart people, this whole age thing is just scratch-your-head puzzling.

GuiA 12y ago
Humans are often silly and irrational and like making up arbitrary rules for the games they play. Don't lose too much time scratching your head about these things, or you'll quickly end up bald.
dxbydt 12y ago
At the risk of downvotes, I will state a whole bunch of [Citation Needed] BS, which is, nevertheless, empirically true & in Hardy's favor - 1. Cerebral atrophy affects left brain disproportionately more than the right 2. Math is predominantly a left-brain activity. 3. Ergo, short-term memory & dexterity with numbers generally degrades with age ( supposedly peaking at 25 & declining from then on). Most math majors I've spoken to ( from prodigies to professors & people in between ) attest to the fact that they were much sharper when they were quite young. It isn't that they become dumber as they age, more like - they pick up a different kind of math to compensate for some of the other math that required them to exercise their symbolic manipulation skills at superior pace, which they have now lost.
- knowtheory 12y ago
  On the flip side, anyone who's in the social sciences can tell you that self-reporting is a terrible gauge.
- convivialdingo 12y ago
  I don't want to disagree with such studies (as I agree with them), but at the same time there is a tendency to derive absolutes when looking at such studies. Reality doesn't tend to support absolutes, however. Biological studies like these still fall onto bell curves, and outliers exist on such spectrums.
hurin 12y ago
I think the degradation with age as in part bio/physiological might also be in part a matter of adjustment to circumstance. That is to say the really hard problems in mathematics (or physics) one generally doesn't get to work on full-time (since it's very likely that one will work on them for years without producing any results); the most likely path in academia is therefore to do mediocre -to fairly good research that produces results and publications. When one compromises in to doing work that's less difficult than one can be doing because it's what's necessary career wise, it's not surprising that one's mental alacrity declines. There are certainly exceptional people that can do one kind of thing for work (or tenure), and at the same time publish significant work in a parallel field - but I think it's rare.
- sdenton4 12y ago
  Once you get enough of an institution built up around you - grad students to bootstrap, grants to write, what have you - there's so much less time to just work on the problems that interest you. I think there's less and less space in Academia for the 'individual contributor.'

GuiA 12y ago

Humans are often silly and irrational and like making up arbitrary rules for the games they play. Don't lose too much time scratching your head about these things, or you'll quickly end up bald.

dxbydt 12y ago

At the risk of downvotes, I will state a whole bunch of [Citation Needed] BS, which is, nevertheless, empirically true & in Hardy's favor - 1. Cerebral atrophy affects left brain disproportionately more than the right 2. Math is predominantly a left-brain activity. 3. Ergo, short-term memory & dexterity with numbers generally degrades with age ( supposedly peaking at 25 & declining from then on). Most math majors I've spoken to ( from prodigies to professors & people in between ) attest to the fact that they were much sharper when they were quite young. It isn't that they become dumber as they age, more like - they pick up a different kind of math to compensate for some of the other math that required them to exercise their symbolic manipulation skills at superior pace, which they have now lost.

knowtheory 12y ago
On the flip side, anyone who's in the social sciences can tell you that self-reporting is a terrible gauge.
convivialdingo 12y ago
I don't want to disagree with such studies (as I agree with them), but at the same time there is a tendency to derive absolutes when looking at such studies. Reality doesn't tend to support absolutes, however. Biological studies like these still fall onto bell curves, and outliers exist on such spectrums.

hurin 12y ago

I think the degradation with age as in part bio/physiological might also be in part a matter of adjustment to circumstance. That is to say the really hard problems in mathematics (or physics) one generally doesn't get to work on full-time (since it's very likely that one will work on them for years without producing any results); the most likely path in academia is therefore to do mediocre -to fairly good research that produces results and publications. When one compromises in to doing work that's less difficult than one can be doing because it's what's necessary career wise, it's not surprising that one's mental alacrity declines. There are certainly exceptional people that can do one kind of thing for work (or tenure), and at the same time publish significant work in a parallel field - but I think it's rare.

sdenton4 12y ago
Once you get enough of an institution built up around you - grad students to bootstrap, grants to write, what have you - there's so much less time to just work on the problems that interest you. I think there's less and less space in Academia for the 'individual contributor.'