[HN Gopher] Major discoveries made by mathematicians past age 50...
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Major discoveries made by mathematicians past age 50 (2010)
Author : happy-go-lucky
Score : 84 points
Date : 2022-05-26 18:21 UTC (4 hours ago)
(HTM) web link (mathoverflow.net)
(TXT) w3m dump (mathoverflow.net)
| spekcular wrote:
| My experience in academia has taught me the following: Any
| slowdown in productivity among mathematicians as they age is more
| a result of increased administrative duties, childcare, or loss
| of interest than it is cognitive decline. The slowdown is real,
| but the commonly suggested reason (biological aging) is not quite
| right.
|
| You can look up cognitive decline studies and see that it really
| doesn't hit in full force until the 60s and 70s, with lots of
| heterogeneity. I've seen plenty of sharp 70-year-old academics
| doing great work (though I can't remember someone at 80 who I
| thought was still going full steam).
| RC_ITR wrote:
| There's also an argument to be made about bias - the younger
| you are the less you 'know,' which can lead to more
| experimentation and creative solutions to problems.
|
| There's also the 'hunger' argument that dovetails with yours -
| are younger people just more incented to 'prove' themselves?
| (since, as you imply, most older people realize a supportive
| family makes them happier than a well-regarded publication
| does)
|
| An interesting question to address is 'Is the status quo just
| fine? Will any solutions to this just make more academics die
| as virgins or can we actually improve the output of older
| academics?'
|
| (cue: a joke about Newton)
| whimsicalism wrote:
| I think it is way too common to look at studies of the median
| person and then generalize to older.
|
| Major discoveries are made by top, top people - it seems not
| unlikely that past a certain age most people cannot remain top.
| The same is true with chess, which does not have the same
| administrative duties problem.
| spekcular wrote:
| I think there are a lot of relevant dis-analogies between
| math and chess. A chess match at the professional level is a
| grueling, multi-hour contest, while math research is a lot
| more chill. Also, the time limit matters a lot in chess.
|
| Anyway, you can look at the pages of Annals of Math and
| Inventiones and see that there is a good mix of ages.
| hervature wrote:
| But I think the OP has a point that falling out of the top
| has nothing to do with cognitive ability. For instance, many
| researchers become known for certain contributions and then
| eventually expected to remain in that field. If the landscape
| changes (say neural networks become the hot topic) then your
| research might fall in prestige but the
| level/complexity/quality does not. There are things beyond
| their control to prevent quick pivots let alone large pivots.
| A biologist cannot start doing NLP stuff. Then there is the
| problem of your graduate students who are doing other things
| and so the momentum to switch is very real.
| whimsicalism wrote:
| Hm. If someone in their 20s is able to make a major
| discovery for a problem they only heard of when they were
| 18, that is maximum 12 years of that line of research,
| which could certainly be replicated by someone older.
|
| you also see people in their 20s make big contributions to
| many disparate fields, like Tao.
| [deleted]
| [deleted]
| JJMcJ wrote:
| Attributing "young man's game" to G. H. Hardy, he'd had a heart
| attack the year before he published _A Mathematician 's Apology_,
| and by all accounts, had lost much of his drive and energy.
|
| The whole book has something of a sad tone to it.
| davesque wrote:
| This really seems like a detail that should be emphasized. One
| famous man uttered a very quotable line that was more
| reflective of his mood at the time than of some universal
| truth. I don't get how the culture of science sometimes has
| this tendency to fetishize things like youth or pedigree. I
| guess it's the classic fallacy of confusing averages with
| maximums or of thinking that summary statistics preclude the
| possibility of individuals with unusual characteristics.
| SemanticStrengh wrote:
| the majority of the damages of a stroke are generally induced
| in the following weeks of the event, e.g. via extremely high
| oxidative stress and apoptotic signaling and impaired
| bioenergetics. Those issues are trivial to fix
| pharmacologically speaking and indeed there are countless
| studies showing a very potent protection against damage
| including neurons death, unfortunately doctors have not the
| required erudition nor do they care to save those lives and
| therefore people are left helpless and suffering.
| silicon2401 wrote:
| Do you have any sources on that? I'd love to have that info
| handy if it ever becomes useful (hopefully it doesn't).
| rendall wrote:
| Favoriting so I too can see the answer
| actually_a_dog wrote:
| I'm surprised Erdos was so far down the list. He very famously
| didn't die until he left[0].
|
| ---
|
| [0]: Erdos had a notoriously quirky way of expressing himself in
| ordinary conversation. To "die" in Erdos-speak is to quit doing
| mathematics, while to "leave" is to actually pass away.
| paulpauper wrote:
| You need a ton of focus to succeed overall, not just math. I
| think people tend to get distracted by things as they get older.
| lapcat wrote:
| > I think people tend to get distracted by things as they get
| older.
|
| What things?
| zahllos wrote:
| Didn't realize Heegner was in that list.
|
| To translate his result for people not familiar, unique
| factorization means that a number uniquely decomposes into
| primes. You almost certainly learned this happened in school for
| integers (Z), but it does not apply to all cases.
|
| Quadratic Numbers in Algebraic Number Theory terms are
| Q[sqrt(-d)], that is, a+b\sqrt(-d) where a and b are rational
| numbers. d=5 is the first number we can pick where unique
| factorization does not hold.
|
| In fact, the Stark-Heegner theorem tells us something even more
| powerful: if d is squarefree, the only imaginary quadratic fields
| containing unique factorization are when d=1, 2, 3, 7, 11, 19,
| 43, 67, and 163. Any other choice (or any choice containing a
| square of any prime, e.g. 4=2^2), and unique factorization will
| fail.
|
| I've left out what a prime, or indeed an irreducible, mean in
| this case, but what's astounding at least to me is that there are
| only 9 such numbers where it works, and this is provable. Heegner
| did that aged 50+.
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