12 ms·
Major discoveries made by mathematicians past age 50 (2010)
- JJMcJ 4y agoAttributing "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.
- SemanticStrengh 4y agothe 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 4y agoDo you have any sources on that? I'd love to have that info handy if it ever becomes useful (hopefully it doesn't).
- davesque 4y agoThis 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.
- interroboink 4y agoThere's also the quote from Einstein: "A person who has not made his great contribution to science before the age of 30 will never do so." I rather dislike it, and am glad Einstein was wrong about various things (:
- JJMcJ 4y agoEinstein published General Relativity when he was 35, and after that he did important work but nothing quite as world shaking as the period 1905-15. So he may have been projecting his own disappointment into a general statement.
- 3a2d29 4y agoMakes all of us (since we will all be 30+ one day if not alright) happy to know that Einstein wasted a lot of time trying extremely hard to disprove quantum mechanics because "God doesn't play dice with the universe."
- JJMcJ 4y agoAlso Unified Field Theory, which has had very little substantive progress since his time.
- daniel-cussen 4y agoWell that's interesting. So what does that mean, has to have been published by 30, or just the successful experiment carried out before 30?
- trenchgun 4y agoYep.From replies: >This isn't exactly what you were asking for, but Littlewood himself, after overcoming depression at age 72, did good mathematics throughout his 80's--it's hardly a young man's game. (Littlewood is Hardy's pen name)
- JJMcJ 4y agoOf course that's not really true. The origin of the story is that so many papers were published by Hardy and Littlewood, that an Indian mathematician thought that Littlewood was a pseudonym that Hardy used for his inferior work. Littlewood was reported to be quite amused when he heard this. And of course the story might be apocryphal. Especially since it's also attributed to Edmund Landau and Norbert Wiener. https://en.wikipedia.org/wiki/John_Edensor_Littlewood https://en.wikipedia.org/wiki/John_Edensor_Littlewood
- JJMcJ 4y agoThat is, that either Landau or Wiener believed this, which seems very unlikely.
- actually_a_dog 4y agoI'm surprised Erdős was so far down the list. He very famously didn't die until he left[0]. --- [0]: Erdős had a notoriously quirky way of expressing himself in ordinary conversation. To "die" in Erdős-speak is to quit doing mathematics, while to "leave" is to actually pass away.
- spekcular 4y agoMy 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 4y agoThere'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)
- SiempreViernes 4y agoNot sure how Newtons later career that sees him going undercover to prowl seedy London bars to hunt coin forgers has anything to do with virginity?
- RC_ITR 4y agoHuh, the more you know. I was just making the tired 'Newton died a virgin joke' but thanks for the history of his life.
- whimsicalism 4y agoI 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.
- zahllos 4y agoDidn'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+.
- paulpauper 4y agoYou 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 4y ago> I think people tend to get distracted by things as they get older. What things?
- TexanFeller 4y agoChildren, paying the mortgage, and taking care of elderly family are among the number one things.
- lapcat 4y ago> Children Some people have no children. People who do have children have them at various ages, sometimes very young. Some people ignore their children. Children tend to leave home within 20 years or so, leaving an "empty nest". > paying the mortgage How is that different from paying rent? And how exactly does it "distract" you? My mortgage payment was automatically deducted from my bank account, I didn't even have to think about it. Not to mention, eventually you pay off your mortgage and don't have to pay anymore. > taking care of elderly family This can also happen at almost any age. Or never. What about the distraction of raging young hormones. The distraction of personal uncertainty about life and the future. The distraction of financial insecurity.
- bumby 4y ago>paying the mortgage I think a more apt description is "owning a home". Owning a home brings all kinds of complications beyond just paying a single bill. One of the major benefits of renting is that you effectively outsource all the maintenance headaches, for example.
- dragonwriter 4y ago
- wanderingmind 4y agoYiting Zhang as discussed in the comments of the MO thread, is one of the most important contemporary examples. He worked as a temporary lecturer and being aged 58 produced one of the finest works in number theory. He solved the long-standing problem infinitely re-occuring consecutive prime numbers (a weaker formulation of twin prime conjecture) [0]. This will be regarded as one of the most important breakthroughs of 21st century in mathematics. New Yorker had an in depth article about him[1] [0] https://annals.math.princeton.edu/2014/179-3/p07 https://annals.math.princeton.edu/2014/179-3/p07 [1] https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
- civilized 4y agoThere has never been more of a Real One than Yitang Zhang. He proved a theorem that had stumped the most eminent professors. While keeping books at a Subway.
- fuzzythinker 4y agoThank you for the newyorker article. It's the most beautiful thing I've read in a while.
- wodenokoto 4y agoI thought the first person I was Yitang Zhang. It’s the author of the piece talking about himself. The first paragraph was so confusing.
- Uptrenda 4y agoWhat do you all think about the role of genius in making discoveries in mathematics today? Are you screwed if you're not a genius? Or is working hard, good collaboration, and wide-reading all that is needed?
- sharikous 4y agoYou need to have a knack for math. This is necessary. Then you need hard work and good collaboration, also necessary . But if you have the latter without the former you risk to end up miserable
- Datenstrom 4y agoFor pure math you certainly need a knack for math, not so for Science in general though with notable cases like Faraday.
- SiempreViernes 4y agoI think a genius is a lucky person whose hard work is not very blatant and has got a good hype-man. If you're unlucky you work hard on a dead end, if people can see you work hard all the time your results are not effortless enough to be the work of a genius, and if you don't have a hype-man you'll at most be seen as very good.
- hamiltonians 4y agois this a trick question. of course u have to be a genius to make interesting, original research. it was that way 200 years, why would it be different now.
- hcta 4y agoAlmost every hard thing people have been doing for 200 years is easier now than it was 200 years ago.
- hamiltonians 4y ago
- k_sze 4y agoI believe an unmentioned counterside to the above question is: how old can you afford to start getting into mathematics in order to still be able to make great discoveries?
- flobosg 4y agoRelated: Late bloomers in several categories, including mathematics – https://en.wikipedia.org/wiki/Late_bloomer#Adults https://en.wikipedia.org/wiki/Late_bloomer#Adults
- nicklaf 4y agoI did not see this mentioned so far, so I'll suggest that perhaps older mathematicians are more inclined to offer statements of solvable problems to their students and colleagues rather than jumping in and trying to knock it out all by themselves. (And after all, simply setting up a problem in a form that points to a plausible solution is at least half the battle.) Surely by the time they reach 50, mathematicians will have the experience to know that mathematics is a collaborative field, and that working alone to get ahead is the less efficient tactic for proving theorems. Some of the most productive mathematicians seem to work with armies of graduate students, and even though an older mathematician may be at the height of their abilities, they will likely be even better at stating unsolved problems that just need more eyeballs.