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Two additional notes: 1. Zhang posted an attempt at solving this problem in 2007 that he later more or less admitted was flawed: https://mathoverflow.net/quest
by gavagai691 4y ago
Two additional notes:
1. Zhang posted an attempt at solving this problem in 2007 that he later more or less admitted was flawed: https://mathoverflow.net/questions/131221/yitang-zhangs-2007-preprint-on-landau-siegel-zeros?rq=1 https://mathoverflow.net/questions/131221/yitang-zhangs-2007.... But speaking with mathematicians who are intimately familiar with Zhang's previous work, there seems to be good reason to be optimistic nevertheless. First, the idea behind Zhang's proof is similar to the zero-repulsion ideas appearing in known results about Siegel zeros, and is thus reasonable. Second, Zhang seems to have matured late, and unlike the flawed 2007 paper, his 2013 paper on bounded gaps in primes is meticulously written. He came a long way between those two papers, and he may have come even further since then.
2. Zhang is 67 years old. If the paper is correct, then Zhang constitutes a strong counterexample to G.H. Hardy's famous claims that "mathematics is a young man's game" and nobody alive today could say, as Hardy did, that "I do not know an instance of a major mathematical advance initiated by a man past fifty."
- markus_zhang 4y agoI think Zhang's previous result was good enough to rebuff Hardy's claims. Actually I think Math is more or less a young people's game is because whence someone be super successful and famous it's kinda difficult psychological to retain the previous mental state and push out similar results.
- gavagai691 4y ago"I think Zhang's previous result was good enough to rebuff Hardy's claims." I agree.
- ConcernedCoder 4y agoage is just a number, some people may have a prejudice against larger numbers, and that to me, seems irrational
- deleted 4y ago[deleted]
- salty_biscuits 4y agoPlenty of counterexamples to the claim https://mathoverflow.net/questions/25630/major-mathematical-advances-past-age-fifty https://mathoverflow.net/questions/25630/major-mathematical-...
- gavagai691 4y agoMore counterexamples here too: https://old.reddit.com/r/math/comments/xw8i9w/oldest_person_to_publish_in_annals_top_5_journal/ https://old.reddit.com/r/math/comments/xw8i9w/oldest_person_....
- markus_zhang 4y agoJust curious how many examples that show FIRST major discovery after say 40? I think I spotted a few.
- astrange 4y agoThis was an interesting one - a proof by a 67 year old retiree that nobody in the field knew about for 2-3 years after because they didn't read their email. https://www.quantamagazine.org/20170328-statistician-proves-gaussian-correlation-inequality/ https://www.quantamagazine.org/20170328-statistician-proves-...
- warbler73 4y agoMarjorie Rice. Housewife. https://www.quantamagazine.org/marjorie-rices-secret-pentagons-20170711/ https://www.quantamagazine.org/marjorie-rices-secret-pentago... Her discoveries first mentioned in a 1988 magazine when she was 65.
- wikfwikf 4y agoThe discovery of these pentomino tilings is an interesting achievement and evidence of an exceptional mind, but it's very far from a major advance in mathematics.
- gradschoolfail 4y agoMight come off as political, but Americans need need to throw off the yoke of British intellectual affectations, especially pre WWI ones.
- mangamadaiyan 4y agoI think you're conflating Hardy's thoughts as a mathematician, with the politics of his country of origin. The two, as far as I know, weren't really connected
- jjgreen 4y agoHuh? Could you expand on this? Disclosure: a Brit who does not see Americans oppressed by compatriot affectations.
- vitiral 4y agoThe structure of the modern education system is what Brittain designed to run an effective empire before any communication system existed. Every student made to operate independently as an arm of the British empire with standardized knowledge and skills, like cogs in an enormous beautiful machine.
- foobarian 4y agoHardy may have a point, on average. And it’s probably because of the responsibilities factor, i.e. older people have kids, families, departments to run, etc that takes them out of the game. If I did math with this level of intensity I would not have time for both without a partner willing to make quite some sacrifices.
- astrange 4y agoI remember from articles about his earlier primes work that his wife lived in San Jose i.e. on the other side of the country from him. They didn't really go into it but neither of them seemed upset by this. That house price appreciation must just be that good. (Also, it was reported he "worked at a Subway" but IIRC he was actually the accountant for a friend's Subway franchise.)
- m_nyongesa 4y agoHe did work behind the counter sometimes. Source: https://yewtu.be/watch?v=88Q2v6FTSBI https://yewtu.be/watch?v=88Q2v6FTSBI 49:03 - 49:56
- forkLding 4y agoIt should be noted that Zhang was a math prodigy when he was young, around 13 years old, however because of the Cultural Revolution in China, school education was stopped for a decade and his parents were purged and he was sent down to the countryside so he could not study at school but was forced to work in the fields and factories as re-education. It was only a decade later that he managed to get into university because universities re-opened after the Cultural Revolution, by then he was 23 already when he started his bachelors' degree. Note that, universities could accept people who did not attend school if they passed their university entry exams because so many people were unable to attend schools because they were all closed and teachers purged during the Cultural Revolution. I would say he "matured" later mainly because he did not have the right opportunities because he could not go to high school and after his university graduation, had no good opportunities because many good professors were purged during the Cultural Revolution so he fled to the US for a better life. Source: https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty And I quote from the above source which is from a 2015 New Yorker interview with Zhang: 'I asked Zhang, “Are you very smart?” and he said, “Maybe, a little.” He was born in Shanghai in 1955. His mother was a secretary in a government office, and his father was a college professor...As a small boy, he began “trying to know everything in mathematics,” he said. “I became very thirsty for math.”...The [Cultural] revolution had closed the schools. He spent most of his time reading math books that he ordered from a bookstore for less than a dollar.' As well: '...when he was fifteen he was sent with his mother to the countryside...where they grew vegetables. His father was sent to a farm in another part of the country. If Zhang was seen reading books on the farm, he was told to stop...After a few years, he returned to Beijing, where he got a job in a factory making locks. He began studying to take the entrance exam for Peking University, China’s most respected school: “I spent several months to learn all the high-school physics and chemistry, and several to learn history. It was a little hurried.” He was admitted when he was twenty-three.'
- bigbacaloa 4y agoThe professional math world is full of smart but delusionally ambitious people who do things like focus all their energy on the Jacobian conjecture and the Riemann hypothesis. Most crash out never finishing their doctorates (because these problems are too hard and working on them does not provide what it takes to survive professionally). Zhang is an example of such a person. What is very unusual about him is not that he continued to work on such things anyway, rather that he eventually found some measure of success. What I infer from his story is that he is tremendously stubborn and genuinely oblivious to ordinary material feedback. Evidently he has some talent too, but that's not the unusual part of his story. Said another way - I've known quite a few people like him to a point - with the difference that none of the others ever produced good mathematics, much less solved a major problem.
- OisinMoran 4y agoIt's also worth noting that the average life expectancy has increased by roughly 20 years since G.H. Hardy first published that claim, so it would extra worrisome if we didn't have any counterexamples.
- lupire 4y agoIt's also unclear how much of Zhang's recent work is recent ideas, vs ideas he had decades ago but only were made presentable recently.
- WiSaGaN 4y agoTrue. I am wondering whether this trend would make Fields Medal (https://en.wikipedia.org/wiki/Fields_Medal https://en.wikipedia.org/wiki/Fields_Medal), the most prestigious award in mathematics, to change its requirement of that recipients must be of age 40 or less.
- impendia 4y agoThey didn't break the rule for Andrew Wiles after he proved Fermat's Last Theorem, which was arguably the most notorious unsolved problem in all of mathematics. So I expect them to stick to their rule.
- random3 4y agoThink Knuth and a few others are good exceptions to the rule.
- anonymous_i 4y agoI disagree with Math had to be learned when you are young. Intelligent people will end up learning something profound when they are young.If they find something else interesting enough at a later stage in their life, they apply some transformation learning. Leibniz did not start his training in Math until he was ~30 > Thus Leibniz went to Paris in 1672. Soon after arriving, he met Dutch physicist and mathematician Christiaan Huygens and realised that his own knowledge of mathematics and physics was patchy. With Huygens as his mentor, he began a program of self-study that soon pushed him to making major contributions to both subjects, including discovering his version of the differential and integral calculus.
- SkyMarshal 4y agoRegarding #2, I think Andrew Wiles already disproved that conjecture, solving Fermat at 41 or thereabouts, but Zhang is certainly another nail in its coffin.
- Jweb_Guru 4y agoThat rejoinder has not been true for a while now. Laszlo Babai's graph isomorphism work is another recent example.
- data_maan 4y agoRaoul Bott is another good example of someone switching from (electrical engineering I believe?) to math in his 40s.
- TrackerFF 4y agoI'd like to think that there's much more socioeconomic diversity among present day scientists, compared to those back in the day of Hardy. Not to mention that up until 1910s, life expectancy was under 50. Being able to work in academia as a tenured professor/researcher probably resulted in drastically different life expectancy, compared to being forced to do something else. I think it's safe to say that Zhang would been forced to live as a peasant, had he been born 120 years ago.
- naasking 4y ago> 2. Zhang is 67 years old. If the paper is correct, then Zhang constitutes a strong counterexample to G.H. Hardy's famous claims that "mathematics is a young man's game" and nobody alive today could say, as Hardy did, that "I do not know an instance of a major mathematical advance initiated by a man past I think the actual truth is more like, "big breakthroughs mainly happen early in one's career". Most mathematicians start their careers young, therefore they publish breakthroughs while young. Zhang started quite late so his innovations are later in his life, but still early in his career. And it makes sense, everyone has a slightly unique way of thinking, and long-standing problems will only yield to unique thinking. Eventually someone will come along that has just that right type of unique thought process that will find a hole to solve such a problem.