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That’s not untrue. But it’s also a misstatement of mathematical history. Many leading mathematicians historically have been highly competitive — Gauss comes to
by vessenes 18d ago
That’s not untrue. But it’s also a misstatement of mathematical history. Many leading mathematicians historically have been highly competitive — Gauss comes to mind. Woe betide the lesser intellect that sent Gauss some ideas. The Newton Leibniz controversy was very serious business at the time in the UK and the continent. It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pythagoras circle.
Mathematics has always been highly competitive.
- enraged_camel 17d ago[flagged]
- usrnm 17d agoDo you have a real argument to make rather than just appealing to authority?
- enraged_camel 17d agoSo let me get this straight: you're saying that Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? And me pointing this out is merely an appeal to authority? Get outta here.
- magicalhippo 17d agoKnowing the math that was developed through history, and knowing how that math was developed and the circumstances around it are two fundamentally different things. Clearly Tao knows the former, but apriori that does not imply he knows the latter. Not saying he doesn't, just saying one does not imply the other. Even if you go back and read the original papers, you'll miss all that which happened beyond the page.
- lo_zamoyski 17d ago> Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? If Tao has a knowledge of the topic (which he does), then it isn't by virtue of being a mathematician per se, but by virtue of an interest in the history of mathematics (which he has). Knowledge of math is enormously helpful here, but it does not imply historical knowledge.
- nomel 17d agoSoldiers rarely know the history of war, and war historians are rarely soldiers.
- magicalist 17d ago> Soldiers rarely know the history of war, and war historians are rarely soldiers. I mean, besides the empty platitude that we have no reason to assume applies here, we can easily search and find Tao commenting on the history and philosophy of mathematics. This is a really weird subthread.
- nomel 17d agoIt's not at all empty. Specific expertise does not imply general knowledge, and shouldn't be assumed. "Commenting on" does not equal historian of mathematics aware of all the past politics and drama from 100 years ago. There's no reason to assume an expert in applied mathematics is also a historian, especially when their statements are somewhat in conflict with history. And, there's nothing wrong with that, if they have a knowledge gap in some boring past bickering when they're one of the best in the world at what they do, ffs.
- dev_dan_2 17d agoIt is a strong argument in this case though, because Terence Taos expertise is directly linked to his ability to not misstate the history of mathematics. Also note how the quote by Tao is in all likelyhood not meant as an absolute; rather than a statement of a trend - a handfull of counterexamples do I no way change anything about the truth value of Tao's quote. On the other heand; consider how absurd it would be if "... in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science ..." would indeed be a misstatement; which would imply that far more promising research directions were not shared with the broader community (i.e.: published). I wonder what different reading of that counterfactual there could be other than secret societies that kept their discoveries and research directions to themselves - which we just learned about (since we would otherwise not be refering to the secret societies and their supposed promising research directions). All pretty straightforward, I would say - both that "misstatement" is hopefully based an overly strict reading of Tao's quote, and that mentioning Tao's background as one of the fields leading practitioners is relevant as well. Again; to make sure: A few counterexamples achieves nothing here. It would need to reach a certain threshold of such counterexamples before we will have to write the history of mathematics; and before Tao actually made a misstatement here.
- contravariant 17d agoI mean mathematics has enough history that something can both have been false for centuries of mathematics research and true for centuries. Sometimes in different places simultaneously. Terrence Tao can do his job perfectly well without being aware of any mathematical history, though I consider it unlikely that he is. I'm not seeing the direct link you're talking about, in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts.
- dev_dan_2 17d ago> in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts. That is well-known I assumed and continue to assume. > I'm not seeing the direct link you're talking about You are stating that link yourself; indirectly: "though I consider it unlikely that he is [being unaware of any mathematical history]". Why is it unlikely, precisely? - Maybe because it is unlikely that he recieved the mathematical teaching that frequently does not contain history of mathematics (wild! I wonder which university you have in mind in particular) that you seem to be refering to? - Maybe because his writing is evidence that he is interested about, incorporates and refers to history of mathematics, refer for example to https://terrytao.wordpress.com/2008/01/04/pcm-article-generalised-solutions/ https://terrytao.wordpress.com/2008/01/04/pcm-article-genera... or https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/theres-more-to-... - Or maybe because he is quite the opposite of a person that never ventures outside of their own area; being blind for other fields, or ones own history; as evidence by being famously collaborative across different fields, having a popular blog where he writes about non-mathematical topics too and last; him being one of the main proponents of foundational topics such as formalization of mathematics; or the use of LLMs for mathematical research. Does all that really make it more likely to you that Tao is not aware of the existence of counterexamples like those the commenter above mentioned - more likely than the commenter simply having missed a nuance or taking something out of context? If so; I would be genuinely curious why - people work differently, and I am always happy to learn, or close gaps in my own understanding.
- epestr 17d agoAnd the other an appeal to tradition. There was only one Gauss to scoop and focusing on him misses the larger math culture which Terry might be aware of, where most trust others to not scoop. And if any mathematician's AI usage on a problem leads to scooping, the volume of agents involved gives them a huge advantage which could prompt mathematicians to not use LLMs. Though you can say Terry's claim is a slippery slope.
- deleted 17d ago[deleted]
- 1w2hagsFa 17d ago[flagged]
- 1w2hagsFa 17d ago[flagged]
- Jtariiiii 17d agoAlso Andrew Wiles working in secret for 7 years out of fear of someone scooping him.
- dev_dan_2 17d agoPartially; but also in order to be able to focus, as stated by himself in https://www.pbs.org/wgbh/nova/transcripts/2414proof.html https://www.pbs.org/wgbh/nova/transcripts/2414proof.html: "But I realized after a while that talking to people casually about Fermat was impossible, because it just generates too much interest, and you can't really focus yourself for years unless you have this kind of undivided concentration, which too many spectators would have destroyed." But yes; him reaping the benefits of himself having the idea first was part of it too; as far as I am aware. ----- Which is still something completely different than some anonymous organisation keeping mathematical research secret because it is better for hype reasons. One is competition between individuals or groups within a field; the other is boring and sometimes borderline nihilistic generating of mathematical knowledge as an marketing asset.
- techas 17d agoI've always found the story of A. Wiles sad and frustrating. He worked in secret for 7 years. He submitted a (incorrect) proof at year 4 or so. Reviewers found a problem, but he decided kept all secret for many years after. He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem... I found this behavior against healthy science practices and only driven by ego. Unfortunately, I find this too often at work (working in academia). Most probably I'm too naive...
- derangedHorse 17d agoWhile I can sympathize with this perspective, I don’t think it’s right to call it driven by “ego.” Sometimes one just wants to go at a problem without being second guessed on approaches or led astray with suggestions by others.
- The_Blade 17d ago
- henryfjordan 17d agoThe story of the cubic equations is another great example: https://en.wikipedia.org/wiki/Cubic_equation https://en.wikipedia.org/wiki/Cubic_equation Dudes straight up used to hoard solutions to equations and use them in math battles.
- connorboyle 17d agoMy computer contains the prime factorization of probably several dozen (if not more) large integers, and I refuse to share them with anyone! (Because they are my private RSA keys)
- mitxela 17d agoWhy are you still using RSA?
- catlifeonmars 17d agoWhere else are you going to keep your large primes?
- gpugreg 17d agoIt is easier to trust what you can understand.
- bohrbohra 17d agoWait what ? Does nobody use RSA anymore ?
- deleted 17d ago[deleted]
- pferde 17d agoYes, last night we all voted and decided to move to its successor RSB instead.
- SAI_Peregrinus 17d agoECC allows greater security for key exchange (because it is so cheap to generate keys we can have "ephemeral" exchanges and forward-secrecy). It isn't significantly better for signatures in most cases.
- mitxela 16d agoECC is much faster (like 1000x) and with much smaller keys (like 10x) that are just random numbers so generating them is also free.
- kzz102 17d agoThe mathematical community was very competitive in its early years, but in the last 70 to 100 years, it has been generally less competitive and very collegial. The community was in a good place, and progress has been very good. In a few cases when competitiveness was ramped up, it lead to bad behaviour and destructive fights. Few would like to return to those competitive years.
- JumpCrisscross 17d agoMaybe it’s a dynamic equilibrium? We will become competitive for a while, then run out of questions, which in turn rewards pockets of collaboration?
- kzz102 17d agoI think both the competitiveness and and lack of problems will mean fewer people will do mathematics. I think collaboration will always be there, but the community as a whole will be smaller and weaker.
- alansaber 17d agoThe overarching geopolitics have always taken precedent over the preferences of the mathematical community as far as I can tell
- embedding-shape 17d agoSame is true for any area/topic though. Countries at war stop playing friendly football games against each other, as a very basic example.
- easterncalculus 17d agoBetween people.
- magicalist 17d agoSurprised to see someone on HN arguing against open science. Seems like the opposite of the lessons we should learn from Newton and Gauss, actually, hoarding results for decades at the expense of progress. (the Pythagorean thing isn't really competition either, is ahistorical, and from what we actually do know it's again people hoarding results instead of sharing them). FWIW, your post comes off as a middlebrow dismissal, surface level and not actually engaging with the substance of the comment. It's also just wrong. You claim "it’s also a misstatement of mathematical history", but don't specify which part. That there's "centuries of traditions of open science"? But your examples are from centuries (and millennia) ago, and there was never any claim that these traditions are universal. But more fundamentally, competition doesn't mean you can't also have open science. And the very long, damaging events like the Leibniz/Newton feud are exactly what make many mathematicians work to maintain a spirit of collaboration and attribution even when they're competing on approaches.
- modemNoises 17d agoNothing in their comment reads to me as "arguing against" Reads like nothing but historical context
- magicalist 17d ago> Nothing in their comment reads to me as "arguing against" If competition is somehow the opposite of "centuries of traditions of open science", and "mathematics has always been highly competitive", then open science is neither sufficient or necessary for the future of mathematics. Their clear implication is that we don't need to worry about it, though, because it's always been that way. > Reads like nothing but historical context They literally accuse Tao of "a misstatement of mathematical history".
- neuroticnews25 17d ago>If competition is somehow the opposite of "centuries of traditions of open science", and "mathematics has always been highly competitive", then open science is neither sufficient or necessary for the future of mathematics For the future of past mathematics, it says nothing about the current future. Also, open science can be nonsufficient and unnecessary but still extremely beneficial and desirable. >Their clear implication is that we don't need to worry about it, though, because it's always been that way. Lets just ask him if that's what he meant, I bet no.
- itemize123 17d agothis is not untrue but it's a pendulum swinging back to ancient times man
- cozzyd 17d agoIt was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pythagoras circle perhaps a 2 sin 45?
- itissid 17d agoYeah but a highly productive last two decades of math research from https://en.wikipedia.org/wiki/Polymath_Project https://en.wikipedia.org/wiki/Polymath_Project has come from collaboration.
- segmondy 17d agoYou miss the point. Humans don't mind competing with others. I love competition, but I don't want to compete with you and your machine. I love to play chess, I don't care if you are grand master, whoop my ass. But not if you are going to pair up with stockfish. I don't even care if you are a newbie that started playing yesterday with an ELO rating of 900. If I wanted to play the damn computer I'll do it myself. Likewise, mathematicians will not mind sharing and competing with other fellows, but if another has a billion dollars worth of GPU and you don't? Then you best be carefully what you say.
- squidbeak 17d agoI agree with you and I'm nitpicking, but if you play a GM, you more than likely are playing Stockfish until your opponent's out of book.
- p1esk 17d agoCould you tell the difference between a grandmaster and stockfish if playing them online? If not, why would you care which one you are playing against?
- sh4zb0t 17d agobecause we value competence
- hananova 17d agoOf course you can. Stockfish plays very different compared to a human, and it never ever blunders or makes mistakes.
- p1esk 17d agoI’ve never played against a grandmaster, but I have a feeling that he/she would play very different compared to me and would never make mistakes I could notice. Though admittedly I’m not very good at chess.
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- 2b3a51 17d agoAndrew Wiles was also careful about communicating progress on his Fermat's Theorem proof during the years in his attic. So yes I take the point. I read the Mastodon thread as more about the 'flattening' and 'rawness' of the proofs these systems and their operators are producing. I mean what is the cultural significance of a lean proof that is half a million lines long or something? And what tools can be extracted for further work from such a construction? The late William Thurston wrote about the culture of mathematics in that sense.
- andrelaszlo 17d agohttps://news.ycombinator.com/item?id=49617391 https://news.ycombinator.com/item?id=49617391 Did you comment on the wrong thread? The original one makes more sense :)
- peri-cl 17d ago/meta Their comment got involuntarily migrated; it was originally a reply to a toplevel comment in the Navier-Stokes thread (before the dedicated Tao thread existed), https://news.ycombinator.com/item?id=49613262#49617249 https://news.ycombinator.com/item?id=49613262#49617249
- caycep 17d agoPersonal competition is one thing, but competition against a corporation?