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I think a big problem is that he is not doing enough legwork to get out and talk about his ideas. Researchers should not publish major papers without doing a 'r
by shas3 11y ago
I think a big problem is that he is not doing enough legwork to get out and talk about his ideas. Researchers should not publish major papers without doing a 'roadshow', especially when it is so dense with new ideas as Mochizuki's abc-conjecture papers. Accounts of proofs and discoveries always have a climax where the author delivers a lecture announcing the discovery. Like Wiles announcing a proof (later shown to be flawed) of Fermat's last theorem at a lecture in Cambridge's Isaac Newton Institute for Mathematical Sciences in 1993. It is immensely helpful to talk through the proof in person facing an audience of experts.
- Mithaldu 11y agoI don't understand. He has already spent 10+ years of the time of his life putting it together, has given it to the world freely, on his own and made no demands whatsoever. Are you possibly arguing that he has any obligation at all to do anything more? If so, on what basis?
- Rangi42 11y agoHe's not obligated to do anything, but it's not surprising that other mathematicians are not too eager to retrace his steps to figure out if the proof is correct, given its length and unique notation.
- Mithaldu 11y agoOp clearly said "Researchers should not", so i am curious to hear on what base they make that claim.
- jordigh 11y agoThe sad reality is that without a good presentation, genius will take a long time to be discovered, if indeed it is genius. There are many examples, but doubtlessly the most dramatic ones are Ramanujan and Galois. Ramanujan had no training and at first glance his work looked indistinguishable from the flood of crank mathematics that most professional mathematicians are familiar with. Were it not for Hardy's work in giving form to Ramanujan's ideas, they may have been lost forever. In Galois's case, he was terrible at explaining his ideas, brilliant as they were. The anecdote of him throwing the eraser at his examiners is an example of his frustrations in trying to communicate to others. He himself was aware of his bad presentation, as he even called his work "gâchis" (mess). Even now, with the hindsight of knowing what he's talking about, it's extremely hard to read his original papers. For example, he doesn't write down formulas and he doesn't fix notation. He just describes them in very ambiguous terms, talking about "this" or "that" where it's difficult to always determine what "this" or "that" refers to. This is why it took over 30 years after his death for Liouville to notice that Galois was a genius.
- unexistance 11y agoit seems that Ivan Fesenko can be the Hardy to Shinichi Mochizuki, or that's how I read it anyway...
- LunaSea 11y ago"gâchis" doesn't mean mess but waste.
- jordigh 11y agoDefinition 3: https://fr.wiktionary.org/wiki/g%C3%A2chis#Nom_commun https://fr.wiktionary.org/wiki/g%C3%A2chis#Nom_commun
- simonbyrne 11y agoExplaining your work is part of the job (as it is for any academic discipline, or indeed most professional occupations).
- impendia 11y agoAny obligation, no. But the consensus among the mathematical community is that Mochizuki probably doesn't have a proof, that his work likely has some fundamental error, that it is probably (but not certainly) not worth taking all that seriously. If Mochizuki doesn't mind this, then that's fine. But if he wants the respect that he claims to deserve, then the 'roadshow' can't be omitted.
- asgard1024 11y ago> the consensus among the mathematical community is that Mochizuki probably doesn't have a proof If that's the consensus (and I don't think it is, it's probably what mathematicians under influence of cognitive dissonance think the consensus is), then it is sadly not based on empirical evidence, which is that 4 other people studied the proof and certified it.
- leeoniya 11y agoit is not a proof until you have convinced at least one other [qualified] person. related rant [1] [1] http://mathbabe.org/2012/11/14/the-abc-conjecture-has-not-been-proved/ http://mathbabe.org/2012/11/14/the-abc-conjecture-has-not-be...
- jsprogrammer 11y agoA proof only requires a valid transformation from axioms to conclusion. No person required.
- leeoniya 11y agountil an automated theorem prover can be made to certify these transformations as valid, a person has to do this work manually. this is particularly true in this specific instance since an enormous, alien framework has been erected to set up what defines a valid transformation within it. on point [1], though i suppose mathematical proofs don't quite align with this characterization. [1] https://www.quora.com/Is-it-possible-to-have-a-world-without-an-observer https://www.quora.com/Is-it-possible-to-have-a-world-without...
- eru 11y agoDepends on your notion of proof. That is one notion. There's the human version, that the other commentors talk about. There's also https://en.wikipedia.org/wiki/Interactive_proof_system https://en.wikipedia.org/wiki/Interactive_proof_system for an interesting formal version that is not `transforming axioms'.
- jsprogrammer 11y agoIn this case, the proof should be formal since it is a statement about the natural numbers. (as far as I can tell)
- eru 11y agoDoesn't really matter too much what the proof is about, does it? You can still choose different notions of proof.
- tikhonj 11y agoIt's only an obligation to the extent that he wants anyone else to appreciate the work. Don't read it as "he should do X" but as "he should do X if he wants others to read his proof". Whether he does or not is a different question. I think it's likely that he does, but perhaps he's content knowing that he devised a proof himself. And, for what it's worth, communicating results and impact are both usually part of a researchers job description. That might not matter so much thanks to tenure, but it's still there in spirit.
- draven 11y agoTo use a software project analogy, it's the difference between working in isolation and dumping a source tarball on a personal website, and creating an nice introductory website, putting the source on github and accepting comments/pull-requests. One has more chances to get used and studied than the other. At least that's how I understood it.
- shas3 11y agoThat is akin to asking, did he owe to it to us to write up his proof rather than lock up reams of papers in his cabinet? As others have elaborated, academics owe it to the community to not just spend their time 'working', but communicating. In fact, where does 'working' end and communicating begin? At writing it up on reams of paper? Typing it up and posting it to Arxiv? Going through peer review? Lecturing about your work and convincing people? It is arbitrary to draw a line at 'posting it to Arxiv'. 'working' only ends when your results are effectively communicated to the community. It is an incomplete project till then. The whole objective of research is to advance the field for the community, not just in one's own head!
- PepeGomez 11y agoThe thing is that his work is basically worthless unless he communicates it to others.