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Ten Signs a Claimed Mathematical Breakthrough is Wrong
- mahmud 13y agoSite is overloaded, so here is the Coral cache: http://www.scottaaronson.com.nyud.net/blog/?p=304 http://www.scottaaronson.com.nyud.net/blog/?p=304 See also the famous Crackpot Index: http://math.ucr.edu/home/baez/crackpot.html http://math.ucr.edu/home/baez/crackpot.html
- wolfganglechner 13y agoMost of the points require reading the whole paper first, isn't it?
- jckt 13y agoSkimming, sure. But really reading the paper, ie confirming its soundedness, requires going through most if not all the ideas and steps presented. Depending on the paper it can take weeks or even months. The ten tests in the OP take at most a few hours, I think.
- mathattack 13y agoLightly reading a paper and working to understand it are two different things, especially for a potentially groundbreaking work.
- jfarmer 13y agoNo, not really. One thing that makes an expert an expert is their ability to filter signal from noise. Sometimes they can prematurely bucket ideas into relevant/not-relevant, but usually not. Have you ever seen a novice programmer trying to find information on a StackOverflow page? The answer might be staring them in the face, but they still scroll past it once, twice, three times, etc. until I point it out. A novice has no sense of what's important and what's not so they tend to think everything is whereas an expert has a set of heuristics (like the ones in this blog) which make them much faster. They'll look for familiar ideas, themes, likely mistakes, etc. first before going into full-on, read-this-thing-line-by-line mode.
- Havoc 13y ago>One thing that makes an expert an expert is their ability to filter signal from noise. Certainly, but will you be able to spot the breakthrough insight if all your doing is filtering it against your notion of signal vs noise. Breakthroughs tend to come at a problem from a totally different angle & generally it takes a bit of time to understand why its brilliant rather than "noise".
- jfarmer 13y agoLike I said, "Sometimes they can prematurely bucket ideas into relevant/not-relevant, but usually not." I wrote that hoping to preempt your exact response. Alas! ;) Even if I grant your premise (which I don't), just because a breakthrough is likely to be written in crazy-talk doesn't mean something written in crazy-talk is likely to be a breakthrough. At that point it becomes a question of opportunity cost, which is exactly where heuristics come in. In fact, what you said could be true and it could still be true that P(breakthrough | does not seem crazy) > P(breakthrough | seems crazy) So, if I were on the hunt for breakthroughs I'd still be better off ignoring the crazy-seeming things. Regarding your premise, can you name, say, ten mathematical breakthroughs since the Enlightenment that came about the way you described?
- Havoc 13y agoPretty sure we're talking past each other, but I'll give it a shot anyway. >Even if I grant your premise (which I don't), just because a breakthrough is likely to be written in crazy-talk Who said anything about "crazy talk"?. My point is simply that your signal/noise filter is by necessity driven by information derived from the status quo. The status quo part being a really big problem if you're hunting for something new.
- Patient0 13y agoThis is from 2008. Could you add (2008) to the title?
- deleted 13y ago[deleted]
- acangiano 13y agoOne of the 'fun' aspects of running a math blog is that you get to see Word documents containing "proofs" of unresolved problems or the existence of God or Allah. A true glimpse into madness.
- cruise02 13y agoI made the mistake of writing a short series of blog posts about unsolved math problems a few years ago. It seemed innocent enough at the time, but I still get "proofs" submitted today. I'm a programmer, not a mathematician, so in a lot of cases I don't even know enough to be able to tell people why they're wrong (other than the fact that they submitted their proof of Goldbach's conjecture to a programming blog).
- buo 13y agoHere's part of the saga of the blogger who got into a similar situation when he explained that 0.999... is equal to 1: http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html http://polymathematics.typepad.com/polymath/2006/06/no_im_so...
- cruise02 13y ago> note: this post has been closed to comments; comments about it on other pages will be deleted! That's not a good sign. :)
- EvanKelly 13y agoThat was a great read. It reminds me of the Monty Hall problem fiasco that arose from the "Ask Marilyn" column about it. I appreciate the author of Polymath actually refuting all of the arguments against his post (to a reasonable degree). Coding Horror describes it here: http://www.codinghorror.com/blog/2009/06/monty-hall-monty-fall-monty-crawl.html http://www.codinghorror.com/blog/2009/06/monty-hall-monty-fa...
- lmm 13y ago
- amirhirsch 13y agoWhen I finally prove the Riemann Hypothesis it will be presented in HTML5 and Javascript with interactive graphs.
- mikevm 13y agoMake sure to include a tl;dr, 'cause ain't nobody got time for that.
- amirhirsch 13y agoi may have come up with a truly clever proof but it won't fit in an HN comment. my homepage amirhirsch.com is an interactive graph of the zeta function (and partial sums) along a horizontal slice with spacings of .05 between 0<Re(s)<1
- derleth 13y ago> Make sure to include a tl;dr You mean the Abstract?
- epochwolf 13y agoYes but label it "TL;DR" instead of "Abstract"
- cruise02 13y agoBrowsers will still support HTML5 and JavaScript when you finally get around to proving RH? Optimistic! ;)
- tjr 13y agoI wonder if there is a context in which preparing a document in TeX would be a strong indicator that you don't know what you're talking about?
- solarmist 13y agoMaybe history. Or another of the humanities. :) But TeX takes time to learn to use properly and only people that expect to use it regularly go through the trouble I'd expect.
- seanmcdirmid 13y agoA conference on Microsoft Office?
- lanaius 13y agoI probably wouldn't make a scrapbook with it.
- Sniffnoy 13y agoNote also signs 11 and 12 in the comments[1], and the later "Eight Signs A Claimed P≠NP Proof Is Wrong"[2]. (OK, so there's a bunch of overlap.) [1] http://www.scottaaronson.com/blog/?p=304#comment-8957 http://www.scottaaronson.com/blog/?p=304#comment-8957 [2] http://www.scottaaronson.com/blog/?p=458 http://www.scottaaronson.com/blog/?p=458
- thejteam 13y agoI probably disagree on the Tex one. I know several people with PhDs in engineering and science disciplines who have never used Tex. Several of them know enough math to at least make a reasonable stab at a few of the problems, even if they are unlikely to be successful.
- jff 13y agoSo what you're saying is that these non-TeX users are unlikely to successfully solve P=NP? I'd say that sort of upholds his premise.
- GhotiFish 13y agoIt would be reasonable to say users, in general, are unlikely to prove P = NP. So I'd say it doesn't affect the premise at all. :)
- seanmcdirmid 13y agoThe SIGHCI/CHI community is noted for using Word more often than not. It is ironic for a field that is supposedly well connected to design to have such horrible looking papers on average.
- sillysaurus 13y agoAre mathematicians going to be using TeX in a hundred years? Two hundred? Five hundred? Two thousand? Math is timeless. TeX may be, but it's too soon to say. It's a recent invention. It's only been around for 35 years.
- cschmidt 13y agoIt wouldn't surprise me if they still use it in a hundred years. It just fits thinking in math. By then TeX will be on version number 3.1415926535897932384626433832795028841971693993751 :-).
- adamgravitis 13y agoIIRC, it's supposed to be set exactly equal to pi upon Knuth's death.
- Zuider 13y agoAnd Emacs (with AUCTeX ) will have reached version 2.7182818284590452353603...
- kyzyl 13y agoPerhaps you're correct, but I would say this article is the author explaining his criteria, and asserting that it might be useful for some other people, on both sides of the line. Given that, I suspect that in one, two, five hundred years neither he nor his blog will be around. Nor anybody who read his blog. Even if his text had survived (perhaps someone goes digging though the NSA archives in a few hundred years), I'm sure that the person reading it will just intelligently substitute in the succeeding technology. So, what I'm trying to say is that the point about TeX is just a point of practicality. It happens to be approximately true right now, and the author has no information to guide him to an alternate conclusion.
- reeses 13y agoTeX is evolving with LuaTeX appearing to get some momentum. Given that almost no one uses TeX directly, I'd expect the biggest change would involve a gradual "improvement" in the macro library. It may even result in an embedded TeX à la sweave. Wolfram is hammering against the interactive element with CDF and I could see TeX being extended to support a more dynamic electronic document format if HTML rendering engines continue to be typographic messes. Perhaps an LLVM-type backend to generate executable ebooks would be an interesting project, but I'm not sure I'd start with TeX except for math markup. I would hope my prediction of the death of TikZ and PGF would come true soon enough, though.
- archagon 13y agoI enjoyed the author's Beijing/Chinatown metaphor in point 10.