ABC's conjecture is really proven? Or is it a "complete disaster"?

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original title: ABC conjecture really proved? Or is it a "complete disaster"?

ABC a new proof of the conjecture Mochizuki may be published, the news that the mathematical community on this very difficult to discuss that warm up, there are some pessimistic opponents. University of Chicago professor Frank Calegari algebra theory on his blog wrote that, according to this paper's form at the moment, can not be called that, even if also published the famous Chinese mathematician Tao Zhexuan It doesn't help the situation.; < / strong> also expressed his doubts in the comments.

Frank Calegari/

Math001 rant Ranger /

Ent/ editor

five years ago, Cathy O Neil gives a very convincing argument, explain why (then just published a new moon) claim (Shang Qie) should not be regarded as a proof of the ABC conjecture. I don't do anything more about the social aspect of mathematics that is discussed in that post. Here I just want to report to you, now, what it is in the eyes of the professional mathematician.

The answer to the

is that is a complete disaster .

abc conjecture (part).

this article is not a new argument to the authenticity of the moon made any sense of epistemology assertions. An extreme example, if a new moon that the ancient Greek linear A carved in stone, and then thrown into the Mariana Trench, so there is no doubt that it is a question whether accurate without important things. Although the statement is extreme, the reality is not very different from that of my description.

, every time I hear an expert analyzing a new paper on a new moon, I find a disturbing resemblance: 's massive and ordinary facts, plus the generally unverified conclusions of mountains. 's defense of Mochizuki Shinichi is usually based on the following view: the output of mathematics of Groton Dick school follows a similar pattern, and facts prove that these outputs have become the cornerstone of modern mathematics. There is such an allusion:

I've heard such a story. One day, Grothendieck said, there are two ways to open the walnut shell. One way is to make a walnut shell with a nut pincer with a strong breath. Another way is to immerse it in a water tank with lots and lots of water, soak, bubble, bubble, and then it soaks itself. Grothendieck's mathematics belongs to the latter.

although this analogy can be said to be very accurate, but with a new moon and a Dick analogy is not good teng. Yes, Grothendieck restructured mathematics in a revolutionary way, "bottom-up" in 1960s. However, the idea of production from the French Institute of higher learning (IHES) has spread rapidly all over the world, and has arrived at the seminar class of Paris University, Princeton University, Moscow State University, Harvard University, Massachusetts Institute of Technology, Harvard University and some universities in Holland. In essence, the success of Dick's school in 1960s is not measured by the theorem of IHES output. Instead, the thought it generated completely changed the way of algebra geometry in everyone of this discipline (and related subjects).

Alexander Grothendieck, French mathematician of German descent. Image source: subhankar-biswas/DA

this is not an idiosyncrasies of a person, nor is it complaining that some people do not go out of the rules of the "system". Perelman more directly refused to academic tradition, simply just put his papers posted on arXiV, and then walk away ( added: Although Perelman never officially submitted papers, but he really held a long lecture tour, allowing him to accept the expert consultation he ). But the final result is that in mathematics, thought is a winner forever. People can read Perelman's papers, and he can perceive all his thoughts in . In five years, a large number of experts have supplemented the whole details which have been omitted in the original proof, and published them in succession) . Usually, if has breakthrough discoveries in mathematics field, when other mathematicians can use this new idea to prove other fields' theorem, this landmark event will cause academic achievement to explode . And the direction of these new results is largely out of the expectation of the original discoverer of the theory.

but it is obvious that it does not happen on the proof of the ABC's conjecture. This fact itself is one of the most convincing reasons for people to be suspicious.

Gregory Perelman, Russian mathematician. Image source: wikipedia

now this is this


From: ABC猜想真的被证明了?或者,这只是“一场彻底的灾难”?
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