August 9th, 2018, 06:01 AM  #21  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 893  Quote:
 
August 9th, 2018, 02:22 PM  #22 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,609 Thanks: 550 Math Focus: Yet to find out.  if a tree falls down in a forest...
Last edited by skipjack; August 9th, 2018 at 06:18 PM. 
August 9th, 2018, 03:34 PM  #23  
Senior Member Joined: Aug 2012 Posts: 1,971 Thanks: 550  Quote:
A mathematical proof is whatever a preponderance of working professional mathematicians say it is. Case in point, Mochizuki's claimed proof of the abc conjecture. Briefly, a known genius mathematician has been working for a decade on his own area of research that nobody else understands. One day he drops 500 new pages in four related papers, and claims to have proved the abc conjecture, a famous and highly difficult conjecture in number theory. To give an example, if abc is true then Fermat's Last Theorem is a trivial consequence. This happened several years ago. Since then, nobody understands the proof. People have been working on it. People have been complaining that Mochizuki hasn't been forthcoming enough in explaining himself. Mochizuki expresses disappointment that everyone is so lazy and dim. This has been going on for years. A handful of specialists are slowly making progress understanding his ideas. Is this a proof or not? Moral of the story: Proof is a social construct. Something is proved when mathematicians say it is. There's no objective standard. For anyone who hasn't heard about this amazing (and ongoing) story, someone wrote up a very nice popular article about it in 2013. http://projectwordsworth.com/theparadoxoftheproof/ There are more technical summaries of the situation as it evolves that can be found via Google. Mochizuki, by the way, graduated from Princeton at age 16 and got his doctorate under one of the world's leading number theorists. That's why he's taken seriously and not labelled a crank. Again, social factors. Nobody can evaluate his math, not even specialists. Last edited by Maschke; August 9th, 2018 at 03:37 PM.  
August 10th, 2018, 12:17 AM  #24  
Senior Member Joined: Oct 2009 Posts: 436 Thanks: 147  Quote:
Let me clarify, a proof is a certain collection of statements, each of which are connected by inference rules. Any computer or human familiar with the limited set of axioms and inference rules, can verify whether a proof is correct. So in that sense, math is not subjective. Of course, nobody ever does it that way. People are merely content with showing that it can be done. And this is where the subjective elements come in, and where a majority opinion can agree a proof is correct, even though it is not correctly spelled out. But in principle, it can be done. If I ever publish a proof, and nobody agrees with me, I can always write it down in basic chunks of elementary statements and inference rules. I can then let a computer check it, and everybody will HAVE to agree. It will take a god awful long time though, but in principle it can be done. And it HAS been done before: Quote:
So if people disagree with zylo, or with the abcformula proof, they can always put in a formal proof and let the computer check it. Awful work, but it is a certain one to make sure everybody accepts you as correct. It's the only proofs in math that are not subjective, but objective. Also see, metamath: Home Page  Metamath  

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