I minded how all examples were about men, yet this wasn't remarked, and how the author describes the original mistake in Wiles' proof as "were found" : brilliant people worked very hard to find the mistake, the system (sometimes?/most of the time?) works. 5/
-
Show this thread
-
There are other methods: we should encourage people, especially young ones, to publish complete proofs of incompletely proved stuff. This has happened in the past (I published a correction to someone's correction to someone's paper) we just need to make it easier. 6/
2 replies 1 retweet 42 likesShow this thread -
Yes, it is bad that "some people know" but we now have plenty of avenues to get out of this. MathOverflow is a good place to startm as are social media of every kind. Again, imperfect but improving. 7/
1 reply 0 retweets 20 likesShow this thread -
Finally, but should have been first "maths that isn't 100% correct is worthless" is an incredibly bad viewpoint. A lot of maths started on wobbly legs, and in fact it's a key part of how maths is the product of a community not individuals. 8/
1 reply 6 retweets 70 likesShow this thread -
There are people who are good at having ideas, people who are good atspotting mistakes, people who are good at fixing proofs, people who are good at writing up clearly. Sometime (rarely) they work together, and you get very good things from the beginning. 9/
3 replies 4 retweets 69 likesShow this thread -
More often they're not, and it takes years, or decades, and papers and people to go from the forst spark to a complete proof which is also readable. Because honestly, unreadable maths doesn't help much either. 10/
1 reply 0 retweets 31 likesShow this thread -
Am I against computer aided proofs? Of course not! I am happy to have a computer help me typeset my papers and check my computations, so I certainly will welcome when I can also get help in checking a proof. 11/
4 replies 0 retweets 27 likesShow this thread -
Replying to @BarbaraFantechi
Rota said that that a proof must provide more insight into the problem being studied, or give more ideas, and that computer aided proofs fail at doing so. What are your thoughts on this?
2 replies 0 retweets 0 likes -
Replying to @cynicaldevil_
If I'm stuck on my way to a result I really care about because there is ONE lemma I can't prove* I am really grateful for ANY proof, whether I can understand it or not. 1/ *This happens all the time.
3 replies 0 retweets 3 likes -
Replying to @BarbaraFantechi @cynicaldevil_
Also, sometimes I try to prove a theorem, and fail and fail. Then I think that maybe it's false, try to find a counterexample, and fail and fail. Then I forget about it. If I were sure the result is true, I wouldn't waste time with 2nd and would have more energy for 1st. /end
2 replies 0 retweets 1 like
Whenever I work on a mathematical problem, I work on both sides of the question because they reinforce each other... Sometimes you should say, “Well, if it’s not true, how would you go about proving that?” Going back and forth is an important part of proving a theorem. S Smale
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.