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The End of Mathematical Proofs by Humans?
vivin writes "I recall how I did a bunch of Mathematical Proofs when I was in high school. In fact, proofs were an important part of Math according to the CBSE curriculum in Indian Schools. We were taught how to analyze complex problems and then break them down into simple (atomic) steps. It is similar to the derivation of a Physics formula. Proofs form a significant part of what Mathematicians do. However, according to this article from the Economist, it seems that the use of computers to generate proofs is causing mathematicians to 're-examine the foundations of their discipline.' However, critics of computer-aided proofs say that the proofs are hard to verify due to the large number of steps and hence, may be inherently flawed. Defenders of the same point out that there are non computer-aided proofs that are also rather large and unverifiable, like the Classification of Simple Finite Groups. Computer-aided proofs have been instrumental in solving some vexing problems like the Four Color Theorem."
And how exacty is a computer going to prove this basic fact to you? Also if you have to ask somthing like this you are either dumb or have missed the 1st grade. Too bad for you in both cases. Oh yeah and 2+2=4 and that IS proven. There are some basic assumptions that people make and some statements are assumed to be true because there is no proof or disproof but this is not one of them.
Why can't I say, "!= is an equivalence relation which is, by definition, reflexive, and therefore 1!=1"? Because, conventionally, that's not what the != symbol is "defined" as, is it? So is convention a "proof"?
Or did you consider that I wasn't asking about the conventional use of the "=" symbol?