To Infinity and Beyond Category: 9 infinity and beyond

Ethan Haffenden
Thu, 16 Feb 2017 08:27 PM

This video focused mainly on Hilbert and his 23 problems that he believed needed to be solved by mathematics and the people who solved some of his problems. One of the more interesting men who solved the problem was Kurt Gödel, he attempted to proved Hilbert's 2nd problem, however, instead of finding what Hilbert believed was true he found the opposite, in any system of mathematics there are statements that are true yet you can't put it, to solve the problem he starts with the statement "This statement can't be proved" he could then change the problem to arithmetic to show the statement must either be true or false, if the statement is false that means that it could be proven which means that it is true by contradiction. I think that this idea is really interesting in the way that it proves any statement by contradiction, I think that it would be interesting to have a deeper look into how this works and how it can be used practically.

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