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keithisco

Non - human mathematics....

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Intriguing... and very fascinating.

If no human can check a proof of a theorem, does it really count as mathematics? That's the intriguing question raised by the latest computer-assisted proof. It is as large as the entire content of Wikipedia, making it unlikely that will ever be checked by a human being.

Read more, courtesy of New Scientist: http://www.newscientist.com/article/dn25068?cmpid=NLC%7CNSNS%7C2014-0220-GLOBAL&utm_medium=NLC&utm_source=NSNS.UwZID2J5PeI

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There's six sections of life, each section containing two opposite ends. 1st section is indentity, second is substance, third is learning, fourth is acceptance, fifth is reliance, sixth I dont have a word for yet. But the third, learning, mathemathicians use only the one end of the two opposites in the learning axis, the end of spesific learning, where we focus on details and what we can confirm. The other end where we handle wholes, big pictures and things we often can't confirm, needs to be used and suitable methods of studying developed to utilise this end of our learning spectrum.

In short, mathemathics will become more reliant on insight and intuition in future.

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My take on this is that humans will become incapable of handling the Big Maths, and therefore any true mathematical proof lie outside of the realm of Human comprehension. In effect we are becoming, very quickly, the slaves of our own inventions (ie computers), and that the big proofs (mathematically) will never be truly understood by this particular iteration of hominids.

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I agree completely. It's a gradual decline. For instance, I'm taking calculus now and some of the problems will say us a computer algebra system to do this problem. The same problem from a 1960's text is done by hand. Even from that point something is being lost.

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What you have to understand in mathematics is that you often have to make an assumption, or for lack of a better term, a leap of faith to go to the next level. Computers can't do that, humans can and do all the time. We have the ability to see beyond the provable and take the step. This is what separates us from machines.

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What happens when computers design better computers than themselves using the math we humans cannot understand?

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The map is not the territory.

Math, like science, is a human reaction to the cosmos, but only describes those parts of the cosmos that math and science can describe.

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