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.
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.
Wherever there's a problem, there's solutions. Answers are found from a wide deep perspective, from opened mind's eyes. From where good and bad stay silent and you hear the real cause and effect, and big picture. Giving up is wasting your time, but also necessary to find the true cause you didn't find yet. Staying in the path is necessary only when there's trueness in that path.
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.
A stinky concoction of wet paper and too much reading
Posted 21 February 2014 - 04:00 AM
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.
The problem with people who have no vices is that generally you can be pretty sure they're going to have some pretty annoying virtues. Liz Taylor
Posted 23 February 2014 - 05:45 AM
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.