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Will Our Understanding of Math Deteriorate Over Time?

blog.computationalcomplexity.org

71–73 of 73 posts

Re: Will Our Understanding of Math Deteriorate Over Time?

#71

Earlier quoted context omitted.

But sometimes the connection between "beautiful art project" and "practical tools" is totally unexpected. We often invest time in projects that seem simply like "beautiful art", and then much later stumble upon something practical. I think a great example of this is cryptography. The foundations of it come from number theory (prime numbers, modular arithmetic, elliptic curves), but the subject of number theory, befor…

That's a popular meme but its mostly false. See http://lesswrong.com/lw/4kt/the_value_of_theoretical_researc... The vast majority of "useless" mathematics really do turn out to be useless. In the rare exceptions, there's not much evidence that doing the work beforehand is actually an advantage. E.g. Einstein wasn't aware of most of the work on non-Euclidian geometry before developing relativity IIRC. Stuff like prime…

I think you are needlessly generalizing the personal argument of the LessWrong post to apply to general epistemology. As a person who is a utilitarian, you cannot fully justify studying pure math. However, at a societal level, you do need critical mass in terms of enough people working on math for practically useful insights to emerge. So 'don't do pure math' (or art, or music, or theoretical CS) is good as a personal goal for someone with utilitarian aspirations, but is inappropriate 'public policy'.

Consider this: a vast majority of mutations are useless, but for this reason, if there were no mutations at all, and mutations somehow willed themselves out of existence, then there would only be primitive lifeforms on earth.

Re: Will Our Understanding of Math Deteriorate Over Time?

#72
post #33

Ah, I remember a lecture course where we classified all groups of order up to 1000. Joy.... "Like having your brains smashed out by a slice of lemon wrapped around a large gold brick."

Not sure why the downvotes, it was an interesting course: a lot of tricks to show isomorphisms / reasons why certain groups couldn't exist. It just went up to order 1000, which was a lot of cases (30 lectures + exercises worth).

Re: Will Our Understanding of Math Deteriorate Over Time?

#73

Most people use math less and less (even your average cashier will have issues if the machine isn't working). Will Myron Aub give us the feeling of power back? http://downlode.org/Etext/power.html by Isaac Asimov on just this topic.

I am a cashier. Never use math. I doubt anyone outside academia and parts of industry ever uses math in its proper sense.

It may be that there are few industries that require it professionally, but just because one's profession doesn't require it doesn't mean that one can't, or doesn't, use it. Consider, for example, Fermat, Young, and legions of other, perhaps less well known, amateur mathematicians (for example, Garfield (http://en.wikipedia.org/wiki/Pythagorean_theorem#cite_ref-Ga...) and Napoleon (https://en.wikipedia.org/wiki/Napoleon%27s_theorem))!
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