Tuesday, November 4, 2008

the problem of proof

[This little rant stems from some of my contemplations of the role of proof in the processes of mathematics education. A detailed scrutiny by a guy like Bertrand Russell would make the best proof look like a pile of unjustified assumptions, which seems to result in a damning sense of futility that nullifies all scientific pretensions. Except, of course, the scientific pretension that identifies and cogently discusses the futility. That one is probably still valid and worthwhile.]

If and when the Riemann Hypothesis is finally proven, there will likely be a dozen people on the planet who understand the proof, a few more who pretend, and an excited population who believes. Is this mathematical rigor? At the very frontiers of mathematics and logic itself, we as a society, as a scientific community, are persistently and ironically burdened with the yoke of deference to an authority. On the simpler end, things are just as bad. I have a respectable degree in mathematics, and I will not pretend to follow the proof by Russell and Whitehead that 1+1=2. If I copied down their stupefying sequence of symbols from 'Principia Mathematica', I would not consider that I had proven the momentous result that 1+1=2. Nor would I consider the Riemann Hypothesis proven to me if I was expected at some point to 'take the professor's word for it'. I suspect that an argument presented as a rigorous proof is only rigorous by its delivery and is only a proof by its reception. But of course, I couldn't prove it.

3 comments:

  1. I have to disagree with your assumption that only a hand full of people will be able to understand proof of the Riemann hypothesis. As a self taught mathematician I’ve written my proof in relatively simple layman’s terms, the only thing one might have troubles grasping within my simple equations is the fact that god was left out. (Which I might add was the key to finding the solution.)

    You can always take a look at my YouTube video or published works and decide for yourself. http://www.youtube.com/watch?v=jFJtp_ZZLp8
    If not then I guess you’ll hear about it when it’s mainstream.

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  2. I am not really assuming the handful of people, I said it was likely. It would naturally be far more satisfying to see an 'elementary' proof of the Riemann Hypothesis, but I chose it as an example of a highly valued proof that is not generally expected to be very simple. So far, none of the simple arguments over the past century and a half have panned out.

    You can choose a different difficult and esoteric and nonetheless celebrated result such as Fermat's last theorem, proven by Andrew Wiles but hinging on some ideas that are pretty inaccessible for most of the people who are interested in the result.

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  3. well my proof is very simple and does pan out because it connects physics with math and ive followed up by using the formula on literally thousands of numbers and it has only left indivisible primes. But I suppose it would be safe to say only a handfull will regard it as proof given the religious influence on earth today. as for the four color theorem I dont regard it as a proof at all. If a human cant understand it, nothing has been proven.

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