How I disproved Riemann Hypothesis

Some time ago I was reading about unsolved problems in mathematics and my attention was caught by Millennium Prize Problems article. It seems that for proof or disproof one of them (Riemann Hypothesis) they give 1000000 $. Well, I thought, should I use my many years' experience in math software, which I used to get my physics degrees in University? Let me try to make a million bucks quickly?

Hypothesis tells that Riemann Zeta Function equals to zero only when the real part of the complex argument is 0.5 (1/2), excluding so-called trivial zeroes, when argument equals -2, -4 etc.

After reading the arguments for and against the Riemann hypothesis I made a small program on professional mathematical software Wolfram Mathematica, which is running over different argument values. After 1 month of work of this program I found something, which is shown in the screenshot below:

So, if the real part of the argument of Riemann Zeta Function equals 0.989999999999999999 and imagine part is 1000000000072486.88, then the absolute value of this function is very small, namely 0.0000000377472, which is almost zero. What was to be demonstrated or Q.E.D :).

One can tell, bwahaha, 0.0000000377472 is not zero exactly! But if one can have a look at the screenshot above, then it is clear, that for first well known zero of Riemann Zeta Function, where the real part of the argument is 0.5 and imagine part is 14.134725, this program gives not really zero, but 0.0000000331023. So, within the acceptable error, everything is correct!

I will not send a letter to Clay Mathematics Institute with the million bucks claim in solidarity with another Russian mathematician Perelman :) (I am Russian by the way).

P.S. everyone can check it easily if pass a free registration on http://develop.wolframcloud.com and run the command:

Abs[Zeta[0.989999999999999999 + 1000000000072486.88*I]] // AccountingForm

04 August 2017 (04.08.2017)


2 comments:

  1. This is just not correct. It violates a proven bound on the roots

    https://en.wikipedia.org/wiki/Riemann_zeta_function#Zero-free_region

    And, a numerical approximation (what the heck is "acceptable error"?) is not a proof, at all. You haven't even calculated error bounds on the approximation you calculated.

    I'm sorry, but in Russian, I would say this is lazha.

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  2. I do not see any problems. Zero free region is real part of argument less than 0.9989250062303953 for imagine part t=1000000000072486.88. I have 0.989... which is less than 0.998

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