The Riemann Hypothesis is one of the most important unsolved problems in mathematics, and even has a million-dollar prize attached.

Every year or so someone comes out with a new proof or disproof of the Hypothesis. Every one of these has either a.) contained a flaw located and pointed out, b.) been so outrageous it was pointedly ignored or c.) is still being checked but nobody makes much of it. Matthew Watkins has a webpage for keeping track of these. Some proofs are even made for humor (although sometimes the humor of mathematicians is on the middle-of-the-Sahara dry side).

In March of 2007 a mathematician in India named Tribikram Pati came out with a new disproof (so he thought the hypothesis was **false**). Unfortunately, like so many other papers of the same type, there was a flaw.

Even though it’s a simpler than many modern proofs, most of the proof is too much for high school students (sorry guys!) But here’s the end of Pati’s proof:

(For my students, and others who want to jog their memory of logarithm properties) Why is the last equation “obviously false”?

(In general) Does anyone have a copy of the debunking PDF? It looks like archive.org has one but I haven’t been able to get at it.

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David, on April 18, 2013 at 10:10 am said:What about Arne Bergstrom’s supposed proof at http://arxiv.org/abs/0809.5120? Has anyone checked it yet?

ShudhG, on December 4, 2014 at 7:16 pm said:The last line would imply that a number is less than itself!

David, on July 6, 2016 at 4:42 pm said:What are you talking about? State the page and the line to which you are referring, and explain your claim.