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.