Yesterday there was a lot excitement in math-land. Prof. Atiyah claims to have a proof for the Riemann hypothesis which is the last famous unproven conjecture of the 20th century. Furthermore, he claims that the proof is simple!
The Riemann hypothesis
Very briefly put, the Riemann hypothesis concerns a very special type of mathematical function which connects different mathematical fields. Here function just means that you put a number in and then a number comes out. It hypothesizes that the output of this special function function is zero for very specific input values.
The proof
Yesterday Prof. Atiyah gave a short talk on the history, the statement and his proof of the Riemann hypothesis. Here is the video
A short document explaining the idea of the proof can be found here -> https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view (many thanks to @dexterdev) The proof is remarkably short for such a complicated problem. Hence, I am highly sceptic about its correctness.
I haven't read all the details but on first glance there are no mistakes in the general idea of the short paper. I think there are problems with the underlying technicalities. The proof of Atiyah relies on the existence of a so-called Todd function. This Todd function satisfies somewhat strange/exotic properties which allows you to prove the Rieman hypothesis in an easy way. What I am concerned with is if this Todd function exists and if the conditions for application of the Todd function are satisfied. However, this requires reading lengthy work by Prof. Atiyah. So in a sense the difficulty lies beyond the short paper of Prof. Atiyah. Hence, it is not really a simple proof.
That is all for now might post some more when some of the big guys in mathematics review Prof. Atiyah's work on the Todd function.
Thanks
Many thanks to @anevolvedmoneky @dexterdev for suggesting me to write about it and forwarding material.
Merchandise :D
There is a MathOwl shop which sells my artsy fartsy stuff. If you got some spare money head over there. I have really cheap stuff available like these stickers They are an absolute hoot.
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