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.
Join #steemSTEM
#steemSTEM is a community project with the goal to promote and support Science, Technology, Engineering and Mathematics related content and activities on the STEEM blockchain. If you wish to support the #steemSTEM project you can: Contribute STEM content using the #steemstem tag | Support steemstem authors | Join our curation trail | Join our Discord community | Delegate SP to steemstem
Convenient Delegation Links:
Reminds me of the story about the former unproven theorem of Fermat. Andrew Wiles used a really big proof with deep math. But maybe Fermat had an easy way to proof it.
I just red the paper. It seems like we need some function theory to understand it properly 😏. I think the this Todd function is more something like a class. He even mentioned some Gödel stuff 😱.
Posted using Partiko iOS
See the @anevolvedmoney. Not sure why it wasn't put as a reply to your comment. HF20? D:
Oooh I remember seeing this article pop up and was like yeah.... gonna just wait and see on this one. This was an obsession of one of my old math classmates. He would dream about solving the Riemann Hypothesis but waking up right before the secret was revealed. Tragic eh.
When I go to bed after spending to whole day "solving" a math problem I usually wake up the next day with the knowledge of where I made a mistake in my proof
So, either a field medal or an interesting failure. I don't have the time to go deep into this, and probably the level of math is way above me, but feel free to follow up the story. For some reasons, I thought the Todd function was related to toads... but was wrong (thanks to @dexterdev's document, now I know better: no tadpoles here ;)
It would be a tad strange if tadpoles were involved :P
Tadpoles are usual stuff when loop corrections in quantum field theory are what we talk about. Therefore, I clearly made a too hasty mental-connection :D
In a way, Atiyah's proof is quite opposite to what Andrew Wiles did with Fermat's last theorem. Andrew Wiles first proved Taniyama–Shimura conjecture which led to the proof of Fermat's last theorem but Atiyah tried to prove Reimann hypothesis without saying much about Todd function.
LOL
oh voted for this without realizing that my VP is now at 20% due to HF20 D:
This post has been voted on by the steemstem curation team and voting trail.
There is more to SteemSTEM than just writing posts, check here for some more tips on being a community member. You can also join our discord here to get to know the rest of the community!
Hi @mathowl!
Your UA account score is currently 3.223 which ranks you at #8027 across all Steem accounts.
Your rank has not changed in the last three days.Your post was upvoted by @steem-ua, new Steem dApp, using UserAuthority for algorithmic post curation!
In our last Algorithmic Curation Round, consisting of 726 contributions, your post is ranked at #113.
Evaluation of your UA score:
Feel free to join our @steem-ua Discord server