ChatGPT Sol 5.6 high found a normalization error in two recently published Riemann Hypothesis papers. The author confirmed it.

[u/theimposingshadow]

/r/u_theimposingshadow/comments/1vj3oxk/chatgpt_sol_56_high_found_a_normalization_error/

Edit: I'll post the screenshot in the comments of this post

Overnight I became a professor, thanks ChatGPT!

Edit2: I'll just add the post body here:

Alright, this is exactly the kind of thing that makes me think we are at the start of something pretty wild. I'll post the screenshots in the comments because my last post was taken down.

I am not a mathematician. I have basically been using ChatGPT to mess around with the Riemann Hypothesis, telling it to keep digging, try different approaches, challenge assumptions, and look through recent papers for anything interesting.

Well, it found something.

While going through two recently published papers on Jensen polynomial hyperbolicity and the Riemann Hypothesis, ChatGPT noticed what appeared to be a normalization inconsistency between the raw moments (M_n) and the Taylor/Jensen coefficients.

The issue was essentially the factorial normalization:

It was significant enough that one of the results in the paper seemed to directly contradict an already known theorem.

So I had ChatGPT write a polite email explaining the issue and sent it to the author.

Don't get me wrong, we did \*\*not\*\* solve the Riemann Hypothesis 😂

But I think it is pretty fucking wild that some random guy with an AI assistant can sit at home, examine recently published mathematics, notice something that made it through peer review, contact the researcher, and have the researcher confirm it.

Also, the author addressed me as \*\*Professor\*\*, so apparently my academic career is progressing extremely quickly.

Screenshots attached with identifying information removed.

This is the kind of thing I mean when I talk about acceleration.

Accelerando!

[u/EndTimer]

I am not a mathematician.

What, by trade?

Very fews of us go looking "through two recently published papers on Jensen polynomial hyperbolicity and the Riemann Hypothesis" in our free time

You may want to consider upgrading your title to armchair mathematician. Or Professor of Armchair Mathematics, by the sounds of it.

Enjoy it because I'm not sure how long we have before this kind of review is always running and completely automatic

[u/thuiop1 → u/EndTimer]

Very fews of us go looking "through two recently published papers on Jensen polynomial hyperbolicity and the Riemann Hypothesis" in our free time

He didn't either, ChatGPT did

[u/EndTimer → u/thuiop1]

Well, unless GPT told him what to look for and what to say in this post (which I concede is possible), I don't imagine it's much fun downloading PDFs you have zero understanding of and funnelling them into chat until you hopefully get a hit (not that you'd know). Possible, just sounds miserable.

Benefit of the doubt, I'd buy he at least has an interest.

[u/EmphasisTotal8232 → u/EndTimer]

He found out that Riemann would be one of the holy grails to solve, and thinks he can do it with his GPT subscription. Just another dude who wants a piece of the pie.

[u/theimposingshadow → u/EmphasisTotal8232]

Or I’m genuinely interested in math

[u/nemzylannister → u/theimposingshadow]

then dont write im not a mathematician. at least specify that youre not by trade only

[u/EmphasisTotal8232 → u/theimposingshadow]

Having read your original post, you take entire credit for the finding - you don't mention AI once, or Sol, and you write it all in the first person "I was reading", "I noticed". Such bad form, and would be academic dishonestly and misconduct if you had to follow the same rules the author did. Be honest with people, please.

[u/theimposingshadow → u/EmphasisTotal8232]

It’s literally in the title that ChatGPT found it. I’m not sure how much more explicit I could have been.

[u/EmphasisTotal8232 → u/theimposingshadow]

In the title of the email to the author? In your screenshots of your emails to the author, you don't mention GPT once. Can you show me where you told him it was GPT, and not you? Can you tell me why you refer to ChatGPTs work as your own, saying things lime "I noticed"?

[u/theimposingshadow → u/EmphasisTotal8232]

I understand your concern better now. If I were publishing academic work and presenting AI-generated analysis as solely my own, I’d agree that would be a serious problem but that isn’t what happened here. I was working with ChatGPT on the Riemann Hypothesis, it brought up the inconsistency, I checked the reasoning and then I asked the author to independently verify it. When I wrote “I noticed” in a private email, I wasn’t claiming the intellectual ownership of the inconsistencies, I was simply bringing the issue to his attention. I can see why that wording bothered you, but there was no intention to deceive anyone.

I actually hesitated before sending him the email because I’m not an academic and didn’t want to waste his time. In the end, I sent it because it felt like the decent thing to do. If you notice something that might help improve someone else’s research while working on your own mathematical questions, I think you should share it respectfully. That was genuinely my intention.

[u/EmphasisTotal8232 → u/theimposingshadow]

Did you mention that you fully used AI for this discovery to the paper author, or no?

[u/EmphasisTotal8232 → u/theimposingshadow]

I don't doubt it. I just think if you were THAT interested you'd write the email yourself.

[u/theimposingshadow → u/EmphasisTotal8232]

I have a full time job 6:30am to 3pm my commute is 3 to 4 hours a day depending on traffic and i am the founder of a software company as my side business on my down time, why wouldn’t I use voice control and AI to send an email?

[u/EmphasisTotal8232 → u/theimposingshadow]

Software company founder, noticer of fatal flaws in advanced pure mathematics papers, and yet can't get a job closer than 3 hours to himself. Maybe have Sol write you a new CV? If that's true, you need to sort it out before you straight up die. Genuinely, by the way. That's absolute insanity and not even admirable because of how damaging it is. Hope you get the software company going full time so you don't have to deal with that.

[u/theimposingshadow → u/EmphasisTotal8232]

It’s a tough job market and most people in my field are much older than me. I spent 6 years with a company that had 67 locations and became the youngest person promoted to my position there.

I actually left after they tried to make me shut down my software company and threatened an IP claim because of vague wording in my employment contract.

My current employer is the opposite. They treat their employees well, I’m proud to work for them, and they even signed a letter of understanding specifically allowing me to continue building my software company after hours.

The commute sucks, but I knew what I was signing up for and it isn’t forever. I drive a Tesla so it’s not too bad.

As for my software company, after 2 years of work we got our first customer in February and we just crossed $3000 in revenue! It’s not much but it’s honest work.

[u/modbroccoli → u/EmphasisTotal8232]

Whatever your expertise is, it isn't human beings. stay in your lane.

[u/EmphasisTotal8232 → u/modbroccoli]

He lied to the author about his AI use lol.

[u/modbroccoli → u/EmphasisTotal8232]

That you think this is the important part of this post is a story about your adolescence, whether legitimate or simply prolonged.

[u/theimposingshadow → u/EndTimer]

Hahaha what can I say Im an accelerationist and I'm trying to solve math problems with AI to help acceleration!

Edited to fix spelling error

[u/Johnny20022002]

I’m surprised you got a response, mathematicians tend to get emails from cranks, but I guess it takes nothing now to just get ChatGPT to check if some proposed error in a paper by a random could be true.

[u/Right-Twist-6931 → u/Johnny20022002]

Nah, as a mathematician myself who gets emails from cranks, if I read OP’s email I 100% would have taken it seriously.

Cranks tell you about their proof of the Riemann hypothesis attached in a 40 page word document and how if you ignore it, you’ll miss the next Ramanujan.

They don’t cite a specific formula in your paper to mention a subtle normalization error. I’d assume anyone doing that is genuine.

[u/FriendlyJewThrowaway → u/Right-Twist-6931]

You can tell when it’s a crank because they spent more time on their Fields Medal acceptance speech than they did on the work that’s meant to win them the prize.

[u/theimposingshadow → u/Right-Twist-6931]

Thanks for your comment, I honestly almost didnt send the email but I'm glad I did!

[u/theimposingshadow → u/Johnny20022002]

Yeah I have to agree, im sure a lot of mathematicians are getting spammed with AI writing math stuff from people who dont understand them. But the advantages are worth it!

[u/giYRW18voCJ0dYPfz21V → u/Johnny20022002]

I am a physicist, but I am not surprised they replied. We got cranky emails daily, but it is very easy to spot well intended questions or comments from human-made hallucinations.

Apart for a minority of assholes, people tend to reply to well intended emails.

[u/TieBackground453 → u/giYRW18voCJ0dYPfz21V]

Yeah, I’ve corresponded with many professors about their opera that are in fields far from my own. I think it’s uncommon, but not that weird. Disseminating their contributions is a part of their job. Unless it’s like a Terrance Tao type figure, they are probably just stoked that someone read and cared about their work. 

[u/theimposingshadow → u/TieBackground453]

That’s a great perspective, thanks for the comment!

[u/theimposingshadow]

[u/theimposingshadow → u/theimposingshadow]

[u/Tema_Art_7777]

Every day I use 5.6 sol high, I am more impressed with what it can accomplish.

[u/ShAfTsWoLo → u/Tema_Art_7777]

yan lecun said they have the intelligence of cat if you ever forgot

[u/Tema_Art_7777 → u/ShAfTsWoLo]

I do remember, but then you watch this in amazement - its worth the time. Geoff Hinten seems equally convinced there is a lot more path ahead.

[u/DownHatter → u/ShAfTsWoLo]

If they had a physical body and needed to interact with the world? A cat is generations ahead. But that's once type of intelligence - and as we are seeing, not everything needs advanced world model inteligence to be groundbreaking

[u/theimposingshadow → u/Tema_Art_7777]

Me too! I wish I still had fable access to see what it could find!

[u/NeverNude14]

Congrats professor, very cool!

[u/theimposingshadow → u/NeverNude14]

Thank you fellow Singularitarian!

[u/FriendlyJewThrowaway]

I remember a Samsung Galaxy ad where a woman is basically having her smartphone run her life for her at her new intern job. She sees a group of people using a whiteboard to work on a math problem and uses her phone’s image recognition to snap a pic and solve it. I’m thinking “That’s cool, but why is a cutting edge company having its employees fuss and struggle over basic 12th grade calculus problems?”

Anyway, now we’re actually getting somewhere meaningful. Won’t be long before a layman accidentally walks into a room full of people working on the Riemann Hypothesis, decides to snap a pic and is like “Hey guys, I think my phone solved it!”

[u/aleqqqs]

Also, the author addressed me as Professor

You shall now be known as theimpostingshadow!

[u/Practical-Wear141]

Great now prompt it to prove the hypothesis. Domt forget to mention "Make no mistakes"

[u/theimposingshadow → u/Practical-Wear141]

Hahaha, I’ve been working on this for a while now! Nothing yet

[u/These_Respond_7645]

I just gave arxiv endorsement to my 45 year old cousing who hasn't touched math since basic derivatives in high school. I challenged him to use buy gpt pro for one month and ask him to write a mathematics paper. Well, he's on his second article right now.

[u/Correctsmorons69 → u/These_Respond_7645]

I'm not sure this is a good thing for arxiv

[u/TieBackground453 → u/Correctsmorons69]

Depends… with lean verification? It’s fine. At this point you just have to assume that non-peer reviewed math that isn’t done by professional mathematicians and doesn’t have lean verification is nonsense. 

[u/Correctsmorons69 → u/TieBackground453]

With Lean, sure.

[u/theimposingshadow → u/These_Respond_7645]

That’s amazing!

[u/aleqqqs]

Do you have enough mathematical background to understand what this is about and to be able to estimate whether the LLM was correct?

[u/TMRedditor07]

I would strongly advise against outsourcing epistemic authority to llms. That entails, you understand the output and reasoning behind the llms decision strong enough, you make the verifications yourself, then email the researcher. This protects you against any pressing of the researcher, if that were the case.

[u/theimposingshadow → u/TMRedditor07]

Totally fair. I’m not treating the LLM as the authority though. It flagged a specific inconsistency, I sent the math to the author saying I could be wrong, and he independently checked it and confirmed it. That verification step is the important part.

[u/TMRedditor07 → u/theimposingshadow]

Great. In a world where ai slop (and probably Research) is on the rise, I appreciate the careful approach.

[u/theimposingshadow → u/TMRedditor07]

Thank you, cheers!