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Constantin Kogler

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@ConstantinKogl

Mathematician, Postdoc at @the_IAS
constantinkogler.com
Trying to be an AI optimist
Princeton, NJ constantinkogler.com Joined December 2021
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Constantin Kogler Verified account @ConstantinKogl
Controversial Opinion: The internal model by @OpenAI that solved all these math problems is better but not crazy better than Astra.

I am an expert on papers 148 and 153. The result of 148, which is stunning, I got with Astra myself after a 6-hour session on September 27 and maybe relying on my local context. The main problem was solved after the model thought continuously for around 3 hours. (See the paper we wrote on it that is now on the arXiv.)

153 is impressive, but I am quite convinced I would have gotten that too if I had tried as hard as with 148.

I am sure that for the Quasi-Riemann result they used significantly more compute. They claim that for most of the 4000 problems, they used 3 hours, which aligns with my experience for 148.

What I am saying is that Astra already can make real breakthroughs in mathematics. The internal model is surely better, but at least in my area of expertise it doesn't seem to strongly outperform Astra.

What are your opinions?
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Constantin Kogler Verified account @ConstantinKogl
Borcherds shouldn't devalue his expertise!

He is a charismatic, inspiring mathematician. Humans will not be motivated by machines and human expertise and understanding are valuable.

Great that @ericweinstein tried to convince him that his work matters more than he thinks.
Curt Jaimungal Verified account @TOEwithCurt 3d
This episode is about mathematics in the age of AI. Richard Borcherds, a Fields Medalist and professor of mathematics at UC Berkeley, and Eric Weinstein @EricRWeinstein, who earned his PhD in mathematics at Harvard, join to take up three questions. What is mathematics about, what is the future for math students, and what is at stake? We discuss whether AI can build theories or only solve problems, why pure mathematics is worth funding, and what is left for human mathematicians. The conversation also covers the sporadic groups, whether math will go the way of chess, and who deserves credit if a stranger with an AI proves the Riemann hypothesis.

youtu.be/XqgnJyQZGG4
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Constantin Kogler Verified account @ConstantinKogl
I liked this essay by an anonymous PhD student.

We should make room for as many people as possible in the maths community.

If anyone works hard to understand the frontier, even with having an unrelated full time job, we should value their work.

proofsandprompts.com/2026/11/05/im-…
proofsandprompts.com I’m Not Done Doing Math! Don’t Ignore Me! “But I am still interested in doing math. I still think my research direction has genuine merit, and I still feel like I have more mathematics to give to the world. Thanks to AI, it is now feasible…
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Constantin Kogler Verified account @ConstantinKogl
Good ideas are possible to find in the current math era.

In the past era, significant ideas were rare. As a result, we worked hard and did technical work to squeeze out everything we could from good ideas.

That ideas are cheaper now is exciting about the future 🚀!