Alvaro Lozano-Robledo @mathandcobb

@mayankjha1089 It looks like there should be yes! I don't think this is the best out there.

Here is my modest contribution! I give you the elliptic curve of rank 13 and Z/2Z-torsion of smallest conductor known to date. In fact, I found many but uploaded 10 curves that have smaller conductors than the previous record on the database: elliptic-rank.icarm.cloud/curve/1920

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Alvaro Lozano-Robledo @mathandcobb

6 hours ago

Super excited that I am going to be able to add my name to the Leaderboard today, with a teeny-tiny modest contribution! :D ... Soon, once I check that what I found is the best I can find with this method. (The method is not even mine, so credit will go to someone else in fact!)

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@mayankjha1089 The rank is the number of generators (of infinite order) needed you generate all the points on the curve. The conductor is an integer that gives you an idea of the arithmetic complexity of the curve. This one has conductor 224593554269612009864883936329730274909323150.

The credit should go to Fermigier and Kihara, who came up with constructions of families of elliptic curves with Z/2Z-torsion, and I am just doing (educated) searches in those families.

@rperezmarco At this time, my university cannot afford AI subscriptions either.

This is an important report! To facilitate discussion, I am pasting below the main recommendations: 1. Programs should add new training opportunities to teach skills that are becoming increasingly relevant. These may include: collaboration, formulating questions, interdisciplinary work, use of AI tools, and formalization. 2. Skill in communication to both expert and broad audiences should be part of the training in a PhD program and an explicit degree expectation. 3. While homework can provide a useful way for students to learn course material, assessment should be based on in-person written or oral assessments. 4. Programs should provide access to AI tools for all graduate students, with use never mandatory and methods subject to the standards of the advisor and department. 5. Advisors should hold regular detailed discussions with their students about expectations for AI use. 6. Three ethical rules: (i) maintain responsibility for the correctness and understanding of the mathematics that appears under your name, (ii) always disclose AI use, and (iii)obtain explicit agreement from all involved parties before entering material into an AI 7. A mathematics PhD program should require rigorous in-person assessment of research plans and progress by multiple faculty at least annually, including meaningful feedback for the student. 8. A thesis should be an original scholarly contribution. This should be understood broadly; for instance, the thesis need not record the first proof of a statement. 9. A PhD should not be awarded primarily on the basis of the text of the dissertation. The text should serve as the foundation for a rigorous thesis defense that requires complete mastery of the thesis content.

Emily Riehl @emilyriehl

7 hours ago

I was part of a group that met last week to try to propose recommended changes to the structure of math PhD programs in an age of AI. Our report, together with a collection of related resources, is now available here: cmsa.fas.harvard.edu/aimathphd_summ…

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@emilyriehl Thank you for putting this together! Very important to start making concrete recommendations.

Super excited that I am going to be able to add my name to the Leaderboard today, with a teeny-tiny modest contribution! :D ... Soon, once I check that what I found is the best I can find with this method. (The method is not even mine, so credit will go to someone else in fact!) elliptic-rank.icarm.cloud

I was part of a group that met last week to try to propose recommended changes to the structure of math PhD programs in an age of AI. Our report, together with a collection of related resources, is now available here: cmsa.fas.harvard.edu/aimathphd_summ…

This skit was about Trump but if you replace him by OpenAI/LLMs in math research, the analogy still works pretty well! youtu.be/JhkZMxgPxXU?t=…

@TaliaRinger Ok but can she formalize a proof?

@amermathsoc That's a great logo! Love Santiago and it's cathedral 🤩

@rperezmarco what did you do now??

The deadline for proposing a Special Session for the Joint International Meeting of the Real Sociedad Matemática Española and the American Mathematical Society in Santiago de Compostelo, Spain, is September 30. Learn more and start your proposal today. Link in comments.

But... Is it... Transcendental?

Alex Kontorovich @AlexKontorovich

2 days ago

WOW!! Zeta(5) is irrational! Here's a Lean formalization: github.com/mo271/zeta5 Amazing what we'll learn (with AI help)

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@RadishHarmers We need a math bar

The videos driving the singularity: (And no... The "N-S Non-Sense" is not the main driver)

You can join the singularity here youtube.com/@mathandcobb?s…

We have reached the singularity (of YouTube views in my channel).

@Exomnium Thank you for pointing this out -- I am discussing this point in my latest video.

"We are currently facing the very specific challenge of advising OpenAI on how to coordinate the release of a large number of significant results in mathematics that they report have been produced by their internal model. We welcome input from the mathematical community on this question." I'm writing my input below, and then will submit thru the link. agmai.org

A few weeks ago Astra gave a stunningly simple proof of the Erdős-Sós conjecture in graph theory (previously thought to be very difficult). It has been a good example of how the lifecycle of AI proofs should be: after the AI formalisation posted at erdosproblems.com/548 1/

Let’s treat these “100 solved open problems” just like we did with the IMO problems. It doesn’t mean shit until you do it in a controlled environment. Also, wasn’t this the entire point of first proof?! To benchmark these things in a standardized and scientific fashion?