Two announcements: AI for Math resources, and erdosproblems.com

This post contains two unrelated announcements. Firstly, I would like to promote a useful list of resources for AI in Mathematics, that was initiated by Talia Ringer (with the crowdsourced assistance of many others) during the National Academies workshop on “AI in mathematical reasoning” last year. This list is now accepting new contributions, updates, or corrections; please feel free to submit them directly to the list (which I am helping Talia to edit). Incidentally, next week there will be a second followup webinar to the aforementioned workshop, building on the topics covered there. (The first webinar may be found here.)

Secondly, I would like to advertise the erdosproblems.com website, launched recently by Thomas Bloom. This is intended to be a living repository of the many mathematical problems proposed in various venues by Paul Erdős, who was particularly noted for his influential posing of such problems. For a tour of the site and an explanation of its purpose, I can recommend Thomas’s recent talk on this topic at a conference last week in honor of Timothy Gowers.

Thomas is currently issuing a call for help to develop the erdosproblems.com website in a number of ways (quoting directly from that page):

• You know Github and could set a suitable project up to allow people to contribute new problems (and corrections to old ones) to the database, and could help me maintain the Github project;
• You know things about web design and have suggestions for how this website could look or perform better;
• You know things about Python/Flask/HTML/SQL/whatever and want to help me code cool new features on the website;
• You know about accessibility and have an idea how I can make this website more accessible (to any group of people);
• You are a mathematician who has thought about some of the problems here and wants to write an expanded commentary for one of them, with lots of references, comparisons to other problems, and other miscellaneous insights (mathematician here is interpreted broadly, in that if you have thought about the problems on this site and are willing to write such a commentary you qualify);
• You knew Erdős and have any memories or personal correspondence concerning a particular problem;
• You have solved an Erdős problem and I’ll update the website accordingly (and apologies if you solved this problem some time ago);
• You have spotted a mistake, typo, or duplicate problem, or anything else that has confused you and I’ll correct things;
• You are a human being with an internet connection and want to volunteer a particular Erdős paper or problem list to go through and add new problems from (please let me know before you start, to avoid duplicate efforts);
• You have any other ideas or suggestions – there are probably lots of things I haven’t thought of, both in ways this site can be made better, and also what else could be done from this project. Please get in touch with any ideas!

I for instance contributed a problem to the site (#587) that Erdős himself gave to me personally (this was the topic of a somewhat well known photo of Paul and myself, and which he communicated again to be shortly afterwards on a postcard; links to both images can be found by following the above link). As it turns out, this particular problem was essentially solved in 2010 by Nguyen and Vu.

(Incidentally, I also spoke at the same conference that Thomas spoke at, on my recent work with Gowers, Green, and Manners; here is the video of my talk, and here are my slides.)

AI Mathematical Olympiad – Progress Prize Competition now open

The first progress prize competition for the AI Mathematical Olympiad has now launched. (Disclosure: I am on the advisory committee for the prize.) This is a competition in which contestants submit an AI model which, after the submissions deadline on June 27, will be tested (on a fixed computational resource, without internet access) on a set of 50 “private” test math problems, each of which has an answer as an integer between 0 and 999. Prior to the close of submission, the models can be tested on 50 “public” test math problems (where the results of the model are public, but not the problems themselves), as well as 10 training problems that are available to all contestants. As of this time of writing, the leaderboard shows that the best-performing model has solved 4 out of 50 of the questions (a standard benchmark, Gemma 7B, had previously solved 3 out of 50). A total of $ ($1.048 million) has been allocated for various prizes associated to this competition. More detailed rules can be found here.

Talks at the JMM

Earlier this year, I gave a series of lectures at the Joint Mathematics Meetings at San Francisco. I am uploading here the slides for these talks:

• “Machine assisted proof” (Video here)
• “Translational tilings of Euclidean space” (Video here)
• “Correlations of multiplicative functions” (Video here)

I also have written a text version of the first talk, which has been submitted to the Notices of the American Mathematical Society.

Salem Prize now accepting nominations

The Salem prize was established in 1968 and named in honor of Raphaël Salem (1898-1963), a mathematician famous notably for his deep study of the links between Fourier series and number theory and for pioneering applications of probabilistic methods to these fields. It was largely administered by Jean Bourgain until his untimely death in 2018; due to this and the COVID-19 pandemic, no prize was awarded for the years of 2019-2022. A list of past winners may be found here.

However, I am happy to report that the prize has been reactivated, and is now formally hosted by the Institute for Advanced Study, with Akshay Venkatesh overseeing the administration of the prize, and is accepting nominations for the 2023 Salem Prize until September 1st. Nominations should include a CV of the nominee and a nomination letter explaining the significance of the nominee’s work. Supplementary documentation, such as supporting letters of recommendation or key publications, can additionally be provided, but are not required.

Nominees may be individuals from any country or institution. Preference will be given to nominees who have received their PhD in the last ten years, although this rule may be relaxed if there are mitigating personal circumstances, or if there have been few Salem prize winners in recent years.  Self-nominations will not be considered, nor are past Prize winners or Scientific Committee members eligible.

The prize does not come with a direct monetary award, but winners will be invited to visit the IAS and to give a lecture associated with the award of the prize.

I will be chairing the Scientific Committee to evaluate the nominations and recommend a prize winner; Guy David and Mikhail Sodin have also agreed to serve. Special thanks also to Peter Sarnak for his tireless efforts to ensure the continuation of the prize after Jean’s passing.

AI to Assist Mathematical Reasoning: A Workshop

The National Academies of Science, Engineering, and Mathematics are hosting a virtual workshop on the topic of “AI to Assist Mathematical Reasoning” from June 12-14. The tentative program can be found here. I am one of the members of the organizing committee for this workshop, together with Petros Koumoutsakos, Jordan Ellenberg, Melvin Greer, Brendan Hassett, Yann A. LeCun, Heather Macbeth, Talia Ringer, Kavitha Srinivas, and Michelle Schwalbe. There is some thematic overlap (and a few speakers in common) with the recent IPAM program on machine assisted proof, though with more of a focus on the current and projected technical capabilities of machine learning algorithms for mathematics. Registration for the event is currently open at the web page for the workshop.

PCAST Working Group on Generative AI Invites Public Input

As part of my duties on the Presidential Council of Advisors on Science and Technology (PCAST), I am co-chairing (with Laura Greene) a working group studying the impacts of generative artificial intelligence technology (which includes popular text-based large language models such as ChatGPT or diffusion model image generators such as DALL-E 2 or Midjourney, as well as models for scientific applications such as protein design or weather prediction), both in science and in society more broadly. To this end, we will have public sessions on these topics during our PCAST meeting next week on Friday, May 19, with presentations by the following speakers, followed by an extensive Q&A session:

• AI enabling science:
  • Anima Anandkumar (Caltech & NVIDIA)
  • Demis Hassabis (Deepmind)
  • Fei-Fei Li (Stanford)
• AI and society:
  • Sendhil Mullainathan (Chicago)
  • Daron Acemoglu (MIT)
  • Sarah Kreps (Cornell)

The event will be livestreamed on the PCAST meeting page. I am personally very much looking forward to these sessions, as I believe they will be of broad public interest.

In parallel to this, our working group is also soliciting public input for submissions from the public on how to identify and promote the beneficial deployment of generative AI, and on how best to mitigate risks. Our initial focus is on the challenging topic of how to detect, counteract, and mitigate AI-generated disinformation and “deepfakes”, without sacrificing the freedom of speech and public engagement with elected officials that is needed for a healthy democracy to function; in the future we may also issue further requests centered around other aspects of generative AI. Further details of our request, and how to prepare a submission, can be found at this link.

We also encourage submissions to some additional requests for input on AI-related topics by other agencies:

1. The Office of Science Technology and Policy (OSTP) Request for Information on how automated tools are being used to surveil, monitor, and manage workers.
2. The National Telecommunications and Information Administration (NTIA) request for comment on AI accountability policy.

Readers who wish to know more about existing or ongoing federal AI policy efforts may also be interested in the following resources:

• The White House Blueprint for an AI Bill of Rights lays out core aspirational principles to guide the responsible design and deployment of AI technologies.
• The National Institute of Standards and Technology (NIST) released the AI Risk Management Framework to help organizations and individuals characterize and manage the potential risks of AI technologies.
• Congress created the National Security Commission on AI, which studied opportunities and risks ahead and the importance of guiding the development of AI in accordance with American values around democracy and civil liberties.
• The National Artificial Intelligence Initiative was launched to ensure U.S. leadership in the responsible development and deployment of trustworthy AI and support coordination of U.S. research, development, and demonstration of AI technologies across the Federal government.
• In January 2023, the Congressionally mandated National AI Research Resource (NAIRR) Task Force released an implementation plan for providing computational, data, testbed, and software resources to AI researchers affiliated with U.S organizations.

Elias M. Stein Prize for New Perspectives in Analysis

The Elias M. Stein Prize for New Perspectives in Analysis is awarded for the development of groundbreaking methods in analysis which demonstrate promise to revitalize established areas or create new opportunities for mathematical discovery. The current prize amount is US$5,000 and the prize is awarded every three years for work published in the preceding six years.

This prize was endowed in 2022 by students, colleagues, and friends of Elias M. Stein (my former advisor) to honor his remarkable legacy in the area of mathematical analysis. Stein, who passed away in 2018, is remembered for identifying many deep principles and methods which transcend their original context, and for opening entirely new areas of research which captivated the attention and imagination of generations of analysts. This prize seeks to recognize mathematicians at any career stage who, like Stein, have found exciting new avenues for mathematical exploration in subjects old or new or made deep insights which demonstrate promise to reshape thinking across areas.

This will be the inaugural year for the prize, and I have agreed to serve on the prize committee. We welcome nominations for the prize, which will be accepted until June 30, 2023, and are seeking a strong and diverse pool of nominees. Nominations (submitted at this link) should include a letter of nomination and a brief citation to be used in the event that the nomination is successful. Alternatively, if you are aware of a strong potential candidate but are not able to provide the nomination yourself, we welcome your suggestion (by private email) along with — if possible — your suggestions of possible nominators. 

For questions about this award, please contact the AMS Secretary at secretary@ams.org.

Mathematics for Humanity initiative – application deadline extended to June 1

The International Center for Mathematical Sciences in Edinburgh recently launched its “Mathematics for Humanity” initiative with a call for research activity proposals (ranging from small collaborations to courses, workshops and conferences) aimed at using mathematics to contributing to the betterment of humanity. (I have agreed to serve on the scientific committee to evaluate these proposals.) We launched this initiative in January and initially set the deadline for April 15, but several people who had expressed interest felt that this was insufficient time to prepare a quality proposal, so we have now extended the deadline to June 1, and welcome further applications.

See also this Mathstodon post from fellow committee member John Baez last year where he solicited some preliminary suggestions for proposals, and my previous Mathstodon announcement of this programme.

Illustrating the Impact of the Mathematical Sciences

Over the last few years, I have served on a committee of the National Academy of Sciences to produce some posters and other related media to showcase twenty-first century and its applications in the real world, suitable for display in classrooms or math departments. Our posters (together with some associated commentary, webinars on related topics, and even a whimsical “comic“) are now available for download here.

Postdoctoral Research Positions in Mathematics and AI at the Sydney Mathematics Research Institute

[The following information was provided to me by Geordie Williamson, who is Director of the Sydney Mathematics Research Institute – T.]

We are currently advertising two positions in math and AI:

• A Level A position (for first time postdocs, upcoming PhDs); and
• a Level B position (for candidates with a postdoc / some research experience):

Both positions are for three years and are based at the Sydney Mathematical Research Institute. The positions are research only, but teaching at the University of Sydney is possible if desired. The successful candidate will have considerable time and flexibility to pursue their own research program.

We are after either:

1. excellent mathematicians with some interest in programming and modern AI;
2. excellent computer scientists with some interest and background in mathematics, as well as an interest in using AI to attack tough problems in mathematics.