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Category: mathematics

AI math genius delivers 100% accurate results

At the 2024 International Mathematical Olympiad (IMO), one competitor did so well that it would have been awarded the Silver Prize, except for one thing: it was an AI system. This was the first time AI had achieved a medal-level performance in the competition’s history. In a paper published in the journal Nature, researchers detail the technology behind this remarkable achievement.

The AI is AlphaProof, a sophisticated program developed by Google DeepMind that learns to solve complex mathematical problems. The achievement at the IMO was impressive enough, but what really makes AlphaProof special is its ability to find and correct errors. While (LLMs) can solve , they often can’t guarantee the accuracy of their solutions. There may be hidden flaws in their reasoning.

AlphaProof is different because its answers are always 100% correct. That’s because it uses a specialized software environment called Lean (originally developed by Microsoft Research) that acts like a strict teacher verifying every logical step. This means the computer itself verifies answers, so its conclusions are trustworthy.

How sound and light act alike—and not—at the smallest scale

A world-famous light experiment from 1801 has now been carried out with sound for the first time. Research by physicists in Leiden has produced new insights that could be applied in 5G devices and the emerging field of quantum acoustics. The study is published in the journal Optics Letters.

Ph.D. student Thomas Steenbergen says, “We saw that in materials behave in the same way as light, but also slightly differently. With a mathematical model, we can now explain and predict this behavior.”

Dr. Julia Moore Vogel — Scripps Research — Visionary, Patient-Centric Health Research For All

Visionary, patient-centric health research for all — dr. julia moore vogel, phd — scripps research / long covid treatment trial.

Dr. Julia Moore Vogel, PhD, MBA is Assistant Professor and Senior Program Director at The Scripps Research Institute (https://www.scripps.edu/science-and-me… where she is responsible for managing a broad portfolio of patient-centric health research studies, including The Long COVID Treatment Trial (https://longcovid.scripps.edu/locitt-t/), a fully remote, randomized, placebo-controlled clinical trial targeting individuals with long COVID, testing whether the drug Tirzepatide can reduce or alleviate symptoms of long COVID.

Prior to this current role, Dr. Vogel managed The Participant Center (TPC) for the NIH All of Us Research Program (https://www.scripps.edu/science-and-me… which was charged with recruiting and retaining 350,000 individuals that represent the diversity of the United States. TPC aims to make it possible for interested individuals anywhere in the US to become active participants, for example by collaborating with numerous outreach partners to raise awareness, collecting biosamples nationwide, returning participants’ results and developing self-guided workflows that enable participants to join whenever is convenient for them.

Prior to joining the Scripps Research Translational Institute, Dr. Vogel created, proposed, fundraised for, and implemented research and clinical genomics initiatives at the New York Genome Center and The Rockefeller University. She oversaw the proposal and execution of grants, including a $44M NIH Center for Common Disease Genomics in collaboration with over 20 scientific contributors across seven institutions. She also managed corporate partnerships, including one with IBM that assessed the relative value of several genomic assays for cancer patients.

Dr. Vogel has a BS in Mathematics from Rensselaer Polytechnic Institute, a PhD in Computational Biology and Medicine from Cornell and an MBA from Cornell.

Continue reading “Dr. Julia Moore Vogel — Scripps Research — Visionary, Patient-Centric Health Research For All” | >

A Mathematician’s Model Brings Science Fiction’s Wormholes Closer to Reality

Could a tunnel through space and time—long a dream of science fiction—ever exist in theory? According to Arya Dutta, a Ph.D. student in Mathematics at the Katz School, the answer might be yes, at least on paper.

Accepted for publication in the International Journal of Geometric Methods in Modern Physics, Dutta’s study, “Thin-shell Wormhole with a Background Kalb–Ramond Field,” explored a mathematical model of a wormhole—a hypothetical shortcut through spacetime that could, in theory, connect two distant regions of the universe. “A wormhole allows faster-than-light travel or even time travel,” said Dutta. “It hasn’t been observed yet, but theoretical research has advanced a lot.”

Automatic C to Rust translation technology provides accuracy beyond AI

As the C language, which forms the basis of critical global software like operating systems, faces security limitations, KAIST’s research team is pioneering core original technology research for the accurate automatic conversion to Rust to replace it. By proving the mathematical correctness of the conversion, a limitation of existing artificial intelligence (LLM) methods, and solving C language security issues through automatic conversion to Rust, they presented a new direction and vision for future software security research.

The paper by Professor Sukyoung Ryu’s research team from the School of Computing was published in the November issue of Communications of the ACM and was selected as the cover story.

The C language has been widely used in the industry since the 1970s, but its structural limitations have continuously caused severe bugs and security vulnerabilities. Rust, on the other hand, is a secure programming language developed since 2015, used in the development of operating systems and , and has the characteristic of being able to detect and prevent bugs before program execution.

Kakutani fixed-point theorem

In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued function defined on a convex, compact subset of a Euclidean space to have a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of the Brouwer fixed point theorem. The Brouwer fixed point theorem is a fundamental result in topology which proves the existence of fixed points for continuous functions defined on compact, convex subsets of Euclidean spaces. Kakutani’s theorem extends this to set-valued functions.

New AI framework can uncover space physics equations in raw data

Artificial intelligence (AI) systems, particularly artificial neural networks, have proved to be highly promising tools for uncovering patterns in large amounts of data that would otherwise be difficult to detect. Over the past decade, AI tools have been applied in a wide range of settings and fields.

Among its many possible applications, AI systems could be used to discover physical relationships and symbolic expressions (i.e., ) describing these relationships.

To uncover these formulas, physicists currently need to extensively analyze , thus automating this process could be highly advantageous.

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