After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved—via a straightforward query to a chatbot. “No previous AI-generated proof has come ...

In October 2024 I attended a workshop at Harvard University where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than ...

Abstract: In this talk, I will discuss applications of spectral theory to problems arising in materials science and physics, focusing on quantum dynamics governed by the Schrodinger equation in three ...

Recent experiments in circuit quantum electrodynamics and electric circuit networks have demonstrated the coherent propagation of wave-like excitations on hyperbolic lattices. The negative curvature ...

In order to realize the real-time processing and analysis of astronomical ultra-wide bandwidth signals, this study proposes a sub-band division algorithm based on RFSoC. The algorithm uses Kaiser ...

Roughly four decades ago, Taher ElGamal put forward what is today one of the most widely known and best understood public key encryption schemes. ElGamal encryption has been used in many different ...

1 On our inability to do much. 4 On the reliability of mechanisms. 8 On our mental aids. 15 An example of a correctness proof. 19 On the validity of proofs versus the validity of implementations. 21 ...

Continued fractions constitute a very important subject in mathematics. Their importance lies in the fact that they have very interesting and beautiful applications in many fields in pure and applied ...

Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, United States Condensed Matter Physics and Materials Science Department, Brookhaven National ...