A team of mathematicians has made a groundbreaking discovery by extending the modularity connection from elliptic curves to more complicated equations called abelian surfaces. This breakthrough has the potential to unlock new insights and solutions to previously intractable problems in mathematics, and may even have implications for other fields such as physics and computer science….
Math on The Soothsayer
Mathematicians at the University of Oxford have finally solved a 60-year-old problem posed by the renowned mathematician Paul Erdős, shedding new light on the mysteries of addition. The breakthrough, achieved by graduate student Benjamin Bedert, reveals that in any set of integers, there exists a large subset of numbers that must be sum-free. This discovery…
A group of 16 aeronauts participating in the 1906 gas balloon race inadvertently contributed to a groundbreaking discovery in mathematical physics. Lewis Fry Richardson’s analysis of their landing spots revealed a pattern of turbulent swirling in the Earth’s atmosphere, which remains a mystery to this day. Despite significant progress in simulating fluids on computers, mathematicians…
June Huh, a 39-year-old professor of mathematics at Princeton University, has been awarded the Fields Medal for his groundbreaking work in geometry and combinatorics. Despite dropping out of high school to pursue a career in poetry, Huh’s chance encounter with mathematics led him to become one of the world’s leading mathematicians. His unique approach to…
Mathematicians have finally solved a 65-year-old problem in the field of topology, which deals with the properties of shapes that are preserved under continuous transformations. The problem, which involved determining the dimensions in which certain twisted shapes can exist, has been a long-standing puzzle in the mathematical community. Researchers at Fudan University and the University…
Mathematicians Noga Alon and Peter Sarnak have been engaged in a friendly debate since the late 1980s about the existence of optimal expander graphs, which are highly interconnected networks with relatively few edges. Recently, three mathematicians have finally settled the debate, proving that such graphs are not as rare as Alon and Sarnak thought. This…
Tai-Danae Bradley, a researcher at SandboxAQ, is using category theory to study language as a mathematical category, aiming to develop new mathematical tools and understand the structure of language. Her work has the potential to revolutionize the field of linguistics and artificial intelligence, enabling more accurate language processing and generation. This breakthrough could lead to…
Mathematicians have made a breakthrough in understanding the process of mean curvature flow, which describes how surfaces evolve over time. The discovery, which confirms the “multiplicity-one” conjecture, has significant implications for the study of melting surfaces, such as ice cubes or eroding sandcastles. This new understanding will enable researchers to analyze the evolution of surfaces…
Researchers at Princeton University have made a groundbreaking improvement to Newton’s method, a centuries-old technique used for optimization problems. The new algorithm, developed by Amir Ali Ahmadi and his team, extends Newton’s method to work efficiently on the broadest class of functions yet, potentially replacing it in various applications. Forecast for 6 months: Expect to…
Mathematicians at New York University’s Courant Institute and the University of British Columbia have finally solved the three-dimensional Kakeya conjecture, a problem that has puzzled experts for over a century. The solution, which involves finding the most efficient way to point a pencil in every direction while minimizing the space it moves through, has far-reaching…