A connection between descriptive set theory and computer science has been discovered, allowing problems in one field to be rewritten and solved in the other by Anton Bernshteyn.
Problems in descriptive set theory (measuring infinite graph colorings) are mathematically equivalent to problems in distributed algorithms (efficient network coloring).
Problems in descriptive set theory (measuring infinite graph colorings) are mathematically equivalent to problems in distributed algorithms (efficient network coloring).
Researchers have refined the simplex method, a key algorithm for optimization, proving it can't be improved further and providing theoretical reasons for its efficiency.
A new paper by SFI Professor David Wolpert introduces a mathematically precise framework for the simulation hypothesis, challenging several long-standing claims and opening up new questions about simulated universes.
Mathematicians are using Srinivasa Ramanujan's century-old formulae to push the boundaries of high-performance computing and verify the accuracy of calculations.
Descriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms.
Manifolds are spaces that look Euclidean when you zoom in on any one of their points. Introduced by Bernhard Riemann, they have become a mathematical staple in fields like geometry, physics, and data analysis.
This study identifies genetic factors associated with quantitative ability, using data from large-scale genome-wide association studies. The research reveals 53 SNPs linked to a latent trait, distinct from general intelligence, and implicates genes involved in neuron projection development and brain function.
For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that model semiconductors.
A new method could change that.
Recent research has made a significant mathematical advance in understanding Anderson localization, the phenomenon where disorder in a material (like impurities in silicon) can stop electron flow. Researchers proved that, for a simplified model called band matrices, electrons do become trapped ("localized") with enough disorder. This breakthrough, achieved by Yan Yau and Jun Yin’s team, uses a new mathematical technique and brings us closer to fully understanding Anderson’s original model and designing materials with specific electronic properties. It’s a key step in understanding systems between order and randomness.
A new method could change that.
Recent research has made a significant mathematical advance in understanding Anderson localization, the phenomenon where disorder in a material (like impurities in silicon) can stop electron flow. Researchers proved that, for a simplified model called band matrices, electrons do become trapped ("localized") with enough disorder. This breakthrough, achieved by Yan Yau and Jun Yin’s team, uses a new mathematical technique and brings us closer to fully understanding Anderson’s original model and designing materials with specific electronic properties. It’s a key step in understanding systems between order and randomness.
The Langlands programme has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore.
The article details the recent proof of the geometric Langlands conjecture, a significant advancement in mathematics that validates a decades-old program aiming for a "grand unified theory" of the field. Led by Dennis Gaitsgory and Sam Raskin, the proof—spanning five papers and nearly 1,000 pages—is expected to open new avenues of research and potentially bridge connections between mathematics and theoretical physics, particularly in understanding symmetries in quantum field theory. While not a complete solution to the broader Langlands program, it provides strong evidence for its underlying principles and offers new tools for tackling complex mathematical problems.
The article details the recent proof of the geometric Langlands conjecture, a significant advancement in mathematics that validates a decades-old program aiming for a "grand unified theory" of the field. Led by Dennis Gaitsgory and Sam Raskin, the proof—spanning five papers and nearly 1,000 pages—is expected to open new avenues of research and potentially bridge connections between mathematics and theoretical physics, particularly in understanding symmetries in quantum field theory. While not a complete solution to the broader Langlands program, it provides strong evidence for its underlying principles and offers new tools for tackling complex mathematical problems.
Mathematicians Ben Green and Mehtaab Sawhney have developed a new counting technique for prime numbers, utilizing tools from additive combinatorics like Gowers norms to explore the distribution of primes, specifically those fitting the form p² + 4q².
