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.
A new study reveals that while current AI models excel at solving math *problems*, they struggle with the *reasoning* required for mathematical *proofs*, demonstrating a gap between pattern recognition and genuine mathematical understanding.
Physicists are revisiting the chaotic region near singularities within black holes, utilizing new mathematical tools to potentially reconcile general relativity and quantum mechanics and gain a deeper understanding of space and time.
A new mathematical proof resolves a 35-year-old bet between Noga Alon and Peter Sarnak regarding the prevalence of optimal expander graphs, demonstrating that both mathematicians were partially incorrect. The proof, building on work in random matrix theory, reveals that approximately 69% of regular graphs are Ramanujan graphs.
A blog post by Valeria de Paiva reflecting on the past four years of the Topos Institute, highlighting milestones, personal and research experiences, and the institute's mission-driven goals.
Matilde Marcolli, a mathematician at Caltech, has developed a new mathematical framework for Noam Chomsky's model of language, using ideas from theoretical physics. Chomsky's latest model, the minimalist program, simplifies language into a single computational operation called "merge," which combines elements of a sentence. Marcolli used Hopf algebras, a mathematical tool used in theoretical physics, to describe this merge operation. She worked with Chomsky and Bob Berwick to create a forthcoming book explaining this mathematical approach to language. Marcolli also taught a course and hosted workshops at Caltech on this topic, bringing together experts from various fields. This research supports Chomsky's philosophy that language should be studied using the methods and tools of the physical sciences.
Pham Tiep, a professor at Rutgers University, has made significant advancements by solving two long-standing problems in the representation theory of finite groups, which could enhance our understanding of symmetries and random processes in various scientific fields.
Height Zero Conjecture: Tiep solved the 1955 Height Zero Conjecture posed by Richard Brauer. This proof is published in the Annals of Mathematics and is considered one of the most significant challenges in the representation theory of finite groups.
Deligne-Lusztig Theory: In a second achievement, Tiep addressed a difficult problem in the Deligne-Lusztig theory, a foundational area in the representation theory of finite groups. This breakthrough is detailed in two papers published in Inventiones mathematicae and Annals of Mathematics.
Height Zero Conjecture: Tiep solved the 1955 Height Zero Conjecture posed by Richard Brauer. This proof is published in the Annals of Mathematics and is considered one of the most significant challenges in the representation theory of finite groups.
Deligne-Lusztig Theory: In a second achievement, Tiep addressed a difficult problem in the Deligne-Lusztig theory, a foundational area in the representation theory of finite groups. This breakthrough is detailed in two papers published in Inventiones mathematicae and Annals of Mathematics.
