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.
This study reveals a role for the superior colliculus in higher-order cognition, independent of its role in spatial orienting. Researchers found that the superior colliculus exhibits robust encoding of learned visual categories and its inactivation markedly impaired category decisions in rhesus macaques.
Scientists are exploring the capabilities of the DeepSeek-R1 AI model, released by a Chinese firm. This open and cost-effective model performs comparably to industry leaders in solving mathematical and scientific problems. Researchers are leveraging its accessibility to create custom models for specific disciplines, although it still struggles with some tasks.
consciousness relates to a dynamic process of self-sustained, coordinated brain-scale activity assisting the tuning to a constantly evolving environment, rather than in static descriptions of brain function (3–5). In that respect, neural signals combine, dissolve, reconfigure, and recombine over time, allowing perception, emotion, and cognition to happen (6).
