Tag: topology
All the articles with the tag "topology".
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The Edge of Mathematics Research: A Citation-Grounded Survey of Open Problems and Recent Breakthroughs (2019–2026)
A subfield-by-subfield survey of the mathematics research frontier, grounded in specific papers from Annals, Inventiones, JAMS, Acta, Publications of the IHÉS, and the work of recent Fields medalists. Covers number theory, algebraic geometry, topology, geometric analysis, PDE, probability, combinatorics, logic, representation theory, harmonic analysis, dynamics, mathematical physics, and the rise of formalization. The through-line: mathematics in the 2020s is fusing — Langlands now spans number theory, geometry, and physics; condensed and prismatic methods unify analysis and arithmetic; and Lean is starting to absorb the load-bearing proofs.