While the Fields Medal celebrates the under-40s, the mathematician Joan Birman has, at the age of 99, solved a major open problem in representations of the Braid groups, a topic she has worked on for more than 60 years.
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Like this, which was solved for a whole bunch of numbers except one for decades on end news.mit.edu/2021/solutio...
After cracking the “sum of cubes” puzzle for 42, mathematicians discover a new solution for 3After solving the elusive “Diophantine equation” for 42, MIT and U of Bristol mathematicians have discovered a new solution for 3.news.mit.edu“The Burau representation of the braid group is faithful for n = 4” Vasudha Bharathram, Joan S. Birman, Tara E. Brendle arxiv.org/abs/2607.05283 I learned this from: www.scientificamerican.com/article/how-... See also: en.wikipedia.org/wiki/Braid_g... en.wikipedia.org/wiki/Burau_r...
The Burau representation of the braid group is faithful for n = 4In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group is faithful for n = ...arxiv.org
Depends what you mean by "application"—experts could tell you plenty of applications to parts of pure math, but it takes a long time to trickle down through physics & engineering to consumer applications; that's hard to predict. Math behind online banking was done in 1700s, math behind GPS in 1800s.
SciAm write-up, republished: www.yahoo.com/news/science...
How a 99-year-old mathematician unraveled a century-old braid mysteryIn the 1930s Werner Burau, a German mathematician, introduced a twisted geometrical mystery that would stand for nearly a century. Previously, mathematicians had shown that knots could be reformulate...www.yahoo.com