The Poincaré conjecture can be understood by analogy with the case in two dimensions. A two-dimensional space, or surface, is like a bubble made from an infinitely thin film of soap. If the bubble is ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

Mahesh Kakde, professor of mathematics at the Indian Institute of Science, Bengaluru(Infosysprize.org) Winner of the the Infosys Prize 2022 in Mathematics for his contributions to algebraic number ...

Monstrous moonshine, a quirky pattern of the monster group in theoretical math, has a shadow -- umbral moonshine. Mathematicians have now proved this insight, known as the Umbral Moonshine Conjecture, ...

One of the oldest unsolved problems in mathematics is also among the easiest to grasp. The weak Goldbach conjecture says that you can break up any odd number into the sum of, at most, three prime ...

Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...