Quanta reviewed the top breakthroughs in maths and computer science in 2021, highlighting deeper analyses of AI, the preservation of topological history, and the concept of infinity amongst other things.
Topologists, who had already had a busy year, saw the release of a book this fall that finally presents, comprehensively, a major 40-year-old work that was in danger of being lost. A geometric tool created 11 years ago gained new life in a different mathematical context, bridging disparate areas of research. And new work in set theory brought mathematicians closer to understanding the nature of infinity and how many real numbers there really are. This was just one of many decades-old questions in math that received answers — of some sort — this year.
All I know about topology is when a coffee mug can be a donut so it was fascinating to read more about how 4D spheres could have more symmetries than their basic set. A better understanding of AI is advantageous but I’d like to see more around its ethics next year. Hopefully, those referenced advancements will aid that.