The Year in Math and Computer Science | 2020 in Review - Quanta Magazine

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics, summarizes Bill Andrews, Senior Editor at Quanta Magazine.

The Year in Math and Computer Science
Photo: Daniel Castro Maia for Quanta Magazine

For mathematicians and computer scientists, 2020 was full of discipline-spanning discoveries and celebrations of creativity. Several long-standing problems yielded to sustained collaboration, sometimes answering other important questions as a happy byproduct. While some results had immediate applications, with researchers improving on the findings or incorporating them into other work, others served for now as inspiration, suggesting that progress is within reach.

Early in the year, Quanta described how five computer scientists established limits on the ability of entangled quantum computers to verify problems. As part of their work, the team also answered long-standing questions in physics and mathematics — much to the surprise of the researchers who had been working on those problems. Another set of collaborations strengthened a far-reaching bridge connecting distant areas of mathematics. Known as the Langlands correspondence, the conjectured bridge offers hope of deepening our understanding of many subfields of mathematics.

This year we also explored mathematicians’ growing familiarity with geometric constructs, examined how computer programs are helping mathematicians with their proofs, and surveyed the current state of mathematics and its problems...

Computers Invade Mathematics

For decades, mathematicians have used computer programs known as proof assistants to help them write proofs — but the humans have always guided the process, choosing the proof’s overall strategy and approach. That may soon change. Many mathematicians are excited about a program called Lean, an efficient and addictive proof assistant that could one day help tackle major problems. First, though, mathematicians must digitize thousands of years of mathematical knowledge, much of it unwritten, into a form Lean can process. Researchers have already encoded some of the most complicated mathematical ideas, proving in theory that the software can handle the hard stuff. Now it’s just a question of filling in the rest.

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Source: Quanta Magazine