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. But not all the news this year was welcome: the spread of COVID-19 complicated the research of working mathematicians, who increasingly rely on collaboration to push the field forward. The pandemic also claimed the life of the great mathematician John Conway about a month before we broke the news that a graduate student had solved a famous problem involving his signature knot.
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