For mathematicians and computer scientists, 2020 was full of discipline-spanning discoveries and celebrations of creativity. We’d like to take a moment to recognize some of these achievements.
1. A landmark proof simply titled “MIP* = RE” establishes that quantum computers calculating with entangled qubits can theoretically verify the answers to an enormous set of problems. Along the way, the five computer scientists who authored the proof also answered two other major questions: Tsirelson’s problem in physics, about models of particle entanglement, and a problem in pure mathematics called the Connes embedding conjecture.
2. In February, graduate student Lisa Piccirillo dusted off some long-known but little-utilized mathematical tools to answer a decades-old question about knots. A particular knot named after the legendary mathematician John Conway had long evaded mathematical classification in terms of a higher-dimensional property known as “sliceness.” But by developing a version of the knot that yielded to traditional knot analysis, Piccirillo finally determined that the Conway knot is not “slice.”
3. 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 proof assistant 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.
This year, two teams of physicists made profound progress on ideas that could bring about the next revolution in physics. Another still has identified the source of a long-standing cosmic mystery.
1. Here’s an extremely brief version of the black hole information paradox: Stuff falls into a black hole. Over time — a long, long time — the black hole “evaporates.” What happened to the stuff? According to the rules of gravity, it’s gone, its information lost forever. But according to the rules of quantum mechanics, information can never be lost. Therefore, paradox. This year, a series of tour de force calculations has shown that information must somehow escape — even if how it does so remains a mystery.
2. Levitating trains, lossless power transmission, perfect energy storage: The promise of room-temperature superconductivity has fed many a utopian dream. A team based at the University of Rochester in New York reported that they had created a material based on a lattice of hydrogen atoms that showed evidence of superconductivity at up to about 15 degrees Celsius (59 degrees Fahrenheit) — about the temperature of a chilly room. The only catch: Superconductivity at this temperature only works if the material is crushed inside a diamond anvil to pressures approaching those of Earth’s core. Utopia will have to wait.
3. A dazzling cosmic strobe has ended an enduring astronomical mystery. Fast radio bursts — blips of distant radio waves that last for mere milliseconds — have eluded explanation since they were first discovered in 2007. Or rather, astronomers had come up with far too many theories to explain what are, for the brief time they’re alight, the most powerful radio sources in the universe. But on a quiet morning in April, a burst “lit up our telescope like a Christmas tree,” said one astronomer. This allowed researchers to trace its source back to a part of the sky where an object had been shooting out X-rays. Astronomers concluded that a highly magnetized neutron star called a magnetar was behind the phenomenon.
News, Views and Reviews For The Intellectually Curious
Boomers Daily 