2+ hour, 30+ min ago  (1141+ words) Samuel Velasco and Hannah Waters/Quanta Magazine This approach is likely to be useful, but for those who crave real understanding of how the genome, and ultimately life itself, works, a computational black box will never suffice. And perhaps more…...

1+ week, 3+ day ago  (1041+ words) Automated proof-checkers such as Lean can provide ironclad assurances that mathematical proofs are valid. The following has been adapted from The Proof in the Code: How a Truth Machine Is Transforming Math and AI by Kevin Hartnett. The Proof in…...

4+ week, 1+ day ago  (663+ words) Let's start with what's probably the most tired, overused joke in math: A topologist is someone who can't tell a coffee cup from a doughnut. Both, you see, have a hole in them. But disconcertingly, topological spaces turn out to…...

1+ mon, 1+ hour ago  (928+ words) Kurt Go'del Papers, the Shelby White and Leon Levy Achives Center, Institute for Advanced Study; Samuel Velasco and Michael Kanyongolo/Quanta Magazine I spent the early weeks of the Covid pandemic learning how the 25-year-old Austrian logician and mathematician did…...

1+ mon, 1+ week ago  (753+ words) Mathematicians spend most of their time thinking about what's knowable. But the unknowable can be just as compelling. More than 50 years after G'del's theorem, cryptographers devised a radical new proof method in which unknowability played a very different role. Proofs…...

1+ mon, 2+ week ago  (816+ words) How do mathematicians decide that something is true? They write a proof. Often they start with proofs that already exist, building on or drawing connections between proven claims. Each of these proofs, in turn, has relied on other proofs to…...

1+ mon, 2+ week ago  (1316+ words) Most mathematicians would say just the opposite " that it's Zeilberger who spews complete nonsense. Not just because infinity is so useful and so natural to our descriptions of the universe, but because treating sets of numbers (like the integers) as…...

1+ mon, 3+ week ago  (1331+ words) Mathematicians recently invented a new way to tell knots apart: by giving each knot a colorful "QR code." Dror Bar-Natan, Roland van der Veen; Quanta Magazine From the tangle in your computer cord to the mess your cat made of…...

4+ mon, 1+ week ago  (734+ words) A machine learning algorithm created maps of the mouse brain with 1, 300 subregions by predicting how brain cell types tend to group together, like buildings in a neighborhood. Irena Gajic for'Quanta Magazine Real estate agents will tell you that a home's…...

9+ mon, 2+ week ago  (650+ words) The Fourier transform breaks a function down into wavelike building blocks. It took mathematicians until the 19th century to master this same calculation. "It's hard to overestimate the influence of Fourier analysis in math," said Leslie Greengard of New York University…...