Quanta Magazine

What’s the worst centrally symmetric convex shape for packing the plane? A hexagonal grid of circles covers 90.69% of the plane when optimally packed. An octagon with rounded corners covers a smidgen less: 90.24%. Mathematicians still don’t know for sure if rounded octagons are the worst shape. https://lnkd.in/ec9m3n3w

As an undergrad, John Jumper studied physics and math, but longed for science that moved more quickly. This led him to use computer solutions to study proteins. Jumper now leads AlphaFold, a machine learning algorithm that has transformed molecular biology. https://lnkd.in/eFWiM76h

According to one researcher, Google DeepMind’s creation of AlphaFold is “the biggest ‘machine learning in science’ story that there has been.” Read the full story of AlphaFold and what it means for the future of AI in biology. https://lnkd.in/eFWiM76h

In 2008, David Baker, one of the world’s leading protein design experts, created an online game called FoldIt, in which players fold strings of amino acids into protein structures. The game inspired computer scientists to study protein folding with AI. https://lnkd.in/eFWiM76h

Scientists have the tools to construct a human cell atlas: a holistic reference map of a human being that could help to pin down which specific cells in which tissues go wrong to cause diseases. Listen to this week’s episode of the Quanta Science Podcast: https://lnkd.in/e2NE4nJF

The world can’t be entirely described by whole numbers and fractions. In the grand scheme of the history of mathematics, it’s only recently that mathematicians have understood how numbers like √2 fit on the number line. https://lnkd.in/eg5kawMj

In 2020, the field of structural biology was transformed by AI, practically overnight. This is the story of decades of work by human beings that enabled that breakthrough. https://lnkd.in/eFWiM76h

Sometimes, a problem is hard to solve no matter how you approach it. Researchers recently proved that multicalibration, an approach for ensuring fairness in algorithms, can also help point out instances of computational hardness. https://lnkd.in/e-MS_d8V

At the heart of everyday calculations is an intuitive understanding of numbers, known as “number sense.”

The 19th-century mathematicians Richard Dedekind (left) and Georg Cantor came up with new, rigorous ways to define numbers. “They were good friends, and they hated each other,” said Leo Corry, a historian of science. https://lnkd.in/eg5kawMj