The article discusses how, 340 years after Newton formulated the law of universal gravitation, physicists still lack a fundamental understanding of why gravity exists or how it fits with quantum mechanics. Known as the "problem of quantum gravity," this unresolved mystery remains one of the biggest embarrassments in modern physics.
A new paper by Thomas Bloom, Will Sawin, Carl Schildkraut and Dmitrii Zhelezov disproves a well-known conjecture in additive combinatorics. The result shows there exist arbitrarily large finite sets A of real numbers where max(|A+A|,|AA|) ≤ |A|^{2-c}. The solution was achieved by humans using methods related to an earlier AI solution to the unit distance conjecture.
John Burn-Murdoch guest-hosted BBC's Radical podcast, speaking with geneticist Sir John Bell about recent and upcoming medical breakthroughs.