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On the advice of a group of physicists, OpenAI hasn’t released a major result that claims to make a theory in particle physics mathematically rigorous. Instead, the physicists are now working to understand the 1,147-page AI proof themselves.

🕸️ New research gives us an atomic-level look into the spider’s silk factory.

New on Transformation: OpenAI releases three landmark results in math, physics, and computer science @kkakaes reports:

How do you take a picture of a black hole? On the latest episode of The Joy of Why, host @JannaLevin sits down with astrophysicist @ShepDoeleman to hear how capturing the first image of a black hole required a telescope the size of the world. Listen now:

Knobs cover the surface of a red blood cell infected with malaria. They make cells clump to the walls of blood vessels, causing the disease’s most dangerous symptoms including organ distress, seizures, and coma.

As Election Day approaches, writer Alex Stone explores what topology teaches us about democracy and the strange paradoxes it can give rise to:

Spider silk is tougher than the Kevlar inside a bulletproof vest and stronger than steel. Researchers are figuring out how the “silk dope” from their glands forms this remarkable substance.

This is the first microscopic video of 𝘗𝘭𝘢𝘴𝘮𝘰𝘥𝘪𝘶𝘮 entering a red blood cell, taken in 1978. Upon entry, the parasite infects a cell with malaria. Within days, millions of compromised cells could be lurking in the bloodstream.

The French mathematician Nicolas de Condorcet identified a paradox about voting in the late 18th century: A majority can sometimes vote itself into a logical loop.

Researchers have gained more insight into how the parasite that causes malaria gains entry into red blood cells. On the latest episode of The Quanta Podcast, writer @jojofoshosho0 dives into just how malaria got caught breaking and entering:

Chi-Min Ho and her team were able to image the exact moment malaria invades a red blood cell, in unprecedented detail. This knowledge could help inform the next generation of malaria treatments.

RT @imalexstone: With 2 candidates, picking a winner is easy. With 3, there’s no perfect way to do it. I wrote about the math behind this for @QuantaMagazine

The French mathematician Nicolas de Condorcet was a passionate believer in democracy. He also discovered a frustrating paradox within it. Now, mathematicians have found that this centuries-old voting paradox has a strange topological shape. @imalexstone reports:

OpenAI’s new proof of the quasi-Riemann hypothesis didn’t introduce any new concepts — it unearthed hidden connections between old ones. “The proof is a surprising synthesis of well-known ideas,” said Alexander Dunn of the Georgia Institute of Technology.

“In science, we often rely on cold data and numbers to understand disease, but photomicrography bridges the gap between logic and emotion.” Enjoy the Nikon Small World competition winners:

In pursuit of an alternative to dark matter to explain the universe we see, some scientists posited that we might not understand gravity as well as we think. But a trio of weird galaxies without dark matter has put that tottering theory to bed. Hear more on The Quanta Podcast:

To study diseases, Gauri Kulkarni of Wake Forest University grows miniature organs in her lab, including the 1.3-millimeter human gut tissue shown in this image.

This is a mouse trachea. That faint layer of blue at upper right? That’s “the kind of mucus you cough and spit out,” said Julien Resseguier, who created the image to study the interplay between neural and immune systems.

To invade red blood cells, malaria parasites create a temporary molecular portal that lets it slip into the cell — and then disappears behind it. Researchers have finally detailed the proteins that let it break in without tripping the alarms.

This is the Weierstrass function, a “monster” that is continuous everywhere but differentiable nowhere. First published in 1872, it prompted scrutiny of assumptions in calculus. Similar functions are used to study random motion and analyze risk.