QUALIA | ALL TOPICS

What Do Gödel's Incompleteness Theorems Truly Mean?

By NATALIE WOLCHOVER

At 25, Kurt Gödel proved there can never be a mathematical “theory of everything.” Columnist Natalie Wolchover explores the implications.

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By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far bigger program to understand why numbers behave the way they do.

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GENOMICS

How Ecotypes Harbor the Genetic Memory of a Species’ Past

By MARLOWE STARLING

Evolutionary biologists are uncovering genomic mechanisms that allow populations to adapt quickly to different, hyperlocal habitats without splitting into new species.

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EXPLAINERS

How Alexander Grothendieck Revolutionized 20th-Century Mathematics

By KONSTANTIN KAKAES

Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions?

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THE QUANTA PODCAST

Ice Is Way More Complex Than It Seems

Podcast hosted by SAMIR PATEL
with SHALMA WEGSMAN

Ice comes in many more forms than the cubes in your water glass. Scientists have found about 20 phases of ice, including hot ice and bendy ice and ice that conducts electricity.

Listen (Apple) | Listen (Spotify)

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Day in Review: NASA Is Using AI to Hunt Toxic Algae Blooms

Missions __ News __ Galleries __ Events

May 21, 2026

Earth

NASA Is Using AI to Hunt Toxic Algae Blooms

By fusing data from multiple space missions, NASA's new AI tool could help create seamless maps of harmful algal blooms and give coastal communities earlier warnings of toxic outbreaks. Full Story