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A graphed cubic equation separates 16th-century scientists Niccolò Fontana Tartaglia, and Gerolamo Cardano

Kristina Armitage for Quanta Magazine

Quantized Columns

The Sordid Past of the Cubic Formula

By David S. Richeson
―

The quest to solve cubic equations led to duels, betrayals — and modern mathematics.

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By David S. Richeson

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Dendritic ice crystals grow from top to bottom across the frame of a video.
condensed matter physics

Controversy Continues Over Whether Hot Water Freezes Faster Than Cold

By Adam Mann
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Decades after a Tanzanian teenager initiated study of the “Mpemba effect,” the effort to confirm or refute it is leading physicists toward new theories about how substances relax to equilibrium.

Micrograph of a neuron showing aggregations of tau protein.
aging

Protein Blobs Linked to Alzheimer’s Affect Aging in All Cells

By Viviane Callier
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Protein buildups like those seen around neurons in Alzheimer’s, Parkinson’s and other brain diseases occur in all aging cells, a new study suggests. Learning their significance may reveal new strategies for treating age-related diseases.

a human figure stacks gold coins on an equally balanced scale
Insights puzzle

How to Weigh Truth With a Balance Scale and Math

By Pradeep Mutalik
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In recreational mathematics, the balance scale is an endless source of puzzles that require precise and elaborate logic and teach the fundamentals of generalization.

A blue virtual being, made of neural networks, plays with colorful blocks inside a glowing sphere
machine learning

By Exploring Virtual Worlds, AI Learns in New Ways

By Allison Whitten
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Intelligent beings learn by interacting with the world. Artificial intelligence researchers have adopted a similar strategy to teach their virtual agents new tricks.

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The Joy of Why

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Computers doing mathematics.

Can Computers Be Mathematicians?

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Artificial intelligence has bested humans at problem-solving challenges like chess and Go. Is mathematics research next? Steven Strogatz speaks with mathematician Kevin Buzzard to learn about the effort to translate math into language that computers understand.


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An illustration that includes a triangular network overlaid by images of spinning particles.
explainers

The Spooky Quantum Phenomenon You’ve Never Heard Of

By Katie McCormick
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Points connected by lines.
graph theory

Mathematical Connect-the-Dots Reveals How Structure Emerges

By Leila Sloman
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A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.

Closeup of Akiko Iwasaki of the Yale School of Medicine against a dark background.
Q&A

An Immunologist Fights Covid with Tweets and a Nasal Spray

By Yasemin Saplakoglu
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Akiko Iwasaki, an immunologist who became a lifeline for the worried and the curious during the pandemic, thinks that nasal spray vaccines could be the next needed breakthrough in our fight against the coronavirus.

Seifert surfaces formed from closed loops.
topology

Special Surfaces Remain Distinct in Four Dimensions

By Kevin Hartnett
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For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

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Art for "Black, Hot Ice, Newly Seen in the Lab, May Be Nature's Commonest Form of Water"

Black, Hot Ice May Be Nature’s Most Common Form of Water

By Joshua Sokol
A GIF of ice melting in a glass of water

Mathematicians Prove Melting Ice Stays Smooth

By Mordechai Rorvig

The Universal Law That Aims Time’s Arrow

By Natalie Wolchover

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biophysics

This Animal’s Behavior Is Mechanically Programmed

By Jordana Cepelewicz
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Biomechanical interactions, rather than neurons, control the movements of one of the simplest animals. The discovery offers a glimpse into how animal behavior worked before neurons evolved.


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Multimedia

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Multimedia

The Map of Mathematics

By Kevin Hartnett
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Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.


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About Quanta Magazine

Illuminating basic science and math research through public service journalism.

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Quanta Magazine is committed to in-depth, accurate journalism that serves the public interest. Each article braids the complexities of science with the malleable art of storytelling and is meticulously reported, edited and fact-checked. Launched and funded by the Simons Foundation, Quanta is editorially independent — our articles do not reflect or represent the views of the foundation.

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