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history of science

Black and white historical photo of eight men in front of a building, including Henri Cartan, André Weil and Szolem Mandelbrojt.
Abstractions blog

Inside the Secret Math Society Known Simply as Nicolas Bourbaki

November 9, 2020

For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.

water molecules, droplets and a wave
Abstractions blog

How Mathematical ‘Hocus-Pocus’ Saved Particle Physics

September 17, 2020

Renormalization has become perhaps the single most important advance in theoretical physics in 50 years.

An abstract illustration showing broken tools, cubes, numbers and other abstract representations of impossible math
Quantized Columns

When Math Gets Impossibly Hard

September 14, 2020

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

A comically long “missing persons” poster for an odd perfect number that shows all the restrictions it has to satisfy.
number theory

Mathematicians Open a New Front on an Ancient Number Problem

September 10, 2020

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.

Photo of a sign reading “To Telescope” near Griffith Observatory in Los Angeles.
Quantized Columns

Social Distancing From the Stars

August 11, 2020

Professional astronomers may not point their telescopes by hand anymore, but COVID-19 has still closed observatories and impeded research.

Visualization of the distribution of prime numbers in the shape of colorful dots in a hexagonal pattern
Abstractions blog

Mathematicians Will Never Stop Proving the Prime Number Theorem

July 22, 2020

Why do mathematicians enjoy proving the same results in different ways?

Photo of various kinds and colors of dice
Abstractions blog

How and Why Computers Roll Loaded Dice

July 8, 2020

Researchers are one step closer to injecting probability into deterministic machines.

Illustration showing an austere number line on one side and various interesting objects on the the other, including a dodecahedron, an armillary sphere, flowers and plants.
Quantized Columns

The Two Forms of Mathematical Beauty

June 16, 2020

Mathematicians typically appreciate either generic or exceptional beauty in their work, but one type is more useful in describing the universe.

Q&A

The Computer Scientist Who Can’t Stop Telling Stories

April 16, 2020

For pioneering computer scientist Donald Knuth, good coding is synonymous with beautiful expression.