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Mathematics

Measuring tapes
infinity

Mathematicians Measure Infinities and Find They’re Equal

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

Rebecca Goldin
Q&A

Why Math Is the Best Way to Make Sense of the World

To tell truth from fiction, start with quantitative thinking, argues the mathematician Rebecca Goldin.

Lucy Reading-Ikkanda/Quanta Magazine
Abstractions blog

The Math That Promises to Make the World Brighter

The color of LED lights is controlled by a clumsy process. A new mathematical discovery may make it easier for us to get the hues we want.

Svitlana Mayboroda
mathematical physics

Mathematicians Tame Rogue Waves, Lighting Up Future of LEDs

The mathematician Svitlana Mayboroda and collaborators have figured out how to predict the behavior of electrons — a mathematical discovery that could have immediate practical effects.

fidget spinners
Quantized Academy

Symmetry, Algebra and the Monster

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.

Classes of geometric structures
Abstractions blog

Why Mathematicians Like to Classify Things

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Heavenly billiards
geometry

New Shapes Solve Infinite Pool-Table Problem

Two “rare jewels” have illuminated a mysterious multidimensional object that connects a huge variety of mathematical work.

Maryam Mirzakhani
Quantized Columns

The Beautiful Mathematical Explorations of Maryam Mirzakhani

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.

Kaisa Matomäki
Q&A

Kaisa Matomäki Dreams of Primes

Kaisa Matomäki has proved that properties of prime numbers over long intervals hold over short intervals as well. The techniques she uses have transformed the study of these elusive numbers.