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number theory

Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

August 3, 2020

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

Abstractions blog

How Physics Found a Geometric Structure for Math to Play With

July 29, 2020

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

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?

Animated illustration of a hand emerging from a black hole, while drawing the black hole by connecting dots flashing 0 and 1.
Quantized Columns

Spotting Quantum Black Holes in the Lab

July 15, 2020

Can we test speculations about how quantum physics affects black holes and the Big Bang?

Gödel’s incompleteness theorems.
Abstractions blog

How Gödel’s Proof Works

July 14, 2020

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

Quantized Academy

The Math of Social Distancing Is a Lesson in Geometry

July 13, 2020

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries.

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.

A photograph of the mathematician James Maynard outside his home in Oxford, England.

A Number Theorist Who Solves the Hardest Easy Problems

July 1, 2020

In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Animated illustration showing vulnerable red shapes become “infected” and turn green, amid immune blue shapes.
Abstractions blog

The Tricky Math of Herd Immunity for COVID-19

June 30, 2020

Herd immunity differs from place to place, and many factors influence how it’s calculated.