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random walk

Abstractions blog

How Randomness Can Make Math Easier

July 9, 2019

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

geometry

Random Surfaces Hide an Intricate Order

July 2, 2019

Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.

Art for "In the Universe of Equations, Virtually All Are Prime"
number theory

In the Universe of Equations, Virtually All Are Prime

December 10, 2018

Equations, like numbers, cannot always be split into simpler elements.

Information dog bottleneck
Wired to Learn: The Next AI

New Theory Cracks Open the Black Box of Deep Learning

September 21, 2017

A new idea is helping to explain the puzzling success of today’s artificial-intelligence algorithms — and might also explain how human brains learn.

insights puzzle

Solution: ‘A Drunkard’s Walk in Manhattan’

September 7, 2016

City blocks help illustrate why walking randomly tends to take you away from your starting point.

insights puzzle

A Drunkard’s Walk in Manhattan

August 18, 2016

Why is it that when you walk randomly, the more you walk, the farther you get from your starting point?

geometry

A Unified Theory of Randomness

August 2, 2016

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

statistical physics

At the Far Ends of a New Universal Law

October 15, 2014

A potent theory has emerged explaining a mysterious statistical law that arises throughout physics and mathematics.