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

Mathematicians and neuroscientists have created the first anatomically accurate model that explains how vision is possible.

Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.

Two women programmers played a pivotal role in the birth of chaos theory. Their previously untold story illustrates the changing status of computation in science.

Your expectations shape and quicken your perceptions. A new model that explains how that happens also suggests it’s time to update theories about sensory perception and decision making.

All descriptions of change are a unique blend of chance and determinism, according to the sweeping mathematical proof of the “weak Pinsker conjecture.”

Akshay Venkatesh, a former prodigy who struggled with the genius stereotype, has won a Fields Medal for his “profound contributions to an exceptionally broad range of subjects in mathematics.”

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.

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

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