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Today’s powerful but little-understood artificial intelligence breakthroughs echo past examples of unexpected scientific progress.

Has physics reached the limits of what we can discover — or are the possibilities only just beginning?

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

Freeman Dyson — physicist, mathematician, writer and idea factory — died on February 28, but his vitality lives on.

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

Scientists seek a single description of reality. But modern physics allows for many different descriptions, many equivalent to one another, connected through a vast landscape of mathematical possibility.

Reductionism breaks the world into elementary building blocks. Emergence finds the simple laws that arise out of complexity. These two complementary ways of viewing the universe come together in modern theories of quantum gravity.

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.