History of science

The quest to make mathematics rigorous has a long and spotty history — one mathematicians can learn from as they push to formalize everything in the computer program Lean.

David E. Dunning explores how mathematical notation is a social, world-building technology.

In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A trove of newly unearthed letters shows that it was also an act of plagiarism.

Today’s observatories document every pulse and flash in the sky each night. To understand how the cosmos has changed over longer periods, scientists rely on a more tactile technology.

Try as they might, scientists can’t truly rid a space or an object of its energy. But what “zero-point energy” really means is up for interpretation.

Over the past 60 years, scientists have largely succeeded in building a computer model of Earth to see what the future holds. One of the most ambitious projects humankind has ever undertaken has now reached a critical moment.

Tipping points in our climate predictions are both wildly dramatic and wildly uncertain. Can mathematicians make them useful?

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, decomposes any function into its parts.

Hundreds of physicists (and a few journalists) journeyed to Helgoland, the birthplace of quantum mechanics, and grappled with what they have and haven’t learned about reality.