Part of Grothendieck’s brilliance was to recognize that there was something grander hidden behind every algebraic equation. He called this something a scheme.

They live in worlds of potentialities, Heisenberg explained; they are not things, but possibilities.

If matter were prone to birthing monsters of this kind, Schwarzschild asked with a trembling voice, were there correlations with the human psyche? Could a sufficient concentration of human will—millions of people exploited for a single end with their minds compressed into the same psychic space—unleash something comparable to the singularity?

he had learned Mongolian chant and could intone multiple notes simultaneously.

He would derive the rules governing existence at that scale armed only with that meagre handful of data. He would rely on no concepts, no images, no models. Reality itself would dictate what could (and what could not) be said about it.

The first great painter to make use of it was the Dutchman Pieter van der Werff, in 1709:

Their two theories could not have been more opposed; while Schrödinger had needed only a single equation to describe virtually the whole of modern chemistry and physics, Heisenberg’s ideas and formulae were exceptionally abstract, philosophically revolutionary, and so dreadfully complex that only a handful of physicists understood how to use them,

Heligoland—the

The Haber–Bosch process is the most important chemical discovery of the twentieth century. By doubling the amount of disposable nitrogen, it provoked the demographic explosion that took the human population from 1.6 to 7 billion in fewer than one hundred years. Today, nearly fifty per cent of the nitrogen atoms in our bodies are artificially create