Benjamín Labatut

In the last letter he sent to his wife from Russia, written the same day he chose to share his discovery with Einstein, Schwarzschild complains of something strange that has begun to grow inside him: “I don’t know how to name or define it, but it has an irrepressible force and darkens all my thoughts. It is a void without form or dimension, a shadow I can’t see, but one that I can feel with the entirety of my soul.”
Soon afterwards, that shadow invaded his body.

“If researchers want to apprehend my work, they must first deactivate the thought patterns that they have installed in their brains and taken for granted for so many years,” Mochizuki wrote on his blog.

Tell me, Professor, when did all this madness begin? When did we cease to understand the world?

but he insisted that all of that, however painful, was secondary to the sudden realization that it was mathematics—not nuclear weapons, computers, biological warfare or our climate
187
Armageddon—which was changing our world to the point where, in a couple of decades at most, we would simply not be able to grasp what being human really meant. Not that we ever did, he said, but things are getting worse. We can pull atoms apart, peer back at the first light and predict the end of the universe with just a handful of equations, squiggly lines and arcane symbols that normal people cannot fathom, even though they hold sway over their lives. But it’s not just regular folks; even scientists no longer comprehend the world. Take quantum mechanics, the crown jewel of our species, the most accurate, far-ranging and beautiful of all our physical theories. It lies behind the supremacy of our smartphones, behind the Internet, behind the coming promise of godlike computing power. It has completely reshaped our world. We know how to use it, it works as if by some strange miracle, and yet there is not a human soul, alive or dead, who actually gets it. The mind cannot come to grips with its paradoxes and contradictions. It’s as if the theory had fallen to earth from another planet, and we simply scamper around it like apes, toying and playing with it, but with no true understanding.

which not everyone can distinguish, as doing so requires a gene absent in forty per cent of humanity

Meanwhile, Nelly said, artists had already fully embraced it; she believed that the rediscovery of the irrational was the driving force behind all vanguard movements, movements that, even to a lay observer, were evidently suffused with a Faustian, boundless energy, a haste, a tragic fall in which everything was permitted.

Cantor could apparently demonstrate that there were as many points in a one-inch line as there were in all of space. He had taken a giant leap into the unknown and found something unique, something that nobody had ever considered before him, but his critics, who were many and varied, argued that he had simply gone too far. His infinities, while undoubtedly interesting, could never be considered objects for serious mathematical study. However, Cantor was armed with a proof that seemed completely airtight. “I see it, but I don’t believe it!” 79he wrote to a close friend when he had finished it, and his biggest problem, from then on, was that so many others were equally unable to accept this new and confounding article of faith.

” Trying to silence his opponents by making his theory complete, Cantor developed an entire hierarchy of infinities, but he struggled with increasingly strong episodes of uncontrollable mania, attacks that were followed by deep melancholy and the darkest possible depression. These spells became so regular that he was unable to work on 81mathematics; as a substitute, he devoted his boundless manic energy to try to prove that Shakespeare’s plays had actually been written by the English philosopher Francis Bacon, and that Christ was the natural son of Joseph of Arimathea, views that only helped to give more credence to the arguments of those who said that he was slowly going insane. In May 1884, he had a massive mental breakdown and had to be institutionalized at a sanatorium in Halle.

When you combined Gödel’s and von Neumann’s ideas, the outcome defied logic itself: from here to eternity, mathematicians would have to choose between accepting terrible paradoxes and contradictions, or work with unverifiable truths. It was an almost intolerable dilemma, but there appeared to be no way around it. Gödel’s logic, however mysterious, was airtight.

We knew the world would not be the same. A few people laughed, a few people cried, most people were silent. I remembered the line from the Hindu scripture, the Bhagavad Gita: Vishnu is trying to persuade the prince that he should do his duty, and to impress him takes on his multiarmed form and says, “Now I am become Death, the Destroyer of Worlds.” I suppose we all thought that, one way or another.

J. Robert Oppenheimer