Steve Nadis writes:

The equations that govern black holes were true before there were black holes. That claim is hotly contested, and cuts through one of the deepest fault lines in the philosophy of mathematics. On one side are those who hold that mathematical structures, including well-established principles and basic geometric shapes like the tetrahedron, exist independently of human thought – not as a language we invented to describe reality, but rather as the substrate of reality itself. On the other side of the debate are those who argue that mathematics is the product of human labours, imposed on a world that would be wholly indifferent to it were we not here.

Sergiu Klainerman, professor of mathematics at Princeton University in New Jersey, stands resolutely in the first camp, affirming that mathematical truth precedes us, and that our job is simply to unearth it. His work includes landmark proofs that empty space is stable and that black holes – collapsed stars so dense that nothing inside can escape their gravitational pull – do not disintegrate when perturbed. Theorems like this that he has proved, and others he has built upon, do not represent human creations, he says, but instead stand as discoveries. While the tools used to uncover mathematical truths may be invented, the truths themselves are things to be found. Conflating the two is a category error, Klainerman believes, with consequences that obscure our understanding of what mathematics is and why it works.

Klainerman, 76 this month, was drawn to mathematics as a youth, partly because he was good at it. But he had a more compelling reason. He was born and raised in Romania under the country’s repressive Communist regime, and when he began his undergraduate studies at the University of Bucharest in 1969, mathematics was one of the few subjects not ideologically controlled. It offered ‘a sense of purity’, he said, an escape from the propaganda that saturated every other corner of public life. In mathematics, which he regarded as ‘a field of uncompromising truth and abstract beauty’, he found both intellectual challenge and something even rarer: a welcome refuge. This was one realm over which Nicolae Ceaușescu’s regime had absolutely no control. Mathematical theorems, once proven with rigour, do not bend to political pressure. Unlike diamonds, they truly last forever. [Continue reading…]