Source: The Guardian (UK), Mar 2015
… in a mathematical proof or in a mathematician’s life, there are hardly any numbers. It’s all about concepts and logical reasoning.
… the same two key steps that a mathematician uses. He uses intuition to guess the right problem and the right solution and then logic to prove it.”
In the book, he writes of “the miracle” when “everything seemed to fit together as if by magic” and quotes André Weil on it, who calls it “lucid exaltation”, a climax that “unlike sexual pleasure” may last “for hours at a time, even days”.
what Villani explains so well is how mathematics lies somewhere between an art and science. “There is a famous quote about mathematics being the poetry of sciences,” he says. “And there really is something in it. First the enormous role of intuition. Inspiration is the key to mathematical work. You need both inspiration and rigour… and mathematicians and poets are people who believe in the power of words, of concepts and giving names to concepts.”