When is better to think without words? - by Henrik Karlsson

In the 1940s, when the French mathematician Jacques Hadamard asked good mathematicians how they came up with solutions to hard problems, they nearly universally answered that they didn’t think in words; neither did they think in images or equations. Rather, what passed through the mathematicians as they struggled with problems were such things as vibrations in their hands, nonsense words in their ears, or blurry shapes in their heads.1 Hadamard, who had the same types of experiences, wrote in The Psychology of Invention in the Mathematical Field that this mode of thinking was distinct from daydreaming, and that most people, though they often think wordlessly, have never experienced the kind of processing that the mathematicians did. When I read this, in December 2024, all sorts of questions arose in me. First of all, what does it even mean? Do they not think in words and equations at all? And secondly, how do I square this with my personal experience, which is that whenever I write wha

In the 1940s, when the French mathematician Jacques Hadamard asked good mathematicians how they came up with solutions to hard problems, they nearly universally answered that they didn’t think in words; neither did they think in images or equations. Rather, what passed through the mathematicians as they struggled with problems were such things as vibrations in their hands, nonsense words in their ears, or blurry shapes in their heads.1 Hadamard, who had the same types of experiences, wrote in The Psychology of Invention in the Mathematical Field that this mode of thinking was distinct from day