Forgetting is not the enemy of scientific progress — it is sometimes the engine of it. The mathematician Henri Poincaré described a peculiar experience: he had been stuck on a mathematical proof for weeks, set it aside entirely, and then — stepping onto a bus with his mind on something else — the solution arrived complete, without effort. He wasn't unusual. This same pattern appears across the records of Helmholtz, Darwin, and Hadamard, who surveyed mathematicians in the 1940s about exactly this phenomenon. What they all described was a process that only works when conscious attention leaves the building. The combinatorial logic of discovery, Poincaré argued, happens in a layer of mind that deliberate focus actively blocks. Now connect this to something the Sufi philosopher Al-Ghazali wrote in the twelfth century in his 'Ihyāʾ ʿUlūm al-Dīn': that the intellect's grasping mode — what he called the ego's effortful self-assertion — is precisely what closes off the subtler channels of knowing. He was writing about spiritual insight, but his phenomenological description of how understanding arrives is nearly identical to Poincaré's mathematical account. The implication for scientific work is practical and slightly uncomfortable: your problem-solving schedule may be structured in ways that prevent the cognitive process that actually solves problems. Protecting unstructured, genuinely idle time is not a luxury — it is a technical requirement for the incubation phase of difficult thinking.

What is the last genuinely difficult problem you're working on, and when did you last spend an hour doing something completely unrelated to it — not as a break, but as a deliberate part of the work?

Drawing from Islamic Sufi Philosophy / Early 20th-Century Philosophy of Mathematics — Henri Poincaré (Science and Method, 1908) in dialogue with Al-Ghazali (Iḥyāʾ ʿUlūm al-Dīn, c. 1107)