Alan Turing — "The most important thing for a mathematician is intuition."
The most important thing for a mathematician is intuition.
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More from Alan Turing
"The human mind is a very complicated machine."
"The problem of creating intelligent machines is one of the most challenging and exciting problems in all of science."
"If the man were to try and pretend to be the machine he would clearly make a very poor showing. He would be given away at once by slowness and inaccuracy in arithmetic."
"The important thing is not to stop questioning."
"The question, 'Can machines think?' should be replaced by 'Are there imaginable digital computers which would do well in the imitation game?'"
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Understanding this quote
What it means
Mathematical progress isn't just rule-following or grinding through proofs. Intuition is the ability to sense which problems matter, which approaches might work, and where truth likely lies before formal proof confirms it. Great mathematicians don't merely calculate—they perceive patterns and make imaginative leaps. This values that inner sense of mathematical direction over mechanical procedure, arguing it is the essential spark driving real discovery rather than something that follows from it.
Relevance to Alan Turing
Turing's landmark breakthroughs—formalizing computation in 1936, breaking Nazi Enigma ciphers at Bletchley Park—began as intuitive leaps made rigorous only afterward. His universal machine concept existed as an imaginative construct before hardware validated it. His later morphogenesis research and artificial intelligence work further demonstrated intuitive thinking about biological patterns and machine minds. His Turing Test itself was an intuitive thought experiment, not a derived theorem, about what intelligence fundamentally is.
The era
Turing worked amid fierce debate between formalism and intuition in mathematics. Hilbert sought to fully mechanize mathematical truth; Gödel's 1931 incompleteness theorems proved formal systems couldn't capture everything. During WWII, Bletchley Park codebreaking required intuitive leaps under life-or-death pressure, validating instinct over procedure. The dawn of computing then sharpened the question: could machines ever replace the intuitive mathematical insight Turing believed was irreducibly human?
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