John von Neumann — "Young man, in mathematics you don't understand things. You just get used to them…"
Young man, in mathematics you don't understand things. You just get used to them.
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More from John von Neumann
"The brain is a logical machine, but it is not a computer."
"The world is not logical, it is psychological."
"My own feeling is that the most important advances in the future will come from the interaction of mathematics with other sciences."
"The atomic bomb is a great invention. It is also a great danger."
"Mathematics is an experimental science, and definitions are its axioms."
Details
Anecdote recounted by several mathematicians, including Paul Halmos.
Date: 1930s-1950s
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Understanding this quote
What it means
Mathematical comprehension isn't about achieving a sudden intuitive 'click.' Instead, proficiency comes from repeated exposure until abstract concepts feel familiar and workable. You don't need to fully grasp why something is true at a gut level — you build comfort through practice and pattern recognition until the strange becomes routine. True fluency is earned through habituation. This pushes back against the idea that struggling to understand means you're failing.
Relevance to John von Neumann
Von Neumann, a prodigy who mastered calculus before age eight and earned dual PhDs by 23, worked across quantum mechanics, game theory, nuclear weapons design, and computer architecture — fields where intuition routinely fails. Reportedly said to a student struggling with a concept, this reflects his own experience: his legendary mental speed came from deep familiarity with abstraction, not from pausing until things made sense at some comfortable intuitive level.
The era
Von Neumann's active years (1920s–1957) coincided with mathematics breaking decisively from classical intuition. Gödel's incompleteness theorems shattered certainty in foundations; quantum mechanics defied physical common sense; the Manhattan Project demanded rapid mastery of unfamiliar mathematics under wartime pressure. Computing emerged as an entirely new discipline with no inherited intuitions. In an era where abstraction was accelerating faster than intuition could keep pace, habituation wasn't merely a learning style — it was the only viable path.
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