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In French we have this word déclic. It's when you have, suddenly, a light shining and you say, "This is what I want to do. "

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Augustus De Morgan

The moving power of mathematical invention is not reasoning but imagination.

Teacher, Moving, Math, Power, Imagination
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I am perfectly convinced that I have both seen, and heard in a manner which should make unbelief impossible, things called spiritual which cannot be taken by a rational being to be capable of explanation by imposture, coincidence, or mistake.

Spiritual, Mistake, Taken, Rational, Make

We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.

Believe, Eye, Science, Morgan, Know

I did not hear what you said, but I absolutely disagree with you.

Said, Disagree, Hear

I was x years old in the year x2.

Education, Math, Years, Year, Old

Wrong hypotheses, rightly worked from, have produced more useful results than unguided observations.

Hypothesis, Observation, Results, Rightly, Unguided, Wrong
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