What did Isaac Newton mean, exactly, when he said "I make no hypotheses"?
Newton wasn't saying he dealt in pure fact, or even pure mathematics. Mathematicians do make hypotheses. I think Newton was saying that intuition is all we really have, and we don't know where it's coming from. It is profoundly ironic that the greatest light of the enlightenment really was an extreme romantic at heart, who didn't even really believe in mathematics, or any scientific method, at all. While Galileo abhorred all theory, believing in pure data, he did have a very high opinion of mathematics, as a means of summarizing data. I think Isaac Newton, although one of the greatest mathematicians in history, actually only saw mathematics as a rather crude way of describing reality, and this view is very far from the Pythatorean view, the view of most mathematicians, that mathematics is actually the language of nature itself.

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