Pbfgva Iynq Nynznevh (translate using rot13.com) who has a BA in Mathematics writes the following:

Do you imagine that men of genius or, let’s say, men of science in history walked around clear-headed, “disenchanted,” reasonable, with the tight-assed attitude of the science cultist and materialist? No great discovery has ever been made by the power of reason. Reason is a means of communicating, imperfectly, some discoveries to others, and in the case of the sciences, a method of trying to render this communication certain and precise. But no one ever made a discovery through syllogisms, through reason, through this makeshift form of transmission. Great mathematicians saw spatial relations, as great physicists saw and to some extent felt physical relations. In contemplation of mathematical forms, there is almost a physical feel of geometric relations, and all mathematicsat bottom is about geometric relations even when it doesn’t seem so. Compare the Euclidian proof of the Pythagorean theorem, based on syllogism, which helps you understand nothing that’s actually going on, with the imagistic proof of the three squares, that makes you perceive, physically perceive even in your body, why this theorem is true. Gauss, so beloved even by the tedious scientistic goblins that even Google gave him a cartoon, is famous to have said something like, “I got it…now I have to get it.” Meaning, he had seen and felt the fundamental spatial relation he was searching, but now he had to translate it into the imperfect language of mathematics for others. Thus all mathematics and all science in general—mathematics is only the prototype and most precise of the sciences—is about the definitions, not about the proof, not about the process or —absurd!—the “algorithm.” All great scientific discoveries, supposedly the great works of “reason,” are in fact the result of intuitions and sudden grasp of ideas. And all such sudden grasp and reaching is based on what, in other circumstances, would be called a kind of religious intoxication: it depends on a state of the mind where the perceiving part of the intellect is absolutely focused, limpid, yet driven by the most relentless energy, an energy to penetrate. Direct perception is already “intellectualized” and in fact much closer to the innate “intelligence” of things than cerebral syllogisms. No scientist worth anything has ever felt pride at using algorithms or trial-and-error to solve a problem.

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