I gave Monsieur Pascal as an example of a genius in past postings. Pascal's father, who schooled his son at home, wanted young Blaise to learn Latin and Greek before mathematics. So, Pascal's father removed all math books from the house and barely mentioned the subject. In spite of this, before he was 12, Blaise derived/invented his own form of Euclidean geometry including theorems and geometric terms. When he was 16, Pascal published his first work (conic sections, a fascinating subject that almost made me major in mathematics; but I also was obsessed by the colors of fireworks, and they won: I became a chemist). Pascal went on to become one of the greatest matematicians (also key contributions in physics) the world has ever known.

Suppose Pascal had died at age 13, before he had had a chance to publish any of his works. He would not have had any impact in the world of mathematics. I would still consider Pascal a genius. As I said, genius is an intrinsic characteristic of a man/woman: just like his/her fingerprints or his/her DNA. It is not necessary for the genius to publish any work. Genius just is.

Albert

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