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Pythagoras founded Greek mathematics and especially geometry in about 550 B.C.. He and his Pythagorean school made the geometry one of the greatest accomplishments of Greek science. For systematically expounding and expanding Pythagorean geometry, however, we owe thanks to Euclid. In Alexandria in about 300 B.C., he wrote Elements of Geometry, and until recent years it was the most translated and copied book in history except for the Bible [Bronowski, 1973]. Many famous scientists in these two millennia thanked Euclid’s book for showing them the beauty of what Pythagoras called the ‘language of nature’.

Leonardo da Vinci (1452-1519) combined the eye of an artist with the curiosity and analytic ability of a scientist. He epitomized the breadth and depth of the Italian Renaissance, by the scope of subjects and the novelty of perspectives in his notes. He was self-taught, with no intellectual training and therefore minimal limiting dogma [Goldstein, 1988].

Unfortunately, Leonardo made absolutely no contribution to contemporary scientific knowledge. He did not interact with scientists and he did not publish anything. His now-famous notes were private, written backwards to prevent casual reading by others. If a researcher publishes nothing and thereby makes no contribution whatsoever to the field of science, can that person even be called a scientist? Such questions are as fruitless as the question of whether a scientist-administrator is a scientist. Certainly Leonardo was an inspiring example to later scientists. Certainly Leonardo’s lack of scientific communications to his peers was a heartbreaking loss to science.

The greatest scientific book of all time is Principia Mathematica, completed by Isaac Newton in 1687. Newton’s paradigm of the physics of motion united terrestrial and planetary motions with simple mathematical laws. He elegantly demonstrated the ability of theoretical physics to derive precise predictions of empirically observable phenomena. Yet Newton was so insecure and so incapable of dealing with the criticisms of others that he nearly failed to make his findings public. He completed much of the work of Principia many years before publishing it. Only Edwin Hubble’s constant encouragement and partial financing eventually compelled Newton to produce Principia.

Twenty years earlier, when Newton began his work on gravitation, he developed the calculus. Rather than publish calculus, he kept it secret, using it to make several discoveries but then couching the presentation of these discoveries in ordinary mathematics. In about 1676 Gottfried Leibniz developed calculus independently. Newton, convinced that Leibniz had somehow stolen the idea from him, started a bitter feud.

Although Newton was undoubtedly one of the most brilliant scientific minds in history, his insecurity fostered arrogance and prevented him from distinguishing scientific criticism from personal criticism. He was ridiculed, and he responded by trying to discredit and destroy other scientists. Personal weakness damped, at least temporarily, his scientific impact. Fortunately, he did publish.

Alfred Russel Wallace and Charles Darwin independently discovered the theory and mechanism of evolution. Both recognized the phenomenon of evolutionary divergence, based on extensive observations as a naturalist (particularly in South America). Both spent years seeking a mechanism for this divergence, and both credited their discovery of that mechanism to reading Malthus.