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Extra info for Actes du Congres International Des Mathematiciens (1970)(fr)(520s)

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There are exact1y 50 such pairs and the sum of the integers in each pair is 101. Hence, the desired sum is the same as 50 times 101, wh ich is 5050. Gauss wrote this number on his slate and handed it to the teacher. The whole process took hirn only seconds. Gauss went on to become a towering figure in mathematics and anyone can make a strong case that he was the greatest mathematician who ever lived. While his insight- PURE MATHEMATICS 41 ful c1assroom ca1culation was not significant mathematics, it was an early indication ofhis genius.

These objects are themselves combined into "spaces" on which certain "functions" are defined. And these functions, which are, by now, at the fourth level of abstraction from anything which can remotely be considered as "natural," become the fundamental objects of the mathematician's interest. The Platonistic point of view must be stretched very thin to provide independent existence to things so estranged from the real world. The creationist viewpoint fails to account, however, for the recurring applicability of some of the purest and most abstract of mathematical structures.

Understand nature. We see this most c1early in the lines and triangles and other figures of Euc1idean geometry whose properties agree almost exact1y with our commonsense notion oftheir real-world counterparts. Nevertheless, the geometrie figures of Euc1idean geometry are abstract objects and live in the mathematical world and not in the real world. A tri angle is an object which exists in the mind of a mathematician. It has properties imposed on it by the axioms ofEuc1idean geometry and other properties which can be deduced from these by the laws of logic and the mIes of mathematics.

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Actes du Congres International Des Mathematiciens (1970)(fr)(520s)


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