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Name: tom karchesy
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995

Can you do mathematics without numbers?



It is terribly unfortunate that "mathematics" is only arithmetic for grade schoolers (at least it was for me). Higher mathematics like geometry, set theory, and trigonometry involve concepts other than just numbers.


Actually, I was reading recently that the ancient greeks may have decided that numbers were not to be trusted after the catastrophe discovered by the Pythagoreans (which they apparently tried to keep secret) that the square root of 2 was not a rational number. Hence Euclid, and the development of geometry as a replacement for arithmetic (arithmetic is all contained in the geometry of line segments on a straight line). Grade schoolers really should be informed that arithmetic and geometry are mathematical develop- ments that are already over 2000 years old, and a lot has happened in mathematics since then!

(Of course I guess it took a while for zero and place-holding numbers to become accepted, but still . . .)


There are some numbers that are important as they represent fundamental concepts. Examples are 0, 1, pi, e, and i. Amazingly, these are all neatly related by the expression e^(i x pi) + 1 = 0.


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