Glenn McDavid (gmcdavid) wrote,
Glenn McDavid
gmcdavid

"A mathematician's reputation rests on the number of bad proofs he has given."

--A.S. Besicovitch. From Cool Math Quotes

The point of this is that the real advances in math are made by very creative minds who have some great idea, and find a way to prove it by any means they can think of, and then move on. Afterwards other mathematicians read about the new theorem or whatever, and then come up with other proofs which are shorter, more elegant, easier to follow, etc. But they are not the ones who have the original idea, and do not become famous for that work. Like in other kinds of exploration, the pioneers get the credit. Finding a shorter or more comfortable way to make the voyage is nice, but not the same.

I was reminded of this because I just started reading Gamma: Exploring Euler's Constant, by Julian Havil. The first chapter is about the invention of logarithms by John Napier, who published his work in 1614. Havil presents Napier's orginal geometrical argument, with commentary. It is quite difficult to follow, and I spent a couple hours with pencil and paper before I felt I understood it. Today we just define them in terms of exponents and avoid all that hassle. Also, Napier's original logarithms are not our contemporary base 10 or base e logs. In modern terms, he used base 1/e.

Henry Briggs, an Oxford Professor of Geometry, quickly became an enthusiastic fan of Napier's ideas. He visited Napier in 1615 and 1616 and they discussed some variations of Napier's concept. It was Briggs who chose to compute logarithms using base 10. But the original idea was Napier's.

Incidentally, I learned how to compute with logarithm tables in High School, back in the 1960's. The advent of (relatively) cheap electronic calculators a decade later rendered them obsolete as a computational tool, but the concept of the logarithm is of enormous theoretical importance, and will always remain so.

Tags: book notes, calculators, history, math
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