A. Martínez,
“Euler’s ‘Mistake’? The Radical Product Rule in Historical Perspective,”
The American Mathematical Monthly
Vol. 114 (April, 2007), pp. 273-285.
Leonhard Euler’s mistake ?
Mathematicians and Historians
claim that He was confused.
Mathematicians widely admire Euler (1707-1783), for his many achievements. Yet for over two hundred years writers have claimed that Euler, though famous for having solved the vexing problem of finding the logarithms of complex numbers, was confused about how to multiply and divide imaginary numbers.
In this article I critically review such arguments and show that actually, Euler’s procedures and results were not wrong— they were quite consistent, yet different from ours. A distinct kind of numerical algebra emerges, similar to ours, but having arithmetical symmetries that are absent in modern elementary algebra.
This episode in the history of mathematics illuminates an alternative direction in which algebra could have developed, but didn’t. It illustrates how variations in the basic rules of math can lead to new kinds of mathematics.
Division by Zero ?
An impossible operation?
This short article discusses a basic
question over which mathematicians,
teachers, and electronic calculators
have disagreed time and again. How do today’s answers compare with answers from hundreds of years ago?
