Someone once said to me that higher mathematics was useless. I replied that since it controlled every computer on the planet, it seemed pretty useful to me. One of my favorite areas of math is abstract algebra. Abstract algebra grew out of the work of French mathematician Evariste Galois around 1830.

In the 1500’s Italian mathematicians had worked to find formulas to solve the cubic (x³) and quartic (x^4) equations. Then, for almost 300 years, mathematicians worked to find a solution for the quintic, or fifth degree equation. Finally, in the early 1800’s, the work of Galois and Abel proved that there is no general solution for equations with powers of x higher than 4.

From this work grew the field of abstract algebra. Prior to Galois and Abel, between 1750 and 1820, many mathematicians contributed significant ideas to what would become known as abstract algebra. Euler, Gauss, Legendre and Lagrange (1750-1820 or so) all worked with what is known as modular arithmetic. Modular systems and discrete mathematics became very important in the mid-20th century with the development of the digital computer.

Here’s a link to a paper I wrote about some of these ideas

Mathematics, Communication and Secrecy

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