History

In Latin, Translated by William of Moerbeke, ca. 1270. William of Moerbeke was the most prolific medieval translator of philosophical, medical, and scientific texts from Greek into Latin. This is the holograph of his translation of the greatest Greek mathematician, Archimedes, with the commentaries of Eutocius. The translations were made in 1269 at the papal court in Viterbo from two of the best Greek manuscripts of Archimedes, both of which have since disappeared. Shown here is a part of Eutocius's commentary on Archimedes' "On the Sphere and the Cylinder" in which he reviews solutions to the classical problem of the duplication of the cube, i.e. how to construct a cube twice the volume of a given cube.

The basis of the monument is not a circle! It is a 17-gon. Although mathematicians have been working on the problem (i.e. to construct regular polygons using a ruler and a compass) in Euclid's time (300 B.C.E.), it was Gauss who discovered it's construction in 1796 when he was an eighteen-year-old. Another significance is it is by this discovery that Gauss decided to spend him life doing mathematics.

The general solution of the quadratic equation was found more than 4000 years ago. The solutions of the cubic and quartic--found in the 1500s--were major results of Renaissance mathematics. Mathematicians struggled for centuries to find formulas for the solutions of equations of higher degree, but despite the efforts of Euler, Bezout, Malfatti, Lagrange, and others, no general solutions were found. Finally, Ruffini (1799) and Abel (1826) showed that the solution of the general quintic cannot be written as a finite formula involving only the four arithmetic operations and the extraction of roots. By 1832 Galois had developed the theory of Galois groups and described exactly when a polynomial equation is solvable.

Galois's work made an important contribution to the transition from classical to modern algebra. Having spent some time in prison for political offences, he was killed in a duel at the age of 21 shortly after his release.