MA 330WX: History of Mathematics

Includes mathematical knowledge in the major civilizations, such as Egyptian, Mesopotamian, Persian, Mayan, and others.

Dates: 600 BC to 400 BC
Because of the foundational role of Greek mathematics, especially geometry, for all subsequent discoveries and developments, this is one of the most prominent fields of research, including the development of the axiomatic method, proof procedures, irrational numbers, and more.

Dates:400 to 1400
A comparatively lesser field somewhat reflecting the decline of mathematics in the West before its resurgence in the work of such figures as Leonardo Pisano and the spread of the Hindu-Arabic numerical notations.

Dates: 1400 to 1600
This period witnessed crucial development beyond the scope of Greek mathematics, including the growth of algebra, including the first solutions to cubic and quartic equations, the early use of negative and imaginary numbers, trigonometric formulae, and more.

"Leonhard Euler, one of the greatest and most prolific mathematicians of all time, dominates this century. This period's central themes include the development of infinitesimal analysis and its notations, power series, the introduction of the concept of function and the early development of number theory."  - Linda Hall Library

Among many other developments, this century saw the creation of non-Euclidean geometries, of projective and Riemannian geometries, and set theory and mathematical logic. It also witnessed the rapid growth of number theory, group theory and topology (analysis situs).

The extreme level of abstraction and generality that characterizes contemporary mathematics renders much of the enormous wealth of this period inaccessible to historians who are not mathematicians themselves. Among the highlights of the past century are the following ones, with implications that are beginning to be felt in physics, cosmology and philosophy: Category theory, topos theory, algebraic geometry, and cohomology theories.