Mathematical Biographies

This set of pages consists of a potted History of Mathematics in the form of a biographical study of famous mathematicians. It covers the period of modern mathematics from Descartes in the early 17^{th} century to the end of the 19^{th} century, when most of what we generally regard as advanced mathematics was created.

The biographies were written by me many years ago, but I have only now brought them up-to-date. They are therefore the product of a considerably younger, though perhaps more enthusiastic mind. I hope to expand on them to make them more readable, accurate, and include just a bit more maths, though I have no intention of laying on any theory. I will, however, try to introduce the mathematical topics in a more meaningful fashion to someone with a basic, modern, scientific background.

As I have indicated, the biographies were written as isolated articles. However, there are enough common threads running through them to give some sense of both the developments made in maths during the period covered, and also the sometime close connections with the more general history of the times. This is most obvious in the explosion of applied maths developed during the French Revolution and its aftermath. In this regard, it would be appropriate to give some sort of introduction, rather than let the reader be thrown into the middle of thousands of years of both mathematical and general history without any preamble. This is something that I intend to develop when I have the chance. However, in the absence of such an introduction at present, I will at least give some sort of idea, as follows.

Arithmetic, in the form of the integer numbers and their most basic manipulation in terms of addition and subtraction, has been with us since prehistoric times: man has always needed to count. As he grew in sophistication, more complicated needs were identified: the ability to measure distance; area; weights and measures; commercial transactions; nautical and astronomical measurements, etc. We can see in this list a requirement for fractions, multiplication and division, simple geometry, together with methods of calculating and recording, which is in essence no different from what the great majority of us still require now.

However, the great developments in maths, or science in general, come not from the demands of everyday life, but from the freedom to explore ideas. The two great periods of mathematical development prior to the modern period are the Greek period, and the Renaissance period, which in common provided this freedom to conjecture, theorise and otherwise expand the subject in every direction.

The Greek Period - from 600BC to 640AD

The Renaissance Period - from 1150AD to 1600AD

Between the destruction of the library at Alexandria and the Renaissance, there is no particular concentration of mathematical activity. However, the increase in population and commerce allowed the survival of much of what the Greeks had produced, and there are notable contributions from the Indian and Arabian civilisations, in particular through the introduction of a sign for zero, decimal notation and other improvements in notation. It should be noted that the preservation of mathematics by the Arabs for many hundreds of years allowed the Europeans time to come out of their dark ages to inherit the Greek legacy and take it to far greater levels.

The Modern Period - from 1640 onwards

The Modern Period is generally recognised to have begun with Descartes, although immediately prior to him there are major advances by several other distinguished mathematicians. I have chosen to end this historical period at the end of the 19^{th} century, although I have not as yet completed biographies of all the mathematicians whom I intend to include. There are a number of reasons for ending my account at this point. Firstly, the explosion in the numbers of people actively employed as research mathematicians in the last hundred or so years has created a subject so vast and diverse that to try to pick a dozen or so of the most significant contributors is impossible. Secondly, a large percentage of recent mathematics is so far beyond the ideas that most people are exposed to in school and work that there is no suitable reference point from where to get a feel for the concepts. I refer in particular to the intense levels of generalisation and abstraction, the imposition of rigour to the theoretical extremes, and sometimes just the obscurity or narrowness of scope. Exceptions to this dislocation are usually found in those branches which find important practical uses, such as the discrete maths of combinatorics, coding theory and graph theory, as well as more analytical branches such as chaos theory. There also remain topics which, although ostensibly having applications elsewhere, exist primarily to exhibit the beauty of maths for its own sake. I am thinking here of elementary number theory, which has had new life provided by the power of modern computers, and finite group theory, which has similarly benefited recently from the use of computers, as well as the contributions of many talented people.