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Great Mathematicians, Great Mathematics

This is a series of lectures to look at the personality and some of the work of a number of famous mathematicians and then discuss more recent developments and applications.

Professor Raymond Flood is Emeritus Fellow and a member of the Continuing Education Department at Kellogg College, Oxford, and is Professor of Geometry at Gresham College.

Raymond Flood has spent most of his academic life promoting mathematics and computing to adult audiences, mainly through his position as University Lecturer at Oxford University, in the Continuing Education Department and at Kellogg College. (from gresham.ac.uk)

Fermat's Theorems
The seventeenth century mathematician Pierre de Fermat is mainly remembered for contributions to number theory even though he often stated his results without proof and published very little.

Newton's Laws
In his Principia Isaac Newton used his law of universal gravitation and three laws of motion to explain elliptical planetary motion, the orbits of comets, the variation of the tides and the flattening of the earth at its poles.

Euler's Exponentials
Leonhard Euler was the most prolific mathematician of all time. He introduced the symbols e for the exponential number f for a function and i for √-1.

Fourier's Series
Joseph Fourier was interested in the mathematical study of the diffusion of heat in solid bodies which he described using infinite trigonometric series which are now known as Fourier series.

Mobius and his Band
Many people have heard of the Mobius band, a one-sided surface, but the work of August Mobius was more far reaching than just inventing a topological curiosity.

Cantor's Infinities
Although many people contributed to the study of infinity over the centuries it was Georg Cantor in the nineteenth century who established its modern development.

Einstein's Annus Mirabilis, 1905
In 1905, his 'year of wonders', Einstein published four papers of ground-breaking importance. First he published the work that introduced quanta of energy - a core idea of quantum theory.

Hamilton, Boole and their Algebras
William Rowan Hamilton (1805-1865) revolutionized algebra with his discovery of quaternions, a non-commutative algebraic system, as well as his earlier work on complex numbers.

Charles Babbage and Ada Lovelace
The central figure of 19th-century computing was Charles Babbage (1791-1871), who may be said to have pioneered the modern computer age with his 'difference engines' and his 'analytical engine'.

Gauss and Germain
Carl Friedrich Gauss (1777-1855) was one of the greatest mathematicians of all time. Possibly his most famous work was his book on number theory, published in 1801.

Hardy, Littlewood, Cartwright and Ramanujan
The collaboration between G.H. Hardy (1877-1947) and J.E. Littlewood (1885-1977) was the most productive in mathematical history.

Turing and von Neumann
Alan Turing (1912-1954) and John von Neumann (1903-1957) had an enormous range of interests not only in pure mathematics but also in practical applications.