We hear a great deal today about the difficulty of persuading school-leavers to take up careers in science. While it was good to see Fintan Gibney's article, "Million dollar prize for mathematical genius", in the Science Today column on July 17th, he failed to comment that one of the seven millennium prize problems for whose solution the Clay Mathematical Institute is offering $1 million, the Navier-Stokes equation, was formulated by that famous son of Skreen, Co Sligo, Sir George Gabriel Stokes (1819-1903).
These days when school-leavers contemplating a university degree in mathematics tell me that "there were no famous Irish mathematicians", this is a golden opportunity to make the point of the headline "Irishman's problem joins million dollar prize list".
The fundamental equations for the motion of incompressible fluids were first written down in 1822 by the French civil engineer Claude-Louis-Marie-Henri Navier, but his analysis was based on a notion of intermolecular forces which would not be accepted by a modern-day physicist.
Using his concept of internal friction of fluids, Stokes was able to put their derivation on a firm basis in 1845, and it is by both names, Navier-Stokes, that these equations are known throughout the world today.
They are used on a daily basis by aeronautical engineers, ship designers, hydraulic engineers and meteorologists. For simple problems such as water flows through a straight pipe or air over a regularly shaped wing, an exact solution to the equations is possible.
In more complex situations, approximate numerical solutions can be found using computers and large-scale computational fluid dynamics software packages. But the problem of finding a general solution to these non-linear partial differential equations remains unsolved.
Part of the problem relates to the existence of boundary or interior layers within the fluid, a situation which means the mathematical solution has to vary extremely rapidly. This makes computation extremely difficult and expensive in time and money.
Mathematical ingenuity could reduce this computational intensity, but our understanding of the existence and uniqueness of such solutions is minimal. The challenge is to find a mathematical theory which will provide the key to the understanding of these phenomena.
Readers interested in making a quick buck (or even just in finding out more about this great Irish mathematical physicist, who became Lucasian Professor of Mathematics at Cambridge) may like to attend the workshop on the Navier-Stokes equations at the third Stokes Summer School in Skreen, Co Sligo, from August 4th to 9th.
The schedule is available on the web at http:// webpages.dcu.ie/ wooda/stokes/ stokes2000.html. Among the speakers is Dr Nick Stokes, a distant relative of G. G. Stokes. The meeting is held in the historic parish hall so attendance is limited to 50. But there are a few places left for those who wish to contact me by email: Alastair.Wood@dcu.ie or telephone 01-7005292. Local residents are welcome to drop in for any lecture without having to pay a registration fee.
Prof Alastair Wood is Wescan Professor of Applied Mathematics in Dublin City University.