A response to Reform MP Randy White

One of the research grants singled out by Reform MP Randy White’s research staff to illustrate waste in government, is entitled “Lie theory and its combinatorics”. Your readers ought to know that this has nothing to do with “lying”.

Lie theory is named after the distinguished Norwegian mathematician Sophus Lie (1844-1899). Lie is a common Norwegian name -the first Secretary General of the United Nations was the Norwegian diplomat Trgyve Lie.

Much of mathematics/sciences involves the discovery and exploitation of patterns in various guises. An intrinsic feature of pattern is symmetry and often the naked eye needs guidance to “see” such symmetry. Now the discovery of such symmetries and their utilization involves complex mathematics and oftens leads to the solution of seemingly intractable problems.

In basic school mathematics, one learns how to bisect an arbitrary angle by ruler and compass and how to solve any quadratic equation (polynomial equation of degree two).
By developing abstract ideas based on symmetry considerations, the 19th century French mathematician Evariste Galois was able to crack two longstanding problems; his work led to showing that it was impossible to trisect an arbitrary angle by ruler and compass and that it was impossible to give a formula to solve an arbitrary polynomial equation of degree at least five.

Lie built on the ideas of Galois to develop methods for finding exact solutions to differential equations (which describe the laws of nature) based on finding the (Lie) symmetries of the equation. Lie’s work has had a pronounced influence in modern particle physics (it led to the correction prediction of the existence of a particle prior to experiment, resulting in the Nobel prize in Physics for Ne’eman and Gell-Mann in 1969. Actually, the most modern theories of elementary particles—gauge and string theories—could not even have been formulated without the work of Lie. His theory explains and abstracts basic ideas in the construction of engineering models based on dimensional reasoning. Current state-of-the-art symbolic manipulation software for finding exact solutions to differential equations are based on “Lie” theory.

Lie himself, in a letter to his friend E. Motzfeldt in 1890, wrote, “…my life’s work will stand through all times, and in the years to come, be more and more appreciated–no doubt about it.” He seems to have been absolutely right!