An explanation of the historical development of English mathematics and higher education by Norbert Wiener, in an obituary for G. H. Hardy – with some parallels for today

Once you read enough books you begin to come across curious bits of knowledge that are rarely mentioned nowadays, often in the most obscure sources.

Although George Harold Hardy (1877-1947) was very well known in mathematics circles in the early to mid 20th century, he never attained the prominence even then of other intellectual peers of his generation, such as Bertrand Russell, Albert Einstein, etc., Nowadays he is a remote figure known only to passionate students of the mathematics and the history thereof.

However, thanks to a very illuminating obituary written in memorial by Norbert Wiener in 1947, a fascinating view of the historical development of mathematics, and more broadly that of the scientific and higher education system in England from the 17th to 20th century, comes to light.

Here are the key passages:

“…

Hardy came from a family with artistic and intellectual traditions. He went to Winchester and then to Trinity College, Cambridge. The milieu in which he developed as a mathematician is one which it is particularly difficult for those outside of the English tradition to understand, and even rather difficult for those belonging to the newer English tradition which Hardy himself had so much hand in establishing.

It all goes back to the disputes between Newton and Leibniz concerning the invention of the calculus. At present we have not much doubt of the fact that Newton invented the differential and integral calculus, that Leibniz’ work was somewhat later but independent, and that Leibniz’ notation was far superior to Newton’s. At the beginning the relations between the Leibnizian and the Newtonian schools were not hostile, but it was not long before patriotic and misguidedly loyal colleagues of both discoverers instigated a quarrel, the effects of which have scarcely yet died out. the British mathematicians to use the less flexible Newtonian notation and to affect to look down on the new work done by the Leibnizian school on the Continent. For a while there was no scarcity of able English mathematicians of the strictly Newtonian school. For example, we must mention Taylor and Maclaurin. However, when the great continental school of the Bernoullis and Euler arose (not to mention Lagrange and Laplace who came later) there were no men of comparable calibre north of the Channel to compete with them on anything like a plane of equality.

Part of this must be attributed to the fallen status the British mathematicians to use the less flexible Newtonian notation and to affect to look down on the new work done by the Leibnizian school on the Continent. For a while there was no scarcity of able English mathematicians of the strictly Newtonian school. For example, we must mention Taylor and Maclaurin. However, when the great continental school of the Bernoullis and Euler arose (not to mention Lagrange and Laplace who came later) there were no men of comparable calibre north of the Channel to compete with them on anything like a plane of equality. Part of this must be attributed to the fallen status of the English Universities during the 18th century.

In the 17th century the English Universities were seats of learning comparable with the greatest schools of the Continent, but in the 18th century the grasping new Whig aristocracy that had risen out of the prosperous middle class (the nabobs) took over the older English institutions, the common land, public schools, universities, lock, stock and barrel, as their private property. The public schools were transformed from institutions of a semi-charitable nature to the place where the children of the new aristocracy were formed after its own pattern. The universities became nests of sinecures for dependent clergymen. In this atmosphere creative scholarship did not and could not flourish, and it is not until the 19th century is well under way that we find the signs of a new awareness of what the continental scholars, particularly Laplace and Lagrange, had done in mathematics. Among the English names belonging to this tentative reformation we may mention Boole, Peacock and DeMorgan. DeMorgan in particular is associated with the new University College at London which by its pressure did so much to bring the older universities back to a sense of intellectual responsibility.

This reform of English education was far from complete. The level of mathematics at Oxford was for many years scarcely more than contemptible, and even at Cambridge the training was devoted to the passing of severe examinations, the Triposes, rather than to the development of original mathematical workers. What mathematical talent there was in the British Isles went rather to the formation of a great school of mathematical physicists. Even here Cambridge entered the game rather late. Clerk Maxwell owes more to Faraday, the self-taught practical experimentor, than to any Cambridge man, and neither George Green nor Hamilton was in the Cambridge tradition. Sylvester, as a Jew, was not permitted to enter the older universities till towards the end of his life, and is another of those seminal figures who center around the University of London. Cayley is the first real great Cambridge pure mathematician of the 19th century. He certainly was in touch with those continental scholars whose interest was primarily in algebra, but algebra was at that time an important secondary mathematical subject rather than one in the main stream of development.

It is not remarkable that in such an environment, secluded from the central activity of world mathematics, mathematical study should be devoted rather to the formation of public school ushers or a trial intellectual run for promising barristers than to research activities. As a matter of fact, the Tripos was made such an ordeal, at least in difficulty though in general not in originality, that it marked the culminating point in the intellectual life of many of those who participated in it, and their subsequent activity became retrospective rather than creative. This was the state of English mathematics to about the turn of the century, when an awareness of the great work of the continental mathematicians smuggles itself into England by non-academic bypaths. The English generation of pure mathematicians of the 19th century and the first decade of the 20th century is curiously tentative. It has many important names, such as A. N. Whitehead, Andrew Forsyth, E. A. Hobson and W. H. Young. These all carry to some degree a mathematical style and ethos formed under the older English tradition into a period when the topics of interest were far more continental.

In addition to his accomplishments in research and teaching, Hardy contributed greatly to the reform of mathematical instruction. He was bitterly opposed to the rigid and unmathematical Tripos system and is unquestionably in a large part responsible for the fact that the order of rank of the Wranglers, those who obtain first class in the Tripos, has not been published since 1912. The present mathematical Tripos and indeed the whole system of training at Cambridge has been modified in the sense of conforming very closely to the actual work and career of the mathematicians of this day. Even this change, which has spread from Cambridge to all the British Universities, is a compromise between the old system and a system where research should even more completely take the place of examinations.

…”

Curious indeed when contemplating alongside with the current trends!

From Volume IV of Norbert Wiener: Collected Works

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