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American Mathematical Society, which sends representatives to attend meetings and conferences in Europe, and to report on the latest investigations and discussions, and whose Bulletin is a chronicle of every event taking place in the mathematical world. The fourth International Congress of Mathematicians which met this year at Rome from April 6th to 12th, was attended by about 530 mathematicians from all parts of the world. Of this number only about four per cent. came from Great Britain. The French Government, on the other hand, was represented by eight official delegates, while several other governments, of course not including ours, sent representatives. A number of foreign insurance companies were also represented officially, and a special sub-section met for the purpose of discussing actuarial problems. No English companies availed themselves of this advantage. A small but amusing illustration of England's neglect of mathematics exists at my college. The Surveyors’ Institute annually awards a scholarship to one of our students, and it might be naturally supposed that mathematics was the one subject of which every surveyor ought to know something. But the examination syllabus includes chemistry, physics, geology and botany, while mathematics is excluded. If England is to hold her own against foreign competition by the endowment of research, adequate provision must be made for mathematical research. The mere building of laboratories fitted with costly apparatus, may be a necessary but it is not a sufficient condition of success. The mathematician carries his laboratory in his own brain. This laboratory requires much more careful maintenance and handling than one built of bricks and mortar. It is much more liable to injury if its resources are unduly taxed, and instances of breakdown are common. There is a considerable difference between mathematical research and research in the applied sciences. I have known a student put on to do research in chemistry who could never learn his Euclid. Such “research ' may be purely unskilled labour. All that the student has to do is to put up certain apparatus and perform certain experiments under the direction of his professor. If the experiments are new their performance is described as a research. The performance of student research has been likened to the weighing of a brickbat fifteen times, obtaining a different result each time. There are so many investigations in physics and chemistry that are really worthy of the title “research that the above remarks must be taken as illustrating the abuse rather than the use of this term. But the mere accumulation of statistical data can never produce any lasting addition to our knowledge unless the facts can be made the subject of a connected theory, and for this the services of the mathematician are indispensable. Mathematical research consists essentially in the performance of original work. It involves continuous and concentrated use of the brain. There is no opportunity for the investigator to rest his thoughts while attending to the minutiae of a laboratory experiment. When he is not at work he must obtain all the relaxation he can, and he should therefore be freed from all the petty troubles and anxieties which are not directly associated with his work. What, then, are the best means of maintaining at its proper efficiency the research laboratory which exists in the brain of the mathematician 2 The offering of prizes is a very inefficient method. If ten people compete for the same prize, they will all be engaged on the same research instead of on different subjects, and only one of them will secure any return for the hours of original work which he has devoted to the investigation. The loss of efficiency will therefore be 90 per cent. Even if only two compete the loss will be 50 per cent., and this loss cannot be safely spared in the present age of international competition. A further loss of efficiency also arises from the fact that the competitors have to carry out the investigations not on the subjects on which they have previously formed their own opinions, but on the themes proposed for the competition. Nevertheless prizes are not to be altogether condemned. The competition for the Smith's prizes is responsible for a large proportion of the original work in mathematics now done in this country and these prizes only involve an expenditure of about 50l. per annum. The most promising field for reform appears to lie in the better endowment and multiplication of the mathematical chairs of our University colleges, the provision of more adequate assistance for relieving professors of the elementary teaching necessitated by the present backward state of English mathematics, and the foundation of studentships and prizes awarded on the results of work actually published without restriction as to subject or age of candidate, not for the purpose of enabling the holder to work at some prescribed centre on investigations which may or may not be successful. At the same time the problem is a most difficult one and many points have been left untouched in this article for want of space. VOL. XXV.-NO. 146, N.S. 16

Let us in conclusion turn to a comparison which has been made in certain recent articles between the cost and national importance of endowing universities as centres of higher study and research, and the cost and national importance of building battleships. The nation which provides for research in every department except mathematics may be likened to a nation which builds a battleship armed with the most modern machine guns, but which fails to make adequate provision for that part of the ship under the control of the chief engineer. Perhaps the engines may be of an antiquated type, quite unadapted to modern requirements, and the chief engineer may not be furnished with an adequate staff of assistant engineers. The mathematical teaching of B.Sc. standard required by the students of applied science may be likened to the steam supplied from the boilers to the donkey engines required for moving the guns. This ship will make a very good show in the first stages of the battle, but when the race starts for the conquest of fresh territory she will be left hopelessly in the lurch by her foreign competitors. The first thing that the officers will do will be to blame the chief engineer, but they will soon find that they have no one to take his place, and that their gunners can only manipulate guns, not engines. By the time new engines have been put in and a more adequate staff of engineers has been provided it will be found that the rival ships of other countries have still further increased their vantage, have further improved the efficiency of their engines, and have again increased the staff of assistants working under the direction of their chief engineers.

It is for these reasons that I apprehend a serious danger lest England's neglect of mathematics should culminate in England's ultimate disappearance from the sphere of international enterprise and activity in which England once occupied the premier position.




THE greater part of his life had been spent upon the island, the little island off the blue green rolling hills of the Northumbrian coast, where rabbits and wild birds and a handful of men and women share the glories of clean sunshine and clean winds. Here he had been born, and here with scarcely a night's exception he had slept; but it is not to be thought that he was wholly insular or untravelled. Every day for thirty years he had driven a queer little shambling yellow trap, laden with letters and parcels and occasional passengers, across the sands to the mainland, and had returned in the same fashion in the evening. Sometimes, at very low water, those sands were bare and brown and hard, with only one narrow shallow channel to be crossed; and sometimes his steady cob must pick his way for a mile or more with the water washing over the footboard of the swaying trap ; but the conditions mattered little to horse or driver. The long line of posts were there as steady guides, and could be followed even in the darkest winter night or when the rolling seafret wrapped the land and sea in a grey misty blanket. Then it was necessary to creep more cautiously from post to looming post, and a man was later in returning to his tea upon the island. That was really all the difference that darkness or eccentricities of the weather made to Michael Stamp. The duty was performed with the mechanical ease of practice, and yet undoubtedly the daily journey and the necessity for conversation with strange folk upon the mainland broadened the man's mind, and lifted him mentally a little above the plane of the shrewdly simple islanders. It is extremely doubtful if Michael Stamp was fully aware of his mercies during those thirty years. Perhaps if he had been it would have proved him more than human. Not that he was a grumbler or discontented, but he did accept as a matter of course certain divine gifts that are beyond the hope of luckless townsmen. For life upon the island held few anxieties of food or health. Illness was almost unknown, old age was the one mortal sickness, and food of its kind was cheap and good and plentiful. Butcher's meat might be rare, but home-cured bacon was not, and the boats brought in fish that could be purchased for a shilling a stone. And there were other better matters provided by the gods for his enjoyment. As he drove towards the mainland, with the good salt smell of the sea in his nostrils, it was given to him to look upon a picture, ever varying but ever beautiful, for the daily sight of which a man might well have sacrificed the chance of wealth. Far away to the left a stately castle towered upon the verge of the sea, and before him rose green sloping pastures that merged into blue and purple hills. The yellow smoky glare of a sunset behind those hills, dancing upon the ripples when the tide is in, or gleaming upon the brown naked sands and burning like a flame upon their shallow pools, can only make a man conscious of the clumsiness of words. Not that Michael Stamp in his great wisdom had need to recognise his limitations and futility. He took such matters as they came, in placid silence. Wherefore no man may know how he was struck by the dark winding line of the island as he faced it daily upon his homeward journey, or by the glimpse of the derelict schooner fast upon the sands that would never know again the heave and lift of the wild North Sea. And yet, despite his silence, it is probable that he had a certain still affection for his daily round, for the sands and the posts and the sea, for the wild duck and the screaming wide-winged gulls, and above all for the island, with its wild flowers, its wild birds, and its sand dunes, that was his home. Early in his twenties he had married a mainland girl, and had brought her to a little stone cottage off the straggling main street of the tiny island village. Their one daughter chose the excitements of domestic service in a far-off town, and, when the pain of her departure had been eased by time, Michael and his wife prepared themselves for an old age that should be as peaceful as their youth. But fate had willed otherwise. Michael was fifty-two when the three things occurred that turned aside the placid current of his life. Within one fortnight he found himself a childless widower and a cripple. His wife had never possessed the stamina of the hardy island women, and when the bleak east winds of that winter were at their keenest she contracted a chill which flew speedily to her lungs. Upon the day they buried her it was broken to Michael that his daughter had died of diphtheria two days before. It is the custom upon the island that the vicar of the little parish, brave above the wont of men, shall go in person

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