484 



NA TURE 



[March 27, 1902 



LETTERS TO THE EDITOR. 



( Tht Editor does not hold himself responsible for ofiiiiions ex- 

 pressed liy his (orrespondeiils. Neither can he undertake 

 to return^ or to (ot respond zvitli the writers of rejected 

 manuscripts intended for this or any ol Iter part of NATURE. 

 No notice is taken of anon vinous communications. ] 



The Teaching of Mathematics. 

 Many correspondents who hold views much like my own are 

 angry that I should lend my countenance to the sort of reform 

 in mathematical teaching which is now being so strongly advo- 

 cated by the recognised teachers and by mathematicians. I beg 

 to assure these friends that I am acting in a very consistent way, 

 and I mean to help the reformers so long as they do me the 

 honour to let me assist them. 



My dearest wish is that Englishmen should prepare for the 

 new phase in the struggle for existence which has so suddenly 

 come upon the world. I believe that it has been growing for 

 sixty years, that it is going to be very intense during the next 

 twenty years, that it will be important for the next hundred 

 years and that the weaker nations will have been completely 

 defeated before the end of that time, before people in general 

 recognise their foolishness in wasting coal. At (Glasgow I was 

 sneered at as thinking that all men were going to be engineers. 

 Would to heaven that I could think of all young Englishmen 

 as being fit to become engineers ! I firmly believe that no nation 

 will survive the coming struggle which does not equip itself with 

 that thorough training in applied science which I call engineer- 

 ing. I do not expect to be believed by our schoolmen. They 

 •do not know, and they would not care much if they did know. 

 The study of natural science has been discouraged by clerical 

 schoolmasters and ecclesiastics, and men like Huxley worried 

 themselves very vainly in consequence. But the time is quickly 

 coming when, instead of the castigating rod of Huxley, we shall 

 feel the stinging scorpions which fate provides for all men who 

 set themselves to believe lies. There is just one chance for us ; 

 it has befriended the English people at several critical times, 

 namely, that however foolish we may be, other nations may be 

 as foolish or even more foolish still ; and possibly our people 

 may attend, in good time, to the sort of advice which they so 

 usually laugh at. 



I say that if even a small amount of knowledge of natural 

 science and of scientific method could be given to our public 

 men it would be a good thing. Now all influential Englishmen 

 pass their youth and get what is fondly called education at the 

 public schools and the two older universities. I have satisfied 

 myself that the authorities of these institutions will steadfastly 

 set their faces against any such large and radical reform as I 

 have asked for ; I was quite sure of this before I gave my 

 address at Glasgow. It was only during the discussion that I 

 began to get hope of any reform whatsoever in these institutions, 

 and now I am sure that, not only is a small immediate reform really 

 possible, but that this reform will increase as the years go on. 



It is true that I was thinking of other universities, of other 

 schools and colleges, but if any reform, however small, is 

 possible in these great institutions, surely it is the duty of every 

 lover of his country to help forward this movement. When 

 one thinks that Clifford and Cayley and Sylvester and the other 

 great mathematicians of the British Association Committee of 

 1S73 advocated for English public schools the very reforms in 

 geometrical teaching which are now being asked for, and that in 

 most of the public .schools the teaching is even more stupefying I 

 now than it was in 1873, one is not likely to be very sanguine. 

 But I have satisfied myself that there is a power now behind the 

 reformers which is very much more earnest and persistent than 

 Clifford could rely upon ; indeed, I am satisfied that the reformers 

 have with them the good wishes of every thoughtful teacher of 

 the whole country. And after all, would not even the smallest of 

 NO. 1 69 I, VOL. 65] 



reforms be exceedingly important in the public schools of 

 England ? 



Eton and Harrow and Winchester and the rest, are they not 

 great in every way? Oxford and Cambridge, what greater 

 names are there than these among universities? These institu- 

 tions in the past have educated the great men of England. I 

 think I see immense faults in them, but when I compare them 

 with all other schools of which I know anything, do I not 

 know that in mental and bodily health their pupils are great 

 in number and in quality ? And if just now a time of strain is 

 coming for which these institutions are quite unprepared, shall 

 I sulk and say that because they will not do as I think they 

 ought to do, then it is better that they should do nothing? To 

 tell the truth, I think that our schools with a small reform will 

 be equal to foreign schools even if these have every advantage 

 that the latest notions in pedagogy can give them. Never- 

 theless, is it not rather the good material that comes to these 

 schools for education than the schoolmasters of the schools that 

 has our admiration ? I feel myself that we are arming our 

 people with bows and arrows when we might easily give them 

 magazine rifles with telescopic sights. But surely, if it must be 

 bows and arrows, and nothing better is possible, one is doing 

 good by advocating the employment of the very best kind of 

 bows and arrows. 



I asked for a countenance from the mathematicians at 

 (jiasgow for a much more radical reform, not in the public 

 schools and the two older universities — there I thought all 

 reform impossible— but in the new universities, in all colleges 

 where the study of natural science, and especially of applied 

 science, is important. Although all the speakers were in favour 

 of reforiTi, quite half of them were out of sympathy with what 

 I consider to be most essential. I know that they represent 

 the great majority of the mathematicians and teachers of the 

 country, and I should like again, however hopelessly, to 

 explain my position to them. They refuse to attempt to look 

 at things from my point of view. Their minds are beautifully 

 in tune ; what one scholar says, the mind of another responds 

 to, but if anyone not a scholar of the orthodox type says any- 

 thing, it is not heard at all, or only that part of the message is 

 heard which is in tune with the receiving brain. My message 

 must continue to seem to them very absurd if they make no 

 effort to synchronise their mental apjiaratus with mine. 



I assert that the orthodox logical sequence in mathematics is 

 not the only possible one. I can imagine a sequence leading 

 men of twenty-five to a proof of the axioms of Euclid ; where it 

 would start I do not know, perhaps in Berkeley's notions of 

 sensation and that all matter and motion and shape are 

 merely forms of consciousness. Surely every academic person 

 will .admit this as feasible. But he will not admit that there 

 might be a thoroughly logical sequence starting with axioms 

 which are now " proved " after many years of study, the notions 

 underlying the infinitesimal calculus, for example ; the notion 

 that a map may be drawn to scale ; the notions underlying the 

 many uses of squared paper ; the notion that decimals may be 

 dealt with like ordinary numbers. 



The swineherd Ho-ti and his son Bo-bo discovered the 

 wonders of roast pork through the burning of their cottage, and 

 they and their neighbours and every mandarin of China who 

 studied the matter considered that it was absolutely necessary 

 to burn a house down if one wanted roast pork. So the cult of 

 house-burning arose in the land. But after many generations 

 there came a sage of the name Pel-li, who pointed out to every- 

 body that it was not necessary to burn houses, as a simple 

 domestic fire was all that was needed. And he and his growing 

 number of disciples were envied till a charge of impiety was 

 brought against him. And of all the hundred accusers of I'elli, 

 all mandarins of high rank, every one was absolutely honest 



