president's address — SECTION A. 11 



declares itself for the first time, wlien the youthful mathematician 

 enters upon the study of Geometry. To Newton the Elements of 

 Euclid appeared so clear and simple that it was a waste of time to go 

 through them. A glance at the enunciation of the theorem, and to 

 him the demonstration was obvious. He passed straight on to such 

 books as Decartes' Geometry and Kepler's Optics. 



Similar stories, if I remember aright, are told of Euler and Lagrange. 

 Again, Clairaut, at the age of thirteen, had written a paper on the 

 properties of some new curves, which was presented to the Academic 

 des Sciences and printed at the end of one of his father's works. 



Clerk-Maxwell, it is hardly necessary to remind the members of 

 this section, published his first mathematical paper at the age of four- 

 teen. For it was at that age that he wrote the paper " On the 

 Description of some Oval Curves and those having a Plurality of Foci," 

 read at the Royal Society of Edinburgh, and published in their 

 Transactions for 1846. 



And, to give one other instance, M. Frederic Masson, in the charming 

 s|)eech which he delivered on the occasion of Poincare's admission to 

 the Academic Frangaise, tells us that his career was settled, when in 

 the Lycee de Nancy, in the Fourth Class, he opened a book on Geometry. 

 His astonished master, who had hoped to make of him a student of 

 letters, hastened to his mother, greeting her with the words — 



" Madame, votre fils sera mathematicien." 

 And we read that she was not dismayed. 



May I be permitted to say, in passing, that the teachers of Mathe- 

 matics in our schools at the present day must be careful if the study 

 of Geometry is to retain its value. Without entering into the vexed 

 question of the extent to which the intuitive method ought to take 

 the place of the deductive, I would only say that the budding mathe- 

 matician must sometimes be troubled by the slipshod argument which 

 he finds in the text-book placed in his hand. Assuming this story of 

 the youthful Poincare is true, it is fair to add that it is most unlikely 

 that the book which roused his ardour was Euclid's Elements. More 

 probably it was Legendre's Geometrie. But Legendre's book stood the 

 test of over a century's use on the continent of Europe, and Legendre 

 was a famous mathematician. Our present trouble is that people are 

 still to be found teaching mathematics in the schools without a proper 

 training for their task. That difficalty we rejoice is passing away 

 with the institution of well-equipped Teachers' Colleges in most of our 

 States. Another cause of the trouble to which I have referred is to 

 be traced to the text-book itself. The authors of these texts are men 

 of a difierent stamp from Legendre. Now that Heath's great edition 

 of Euclid's Elements has appeared, and that the story of the rise and 

 development of the Non-Eaclidean Geometries is more widely known, 

 a more satisfactory state of affairs may arise. 



