The old Scottish sermon used to end with an application, just as many of the stories of my boyhood would have been considered incomplete unless they contained a moral. I cannot end without suggesting that there is a lesson for us in the history I have so imperfectly sketched. The lesson is this, that we must be careful
(i) to preserve a balance in our studies, and
(ii) to remember that science is not the peculiar possession of any one nation.
(i) I believe that Simson did a great work for sound mathematics in his exposition of the ancient geometry, but his admiration for the ancients prevented him from seeing the value of the analytical methods that were beginning to make their way on the Continent and in England. Much as I admire Simson I cannot but think that he did not make the contribution that he was capable of making to the advance of mathematics as a whole; he might have limited his own researches to his chosen field, but he should have been more alive to the importance of introducing his students to the newer disciplines that were transforming the traditional methods.
(ii) The other phase of this one-sidedness is the long neglect of the calculus except in its purely Newtonian form. I think it may be held with good ground that Newton's work was better understood and more fruitfully applied on the Continent than in England. The fatal controversy on the relative merits of Newton and Leibniz worked untold mischief in this country; I hope we may learn the lesson which just at present there may be a danger of neglecting.
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