Noti-Academic Mathematics and Mathematiciajis. 89 



lication, may certainly find a rich treat, but it is intended for 

 mathematicians already made', how they are to be made, or 

 make themselves, are other questions. 



It was with a feeling very like regret that I first read the 

 concluding part of the preceding citation, that is, " we hope 

 to render this department free from the reproach so often ap- 

 plied to works of this class, ^that of creating a race of problem- 

 solvers.^ " I wonder who the cynics were that uttered this re- 

 proach ; depend upon it they were no problem-solvers. If I 

 knew them I would venture to pay them a little attention in 

 passing, even at the risk of being bitten for my politeness; but 

 be the snarlers who they may, it would be difficult to find these 

 gentlemen better qualified, and I should have supposed more 

 fully prepared, to defend the race of problem-solvers from the 

 aspersion, than the three talented editors themselves: this 

 being my impression, I was not a little surprised and sorry to 

 learn that they had shaped their course at all agreeably to 

 the tendency of that reproach ; if my influence with them were 

 half as great as is my respect for their accomplishments, I 

 would induce them to modify that part of their plan; by 

 doing so, in my opinion, they would very considerably extend 

 the usefulness of their praiseworthy undertaking. 



The race of problem-solvers, however, in answer to such 

 reproaches, might exultingly refer to the results of merely sol- 

 ving problems. The theory of the tides, much that is valuable 

 in physical astronomy, various branches of dynamics, &c., owe 

 their neatness and perfection to the solution of some problem 

 once proposed as a challenge or a prize. You cannot read a 

 treatise on the theory of numbers or on any subject connected 

 with the higher branches of the mathematics without finding 

 ample proofs of the fact. All mathematicians are "problem- 

 solvers;" there is scarcely an English mathematician of any note 

 who has not joined or does not at present belong to the race of 

 problem-solvers. As a mental discipline, the theory of the ma- 

 thematical sciences would deserve esteem ; but it is not easy to 

 see how they can be actually applied to useful purposes, ex- 

 cept through the medium of problems. I suppose that all 

 problem-solvers must have a commencement; they can hardly 

 begin at the top, but must work up from questions of mere 

 calculation and petty detail. 



Prof. De Morgan, in a very interesting article in the British 

 Almanac of this year, says, " The higher classes of mathemati- 

 cians at the end of the seventeenth century became excellent 

 computers, and this was particularly the case in England, of 

 which Wallis, Halley, Newton, the Gregories, and De Moivre, 

 were splendid examples During the last century, 



