Tankred Tunstall-Behrens, commissioned into the Royal Engineers in 1897, entered Clifton College in 1892 at the age of 14 intent on sitting the chiefly mathematical entrance exam for the Royal Military Academy, Woolwich. Three hundred and eighteen letters, by, from and concerning Tankred give a vivid picture of the boy's mathematical progress towards this goal.
Between the ages of eight and 13, at the Dragon School in Oxford under its progressive and enlightened headmaster, C C Lynam, himself a mathematician, Tankred had shown marked ability. He writes from Clifton in his third term:
"I don't know as much Maths as I did when I 1st came here, I am still doing, Combinations, Permutations, amp; Binomial Theorem, which I have been doing every term since I have been here. In Euclid I am doing the 3rd amp; 4th books. In Trigonometry I am beginning Logarithms and the solution of (triangles) with Logs as if they were new I have so utterly forggoten them although I knew them fairly last year".
Clifton was a different world from the Dragon School. Tankred was taught by the later famous author of mathematical textbooks, H S Hall, of whom the boy was easily contemptuous, and judged him short on explanation and insistent on drill and learning the method, and rigorously intent on getting his pupils through the Woolwich examination.
Clifton was a mathematical success story in the competitive world of the new public schools, and Hall embodied that competitive ethos. He would have things done his way. In a letter to Tankred's father in the boy's fifth term, he writes of: "the folly of trying to take a line of his own in defiance of all the teaching amp; warning he gets from me...there are certain recognised canons of good style, amp; 'good form' in mathematical work - without appreciating these fundamental principles of style and method a boy cannot become a Mathematician in any real sense. Moreover, in working for a competitive exam it is of the utmost importance that good methods wich conduce to accuracy amp; pace, shd be enforced."
Tankred was successfully drawn along by Hall: he was beginning analytical conics in January 1894 at the age of 15-and-a-half, couldn't understand a word of it and was "very hazy about my Dynamics". But two months later he could do problems in analytical conics "if I have the formulae before me but I dont know my formulae". By the age of 16 he could tackle problems of the kind reproduced here (taken from 1892 Clifton higher exam papers).
Plainly Hall's methods worked, though Tankred also had quiet assistance from a non-schoolmaster mathematician drafted in to help during the flu epidemic of 1895: "he is very patient amp; does not mind explaining I like him very much" and, during the holidays, from Mr Edwards, the head of the National school near his home in London, who was plainly a teacher of genius.
It is clear from these letters that Tankred loved mathematics at the Dragon School and hated it at Clifton. He writes to his father after only a week there: "Mr Hall teaches me Maths, but he makes the lessons intolerable amp; if it does not alter soon somehow, I shall begin really to hate Maths altogether. He growls at my style not of writing but of putting down my sums with a very few words, I know it is not quite right how I do them."
Clifton and H S Hall got him into Woolwich but perhaps at some cost to his mathematical energies. A friend of his family was the wife of the mathematician, George Boole. Three days after Tankred had written to his father, on December 2 1894, detailing textbooks he needed for the holidays - Salmon's Conics, Loney's Elements of Statics and Dynamics, Greaves' Elementary Statics - Mrs Boole addressed a meeting on "the safeguarding of the faculty of originality in children". It was not her view of mathematical education, nor C C Lynam's, that would do for Clifton and Woolwich.
'Letters between a Victorian Schoolboy and his Family 1892-1895', edited by David and Julie Crane, published privately, 1999 (ISBN 0 948545 11 9) or tel: 0191 384 7859