Rest assured, however, that I am myself absolutely convinced that the man educated on old-fashioned lines, equally whether this education was practical in tendency or dealt largely with traditional learning, will not be fitted for living in the new world which is becoming. To be able to think even is not enough; it must be the man who thinks without effort, to whom thinking is a natural process, who is, so to speak, going on thinking all the time (the man who at most thinks about his job and finds thinking at other times an intolerable effort, is not adequate) who alone will be capable of dealing with new conditions as they arise, who will have the imagination to foresee undreamt of possibilities of which the past offers no examples. The man of the future must, I say, be above all things a thinker, and a thinker of the dynamic type whose subject of thought is a universe of events and not one of things. My reasons for talking to you about the Theory of Functions of a Real Variable are : (i) It is a new subject introduced into your curriculum. (ii) It is a living subject to-day, growing and likely to grow for some time to come; so that it does not yet belong to the codified type of mathematics. Accordingly anyone studying it, has impressed upon him the fact that there is no such thing as absolute knowledge, that there are always problems which are unsolved at any given moment, but which will certainly be solved. A student in such a branch will certainly in the course of his training come across problems which, when he first hears of them, are unsolved, which as time goes on are being seriously attacked, and which, before he has completed his studies, are solved. If he is really an able man, he may himself take a part in such a solution. In any case, his attitude of mind toward the innumerable problems which present themselves in ordinary human affairs, will not be that of a fatalist; he will have no use for the man who explains to him more or less elaborately that such problems are necessarily insoluble. (iii) It is not only a living and a growing subject, it is a subject which is particularly characteristic of the twentieth century. The advances made in it are without a doubt the most remarkable advances which mathematical science has to show in the twentieth century so far, and it accordingly finds its adherents all over Europe. (iv) Its results, and more especially its leading ideas, are of fundamental importance in that branch of mathematics which in the last half of the nineteenth century held the field and still has many disciples, as it is bound always to have, viz., the Theory of Functions of a Complex Variable. (v) It is almost certain that it is the most admirable example in mathematical science, which is itself a science of pure thought, of the creative power of the human mind. The steps taken in its elaboration at once dwarf and render intelligible earlier steps in the progress of the science. No more sharpening process can be imagined for the intellect than that which its study requires. It deals too with the very latest of the new sciences which the human mind has created for itself. For the first time that which is in itself a mere negation, the finite or the non-finite species of the impossible, has been yoked to the car of intellectual progress and rendered completely subservient to the needs of the intellect. (vi) I may perhaps be allowed to add as a further reason-not so much the fact in itself that I have actively occupied myself with researches in the Theory of Functions of a Real Variable, but rather the connected circumstance, that the somewhat numerous papers which I have written on the subject are almost all of them in the English language and are published in periodicals which should be easily accessible to you. These papers are, for anyone who has the time, energy and will power necessary for their systematic study in chronological order, a convenient means of approach to the very heart of the subject. I give these as my reasons for talking to you about the subject, and I hope when I am gone they will be regarded as reasons why it should continue to be studied, if possible, in an ever-increasing degree. Some present may feel daunted with the prospect of the hard thinking which may be involved; to such I do not address myself. Nations which have become great have owed it to their possession of only a few great men and to the willingness of others to follow them. It is those who would fain become leaders that I have in mind. Such men must be capable of sustained mental effort, and the training in accurate thinking and in the attacking of new problems that I am now advising for them, is the best purely intellectual training which in the present state of human intellectual progress can be conceived. (Even the older mathematics has been acclaimed by the best lawyers both in England and in India as the study which best prepares a student for the study of law. The legal system, however, is even in the British Empire, more or less codified, and we may use a proportion and say that, as codified mathematics is to the study of other codified knowledge, so is growing mathematical science in its subtler forms, to the investigation of the various problems of human life and learning in all their complexity and difficulty. The growing mathematical science exercises in fact those additional faculties of the mind which codified mathematical science does not.) But it would lead me too far afield if I were to attempt now even to enumerate reasons for the study of mathematics as I here understand the term. I can only say that the more distinguished men of science and learning whom I have met, are expecting a magnificent future for mathematical studies, and it is but slight exaggeration to say that some of them are even now all but counting the days to the time when they will be able to work hand in hand with the mathematician, and this not by his descending to their non-mathematical level, but by their rising to his. Calcutta. W. H. YOUNG. VERNACULAR EDUCATION IN BY HERBERT A. STARK. ADDITIONAL BIBLIOGRAPHY. Banerjee, Sir Gooroo Dass.-A Personal Letter, dated 3rd September, 1914, relating Boutros.-An Enquiry into the System of Education in India. (Serampore, 1842.) Cameron.-An Address to Parliament . . . in respect of the Education of the Chakrabarti, Thakur Das.-Thoughts on Popular Education. (Calcutta, 1870.) Day, Lal Behari.-Primary Education in Bengal. (Calcutta, 1869.) Four Articles on Mr. A. M. Monteith's Report, 1867. Hunter, Sir W. W.-Life of Lord Mayo. Johnston.-Abstract and Analysis of the Report of the Indian Education Commission, with Notes, and Recommendations in full. (London, 1884) Junius (Pseud.)-Two Letters on the Education of the People of India. (Serampore, 1835.) (London, 1860.) (Madras, 1881.) Marlborough.-Education in India. Short Essays and Reviews on the Educational Policy of the Government of Sykes. Statistics of Education at Institutions of the East India Company in India. (Calcutta, 1845.) Treatise on Popular Education in India. (Calcutta, 1841.) From the Resolution of Lord William Bentinck to the Abolition of the Committee of General Instruction in 1842. LET us return to the promulgation by Lord William Bentinck of his Resolution of the 7th March, 1835. Within a fortnight of that date he quitted the shores of India, and heard but little of the keen disappointment with which his pronouncement was received by the Orientalists. They had not altogether expected his verdict; and his new (but not quite new) policy was unpalatable to them. The Hon'ble Mr. Shakespear, from conscientious scruples, resigned his seat on the Committee of Public Instruction. The numerous pandits of tols and maulavis of madrasahs knew that their day was gone. The scores of pupils who, in the institutions of "indigenous learning," for a long series of years had been "maintained from childhood" on "bounties and premiums" lavished upon them by the Honourable East India Company, realized that they must now lose their "decent living." The cry, therefore, went up, loud and strong, against the edict of the departing Governor-General. It reached the ears of Lord Auckland the moment he entered upon his exalted office. He examined the whole position, and in a Minute, dated the 24th November, 1839, he expressed the belief (the Court of Directors concurring) that the insufficiency of funds assigned for the purpose of native education was the chief cause of the disputes which had arisen in the Committee of Public Instruction, and of the complaints (1) that oriental colleges had been weakened by the transfer of funds from them for the support of English classes under the same roof, or to other institutions where English instruction was being imparted; (2) that instruction in English had become the main teaching, and that only a subordinate position was given to the vernaculars; and (3) that the abolition of stipends in oriental seminaries had caused much suffering to those who had been drawing them. He, therefore, ordained that all the funds which, previous to Lord William Bentinck's Resolution, had been assigned to oriental instruction, should be restored to the oriental colleges; and that any additional funds which might be required for the promotion of English instruction, should be supplied by new grants from the public purse.* With regard to the medium of instruction he held that two great experiments were in progress-one in Bengal, where education was being imparted through the medium of English, and the other in the Bombay Presidency, through the medium of the vernacular language. He was in favour of both experiments * In 1836 the sum of Rs. 3,89,500 was at the disposal of Government for educational purposes. In 1840 Lord Auckland increased the allotment by Rs. 1,50,000, |