The Education of a Pure Mathematician

Alfred North Whitehead was born on 15 February 1861, the son of the Reverend Alfred Whitehead, at that time the headmaster of a private school in Ramsgate, and later Vicar of St Peter’s, Isle of Thanet, and honorary Canon of Canterbury. Another son, Henry, became Superior of the Oxford Mission to Calcutta, and ultimately Bishop of Madras. From Sherborne School Whitehead proceeded in 1880 to Trinity College Cambridge, where he remained for the next thirty years. In the Mathematical Tripos of 1883 he was bracketed third wrangler, the senior being G. B. Mathews, afterwards Fellow of St John’s, F.R.S., and a distinguished pure mathematician: in 1884 he was elected a Fellow of his college, and a few months afterwards was put on the staff as an assistant lecturer. In 1890 he married Evelyn, daughter of Captain A. Wade of the Seaforth Highlanders, and niece of the famous Chinese scholar and diplomat Sir Thomas Wade. In my undergraduate days at Trinity when he was the junior member of the mathematical staff, he had a place apart among our teachers, chiefly because his philosophic urge to grasp the nature of mathematics in its widest aspects led him to study what were at that time considered out-of-the-way branches of the subject: for instance, he offered a course of lectures on ‘Non-Euclidean Geometry’: this would not be thought remarkable nowadays, but the schoolmasters of that day had not prepared us for the existence of any alternative to Euclid: and we became much interested, particularly when we found that the lecturer could tell us also about algebras in which the commutative rule of multiplication, ab=ba , was not obeyed. He was in fact at this time writing a book on such topics, which was published in 1898 under the title A Treatise on Universal Algebra, with Aplicatons , the title being taken from a paper of Sylvester’s which had appeared in 1884. ‘The purpose of this work’ he said in the preface, ‘is to present a thorough investigation of the various systems of symbolic reasoning allied to ordinary algebra. The chief examples of such systems are Hamilton’s Quaternions, Grassmann’s Calculus of Extension and Boole’s Symbolic Logic.’

The contributions of J.J. Sylvester, F.R.S., to mechanics and mathematical physics

Notes and Records the Royal Society journal of the history of science ◽

10.1098/rsnr.2001.0142 ◽

2001 ◽

Vol 55 (2) ◽

pp. 253-265 ◽

Cited By ~ 1

Author(s):

I. Grattan-Guinness

Keyword(s):

Mathematical Physics ◽

Professional Career ◽

Pure Mathematics ◽

Pure Mathematician

A survey is made of the papers written by J.J. Sylvester (1814–1897) on mechanics and mathematical physics. Some relate to aspects of his professional career. They form only a small part of the output of this largely pure mathematician, but are of variety and intrinsic merit. Their limited total exemplifies the limited measure of interest that physical applications sustained among some mathematicians during a period when the preference for pure mathematics was increasing worldwide.

Solomon Lefschetz, 1884-1972

Biographical Memoirs of Fellows of the Royal Society ◽

10.1098/rsbm.1973.0016 ◽

1973 ◽

Vol 19 ◽

pp. 433-453 ◽

Cited By ~ 3

Keyword(s):

Personal Influence ◽

Mathematical World ◽

Pure Mathematician

Solomon Lefschetz, who died on 5 October 1972 at the age of 88, was a dominant figure in the mathematical world, not only for his outstanding original contributions to at least three branches of mathematics, but also for his personal influence in creating world famous centres of mathematics at Princeton, Mexico and elsewhere. All this was achieved in spite of a crippling handicap caused by an accident in 1910 which forced him to abandon his chosen career as an engineer and begin again from scratch as a pure mathematician.

The Pure Mathematician as Hero

From Servant to Queen: A Journey through Victorian Mathematics ◽

10.1017/9781316415726.004 ◽

2019 ◽

pp. 111-144

Keyword(s):

Pure Mathematician

Discrete random Processes

Journal of the Staple Inn Actuarial Society ◽

10.1017/s0020269x00003686 ◽

1949 ◽

Vol 8 (04) ◽

pp. 204-209

Keyword(s):

Random Process ◽

Random Variable ◽

Random Processes ◽

Discrete Random Variable ◽

Pure Mathematician ◽

Discrete Values

If a variable assumes the discrete valuesxj(j= 1, 2, 3, …) with specified probabilitiesf(xj), wheref(xj) it is said to be adiscrete random variable. If a discrete random variable is also a function of a continuous (non-random) variable, for convenience usually assumed to be ‘time’, it is called adiscrete random process.A class of discrete random processes of particular interest to the pure mathematician and to the mathematical statistician has been calledstochastically definiteby Kolmogoroff (1931). Such a random process is distinguished by the fact that the probability that the random variable concerned assumes a given valuenat timetdepends only on the valuemassumed by the variable at times(s < t) and not on the values assumed at any intermediate or earlier points of time. This circumstance is allowed for by writing the probability of the valuenat timetin the form Pmn(s, t).

The Theory of Order, as Defined by Boundaries

The Mathematical Gazette ◽

10.1017/s0025557200012882 ◽

1911 ◽

Vol 6 (94) ◽

pp. 135-142

Author(s):

E. T. Dixon

Keyword(s):

General Theory ◽

Objective Measurements ◽

Concrete Application ◽

Pure Logic ◽

Pure Mathematician

I propose in these papers to demonstrate, or rather to indicate the nature of the demonstration of, the proposition that—All Geometry, whether projective or metrical, may logically be regarded as merely a particular concrete application of the general theory of Order, as defined by Boundaries. It is true that Geometry, as ordinarily understood, is something more than this; it is concerned with the actual subjective conceptions we entertain of Space, and so far provides matter of discussion to the Psychologist; and it is concerned with the actual objective measurements we make upon physical bodies in Space, and so far concerns the Physicist; while in both these respects it extends beyond the region of pure Logic into those of Epistemology and Philosophy generally. But so far as the pure Mathematician is concerned, every geometrical theorem is embraced in the Theory about to be discussed.

The Education of a Pure Mathematician

American Mathematical Monthly ◽

10.1080/00029890.1999.12005111 ◽

1999 ◽

Vol 106 (8) ◽

pp. 720-732

Author(s):

Bruce Pourciau

Keyword(s):

Pure Mathematician

The Practical Man and the Pure Mathematician: A Moral Essay

Mathematics Magazine ◽

10.2307/3029466 ◽

1959 ◽

Vol 33 (1) ◽

pp. 33

Author(s):

Lyle E. Pursell

Keyword(s):

Pure Mathematician

Address of the President, Sir Cyril Hinshelwood, at the Anniversary Meeting, 1 December 1958

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1959.0002 ◽

1959 ◽

Vol 249 (1256) ◽

Keyword(s):

Finite Order ◽

Tauberian Theorem ◽

Tauberian Theorems ◽

Minimum Modulus ◽

Pure Mathematician ◽

Original Theorem ◽

The Way

Award of Medals 1958 The Copley Medal is awarded to Professor J. E. Littlewood, F. R. S. At the present time J. E. Littlewood is, by general agreement among mathematicians, by far the most eminent pure mathematician in this country. His papers contain deep and difficult solutions of important problems, and have opened new fields for investigation. The papers on the minimum modulus of integral functions of finite order (1908) led the way to further developments including a major problem only recently solved. The Tauberian theorem for powers series (1915) was an important step forward from Tauber’s original theorem and even from Hardy’s Tauberian theorem for Cesaro summation, and might be regarded as the true beginning of what is now recognized as an independent subject, Tauberian theorems.

Obituary Notice of Fellow deceased

Proceedings of the Royal Society of London ◽

10.1098/rspl.1883.0070 ◽

1883 ◽

Vol 36 (228-231) ◽

Keyword(s):

British Association ◽

Mathematical Science ◽

Exact Science ◽

Naval Architecture ◽

Inherent Difficulty ◽

Great Loss ◽

Rule Of Thumb ◽

Pure Mathematician ◽

Obituary Notice ◽

The Revolution

In the death of Mr. Charles Watkins Merrifield, mathematical science generally, but particularly those branches which relate to nautical matters, have suffered great loss. Since the deaths of Rankine and William Fronde, no one has passed away whose presence will be so greatly missed at the annual gatherings of the Institution of Naval Architects, and that of Section G of the British Association. Mr. Merrifield, although essentially a mathematician, and even a pure mathematician, was one of the few to whom the revolution from the rule of thumb to that of exact science in naval architecture was immediately due. The part which he undertook in this movement, although of the greatest importance, is from its nature unlikely to attract notice. And for this reason, perhaps, as well as from the labour involved, as much as its inherent difficulty, was much neglected at the time when Merrifield commenced his work.