Day 53

Grothendieck, A.

Now in the past two decades, the ethics of the scientific profession (at least among mathematicians) have become so degraded that wholesale plundering of ideas (and particularly at the expense of those in no position to defend themselves) has become almost the general rule among scientists. It is at any rate tolerated by all, including in the most glaring and ubiquitous of cases.

Under the circumstances, agreeing to play along with the practice of granting prizes and rewards would also be endorsing a spirit and a development in the scientific world that I see as unhealthy and bound to disappear in the near future, for it is so suicidal spiritually as well as intellectually and mate­rially.

‘The mathematician who turned down a $150,000 prize’ in the ‘Le Monde’ section of The Guardian Weekly, May 15 1988 p. 17.

Day 52

Hardy, G.H.

I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ‘Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms’.

A Mathematicians Apology (Cambridge University Press; 149, reprinted 1967) p. 148

Day 51

Hardy, G.H.

… I will state my own position dogmatically in order to avoid minor misapprehensions. I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations', are simply our notes of our observations.

A Mathematicians Apology (Cambridge University Press; 149, reprinted 1967) p. 123.

Day 50

Russell, B. (1872-1970)

One effect of [the First World War] was to make it impossible for me to go on living in a world of abstraction. I used to watch young men embarking in troop trains to be slaughtered on the Somme because generals were stupid. I felt an aching compassion for these young men, and found myself united to the actual world in a strange marriage of pain. All the high-flown thoughts that I had had about the abstract world of ideas seemed to me thin and rather trivial in view of the vast suffering that surrounded me. The non-human world remained as an occasional refuge, but not as a country in which to build one’s permanent habitation.

In this change of mood, something was lost, though something also was gained. What was lost was the hope of finding perfection and finality and certainty. What was gained was a new submission to some truths which were to me repugnant. My abandonment of former beliefs was, however, never complete. Some things remained with me, and still remain: I still think that truth depends upon a rela­tion to fact, and that facts in general are non-human; I still think that man is cosmically unimportant, and that a Being, if there were one, who could view the universe impartially, without the bias of here and now, would hardly mention man, except perhaps in a footnote near the end of the volume; but I no longer have the wish to thrust out human elements from regions where they belong; I have no longer the feeling that intellect is superior to sense, and that only Plato’s world of ideas gives access to the ‘real’ world. I used to think of sense, and of thought which is built on sense, as a prison from which we can be freed by thought which is emancipated from sense. I now have no such feelings. I think of sense, and of thoughts built on sense, as windows, not as prison bars. I think that we can, however imperfectly, mirror the world, like Leibnitz’s monads; and I think it is the duty of the philosopher to make himself as undistorting a mirror as he can. But it is also his duty to recognize such distortions as are inevitable from our very nature. Of these, the most fundamental is that we view the world from the point of view of the here and now, not with that large impartiality which theists attribute to the Deity. To achieve such impartiality is impossible for us, but we can travel a certain distance towards it. To show the road to this end is the supreme duty of the philosopher.

‘The Study of Mathematics’ The New Quarterly (1907) reprinted in Philosophical Essays (1910) and in ‘The Retreat from Pythagoras’ in My Philosophical Development (George, Alan and Unwin Books, London, 1975) p. 158.

Day 49

Russell, B. (1872-1970)

Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and aus­tere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement. Real life is, to most men a long second-best, a perpetual compromise between the ideal and the possi­ble; but the world of pure reason knows no compromise, no practical limitations, no barrier to the cre­ative activity embodying in splendid edifices the passionate aspiration after the perfect form from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world.

‘The Study of Mathematics’ The New Quarterly (1907) reprinted in Philosophical Essays (1910) and in ‘The Retreat from Pythagoras’ in My Philosophical Development (George, Alan and Unwin Books, London, 1975) p. 155.

Day 48

Galileo Galilei (1564-1642)

Philosophy is written in that great book which lies before our gaze ... I mean the universe ... but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without the help of which it is impossible to conceive a single word of it, and without which, one wanders in vain through a dark labyrinth.

Le Opera di Galileo Galilei by G. Barbera, Florence, 1890 4, p. 171 and cited by J. Needham ‘Mathematics and Science in China and the West’ in Sociology of Science edited by B. Barnes p. 32 (Penguin, 1972).

Day 47

Einstein, A.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without expe­rience, merely by taking thought, able to fathom the properties of real things?

In my opinion the answer to this question is, briefly, this: as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

From ‘Geometry and Experience’ Lecture before the Prussian Academy of Sciences, January 27, 1921. Reprinted in Ideas and Opinions (Bonanza Books, New York, MCMLIV) p. 233.

Day 46

Al Hazen (Ibn al-Haytham) (c. 965—1039)

Thus the question what it means that bodies are transparent, so that light shines through them, is a part of physics. But the discussion of how light travels in them is part of mathematics. Hence the discus­sion of light rays and transparent matter, must consist of both physics and mathematics.

From ‘Abhandlung uber das Licht’ edited by J. Baarmann, Zeitschr. d. deutschen morgenlandischen Gesellschaft 36 1882, translated by M. Schwarz and cited by S. Sambursky in Physical Thought from the Presocratics to the Quantum Physicists (Hutchinson, London 1974) p. 135.

Day 45

The problem of evolution is a problem in statistics ... we must turn to the mathematics of large numbers, to the theory of mass phenomena, to interpret safely our observations ... The characteristic bent of C. Darwin’s mind led him to establish the theory of descent without mathematical conceptions; even so Faraday’s mind worked in the case of electromagnetism. But as every idea of Faraday allows of mathematical definition, and demands mathematical analysis ..., so every idea of Darwin—variation, natural selection... —seems at once to fit itself to mathematical definition and to demand statistical analysis.
Editorial in Biometrika (1901). Quoted by John D. Barrow in ‘Theories of Everything: The Quest for Ultimate Explanation’ (Vintage Books, London, 1992) p. 121.

Day 44

One plus one equals three for large values of one.

Day 46

The world is divided into three kinds of people, those who can count and those who can't.

Day 45

Anonymous

The world is divided into two classes of people: those who divide the world into two classes of people and those who don’t.

Day 44

Tennyson, A. (1809—1892)

Come, my friends,
’Tis not too late to seek a newer world,
Push off, and sitting well in order smite
The sounding furrows; for my purpose holds
To sail beyond the sunset, and the baths
Of all the western stars, until I die.
It may be that the gulfs shall wash us down:
It may be we shall touch the Happy Isles,
And see the great Achilles, whom we knew.
Though much is taken, much abides; and though
We are not now that strength which in old days
Moved earth and heaven; that which we are, we are;
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield.

Ulysses (1833)

Day 43

Maugham, W. S. (1874—1965

What makes old age hard to bear is not a failing of one’s faculties, mental and physical, but the burden of one’s memories.

Points of View (1959). Quoted by R. N. Butler in ‘The life review: an interpretation of reminiscence in the aged’ Psychiatry 26 (1963) 65—76.

Checked

Day 42

Einstein, A. (1879-1955)

I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know his thoughts, the rest are details.

In Einstein: The Life and Times by R.W. Clark (World Publishing, New York, 1971; Hodder & Stoughton, London 1979), cited in Nature 278(1979).

Day 41

Einstein, A (1879-1955)

What I’m really interested in is whether God could have made the world in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all.

To Ernst Strauss, quoted in The Scientific Imagination - Case Studies by G. Holton (C.U.P., 1978).