He never shirked arithmetical work: the longest and most laborious reductions had no terrors for him, and he was remarkably skilful with the various mathematical expedients for shortening and facilitating arithmetical work of a complex character. This power of handling arithmetic was of great value to him in the Observatory... He regarded it as a duty to finish off his work, whatever it was, and the writer well remembers his comment on the mathematics of one of his old friends, to the effect that "he was too fond of leaving a result in the form of three complex equations with three unknown quantities."
George Biddell AiryRelated topics
arithmetic character complex duty finish fond form great leaving mathematics observatory off power result shortening three unknown value well whatever work FriendsRelated quotes
Motion with respect to the universal ocean of aether eludes us. We say, "Let V be the velocity of a body through the aether", and form the various electromagnetic equations in which V is scattered liberally. Then we insert the observed values, and try to eliminate everything which is unknown except V. The solution goes on famously; but just as we have got rid of all the other unknowns, behold! V disappears as well, and we are left with the indisputable but irritating conclusion -
::: 0 = 0
This is a favourite device that mathematical equations resort to, when we propound stupid questions.
Arthur Eddington
He left in his Optics, the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience.
Ptolemy
In the original discovery of a proposition of practical utility, by deduction from general principles and from experimental data, a complex algebraical investigation is often not merely useful, but indispensable; but in expounding such a proposition as a part of practical science, and applying it to practical purposes, simplicity is of the importance:-and... the more thoroughly a scientific man has studied higher mathematics, the more fully does he become aware of this truth-and... the better qualified does he become to free the exposition and application of principles from mathematical intricacy.
William John Macquorn Rankine
It is hard for you to appreciate that modern mathematics has become so extensive and so complex that it is essential, if mathematics is to stay as a whole and not become a pile of little bits of research, to provide a unification, which absorbs in some simple and general theories all the common substrata of the diverse branches if the science, suppressing what is not so useful and necessary, and leaving intact what is truly the specific detail of each big problem. This is the good one can achieve with axiomatics (and this is no small achievement). This is what Bourbaki is up to.
André Weil
The first two things to study are form and values. For me, these are the bases of what is serious art. Color and finish put charm into one's work.... it seems to me very important to begin by an indication of the darkest values (assuming that the canvas is white), and to continue in order to the lightest value. From the darkest to the lightest I would establish twenty shades... Never lose sight of that first impression by which you were moved. Begin by determining your composition. Then the values – the relation of the forms to the values. These are the basis. Then the color, and finally the finish.
Jean-Baptiste-Camille Corot