My conviction was justified: art, that which lasts, is based on mathematics.

All art is founded in science, and the science is of little value which does not serve as a foundation to some beneficial art. On the most sublime of all sciences, theology and ethics, is built the most important of all arts, the art of living. The abstract mathematical sciences serve as a groundwork to the arts of the land-measurer and the accountant; and in conjunction with natural philosophy, including geography and astronomy, to those of the architect, the navigator, the dialist, and many others. Of what consequence anatomy is to surgery, and that part of physiology which teaches the laws of gravitation and of motion, is to the artificer, is a matter too obvious to need illustration. The general remark might, if necessary, be exemplified throughout the whole circle of arts, both useful and elegant. Valuable knowledge, therefore, always leads to some practical skill, and is perfected in it. On the other hand, the practical skill loses much of its beauty and extensive utility which does not originate in knowledge. There is, by consequence, a natural relation between the sciences and the arts, like that which subsists between the parent and the offspring.

Mathematics lays the foundation of all the ex­act sciences. It teaches the art of combining num­bers, of calculating and measuring distances, how to solve problems, to weigh mountains, to fathom the depths of the ocean; but gives no directions how to ascertain the existence of a God.

Mathematics lays the foundation of all the ex­act sciences. It teaches the art of combining num­bers, of calculating and measuring distances, how to solve problems, to weigh mountains, to fathom the depths of the ocean; but gives no directions how to ascertain the existence of a God.

The Mathematics which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately overreach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adheres to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depend upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the 47 unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.

For the great majority of mathematicians, mathematics is... a whole world of invention and discovery—an art. The construction of a new theorem, the intuition of some new principle, or the creation of a new branch of mathematics is the triumph of the creative imagination of the mathematician, which can be compared to that of a poet, the painter and the sculptor.

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics...

Art is science made clear.

Mathematical activity has taken the forms of a science, a philosophy and an art.

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.

It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.

[A]ll science as it grows towards perfection becomes mathematical in its ideas.