Mathematics, such as appertain to painting, are necessary to the painter, also the absence of companions who are alien to his studies: his brain must be versatile and susceptible to the variety of objects which it encounters, and free from distracting cares.

In the beginning of the year 1665, I found the method of approximating series and the rule for reducing any dignity of any binomial into such a series.

I do not love to be printed on every occasion, much less to be dunned and teased by foreigners about mathematical things or to be thought by our own people to be trifling away my time about them when I should be about the king's business.

All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.

A bird is an instrument working according to mathematical law, which instrument it is within the capacity of man to reproduce with all its movements, but not with a corresponding degree of strength, though it is deficient only in the power of maintaining equilibrium. We may therefore say that such an instrument constructed by man is lacking in nothing except the life of the bird, and this life must needs be supplied from that of man.

No human investigation can be called real science if it cannot be demonstrated mathematically.