As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.

It is a curious historical fact that modern quantum mechanics began with two quite different mathematical formulations: the differential equation of Schroedinger and the matrix algebra of Heisenberg. The two apparently dissimilar approaches were proved to be mathematically equivalent.

Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

Many people believe that the grains of sand are infinite in multitude ... Others think that although their number is not without limit, no number can ever be named which will be greater than the number of grains of sand. But I shall try to prove to you that among the numbers which I have named there are those which exceed the number of grains in a heap of sand the size not only of the earth, but even of the universe

The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.

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