No human investigation can be called real science if it cannot be demonstrated mathematically.
That the divided but contiguous particles of bodies may be separated from one another is a matter of observation; and, in the particles that remain undivided, our minds are able to distinguish yet lesser parts, as is mathematically demonstrated.
Proof, one might say, does not merely shew that it is like this, but: how it is like this. It shows how 13+14 yield 27.
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
God forbid that Truth should be confined to Mathematical Demonstration!
His epitaph: Who, by vigor of mind almost divine, the motions and figures of the planets, the paths of comets, and the tides of the seas first demonstrated.
The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
But it is impossible to divide a cube into two cubes, or a fourth power into fourth powers, or generally any power beyond the square into like powers; of this I have found a remarkable demonstration. This margin is too narrow to contain it.
Mathematical demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick are the only truths that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth according as their Subjects are more or less capable of Mathematical Demonstration.
I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.
