Of possible quadruple algebras the one that had seemed to him by far the most beautiful and remarkable was practically identical with quaternions, and that he thought it most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature's God must work in the same channels.

What is man? ... What a strange union of matter and mind! A machine for converting material into spiritual force.

Mathematics is the science which draws necessary conclusions.

There are many cases of these algebras which may obviously be combined into natural classes, but the consideration of this portion of the subject will be reserved to subsequent researches.

Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth.

Of possible quadruple algebras the one that had seemed to him by far the most beautiful and remarkable was practically identical with quaternions, and that he thought it most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature's God must work in the same channels.

I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future.