All the mathematical sciences are founded on relations between physical laws and laws of numbers.

In speaking of the Energy of the field, however, I wish to be understood literally. All energy is the same as mechanical energy, whether it exists in the form of motion or in that of elasticity, or in any other form. The energy in electromagnetic phenomena is mechanical energy.

In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data.

One of the chief peculiarities of this treatise is the doctrine that the true electric current, on which the electromagnetic phenomena depend, is not the same thing as the current of conduction, but that the time-variation of the electric displacement must [also] be taken into account.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express.

Francis Galton, whose mission it seems to be to ride other men's hobbies to death, has invented the felicitous expression 'structureless germs'.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.