together because the onward progress of science has brought them to the
same summit: this is the condition; and because they have the same power
of vision: this is the cause. There is therefore a method for putting
ourselves on the road to discovery, but no method for making the
discovery itself. The man of genius sees where others do not see; and
when he has seen, everybody sees after him. If, furnished with Gyges'
ring, you could gain access to the studies of savants at the moment when
a great discovery has just been made, you would see more than one of
them striking his forehead and exclaiming: "Fool that I was! how could I
help seeing it? it was so simple." Truth appears simple when it has been
discovered.

Discovery therefore, which has labor for its condition, is the principle
of the progress of science. Under what form does a discovery present
itself to the mind of its author? As a supposition, or, which is the
same thing, as an hypothesis. Hypothesis is the sole process by which
progress in science is effected. If we supposed nothing, we should know
nothing. In vain should we look at the sky and the earth to all
eternity, our eye would never read the laws of astronomy in the stars of
heaven, nor the laws of life upon the bark of trees or in the entrails
of animals. This is true even of mathematics. The contemplation,
prolonged indefinitely, of the series of numbers, or of the forms of
space, would produce neither arithmetic nor geometry, if the human mind
did not suppose relations between the numbers and the lines, which it
can only demonstrate after it has supposed them. The conditions are very
clearly seen which have prepared and made possible a fruitful
supposition, but the hypothesis does not itself follow of any necessity.
It appears like a flash of light passing suddenly through the mind.

The carpenter's saw opens a plank from end to end on the sole conditions