One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.

I having from the consideration of the sesquialter proportion of Kepler concluded that the centripetall force [to the Sun] decreased in the proportion of the squares of the distances reciprocally, came one Wednesday to town, where I met with Sr Christ. Wren and Mr Hook, and falling in discourse about it, Mr Hook affirmed that upon that principle all the Laws of the celestiall motions were to be demonstrated, and that he himself had done it. I declared the ill success of my attempts; and Sr Christopher to encourage the Inquiry said that he would give Mr Hook or me 2 months time to bring him a convincing demonstration thereof, and besides the honour, he of us that did it, should have from him a present of a book of 40 shillings. Mr Hook then said that he would conceale [his] for some time that other triing and failing, might know how to value it, when he should make it publick.