John Collins describes meeting Isaac Newton in a letter to James Gregory dated 24 December 1670. This meeting must have occurred shortly after Newton had been appointed Lucasian Professor following Isaac Barrow’s resignation:
Mercator pretends to sum a harmonic progression with ease … I never saw Mr Isaac Newton (who is younger than yourself) but twice, viz somewhat late upon a Saturday night at his Inn, I then proposed to him the summing of a harmonic progression, which he promised to consider and send up. I told him I had done something in it, and would send him what considerations I had about it but his considerations came up (before I sent him mine) without any indication of his method. And again I saw him the next day having invited him to dinner: in that little discourse we had about mathematics, I asked him what he would make the subject of his first lectures. He said Optics proceeding where Mr Barrow left, and that he himself was a practical grinder of glasses, and had ground glasses for a pocket tube, but 6 inches long, that magnified the object 150 times whereby he did frequently observe the satellites of Jupiter, and that such a glass was naught for a short distance. Having no more acquaintance with him I did not think it becoming to urge him to communicate any thing, the rather in regard Mr Barrow told me the Mathematics Lecturer there is obliged either to print or put 9 lectures yearly in manuscript into the public library, whence copies might be transcribed.