Mary Somerville, in her reminiscences, gives the impression (though she does not say definitely) that she first met John Herschel when she visited his father, William Herschel, in 1816.
However, a letter I came across in the summer in the Herschel papers at St John’s College in Cambridge, shows that they had actually met in 1812 – though he did not mention her by name, and he doesn’t seem to have made an impression on her. But the dates correspond to the Somervilles’ visit to London soon after they were married, and it seems unlikely that there were two such ladies around at the same time.
In August 1812, John Herschel wrote to his friend Rev. John William Whittaker :
I had the happiness of an introduction to a Dulcinea who reads the Mec. Cel__ and Mec. Analytique _ What say you to that?_ To use Playfair’s expressions she “possesses a degree of Math. Knowledge rarely found in the other sex and is at once an ornament & example to her own – to her Country & to the human race!! _ No mortal however would have been able to read a page of La Grange in her eyes. Or to discover the Analyst in her manner, her conversation or her appearance NB. Corol. She is Confoundedly not-beautiful. Of course one ought never positively to affirm the reverse of beauty to belong to any woman_ (St John’s College, Herschel papers, Herschel/box1/letter 1)
His views on whether female mathematicians can or should be beautiful are intriguing and well worth exploring, and play very well to the themes that Eva Kaufholz explored in her talk on Sofja Kowalewskaja at the Mathematical Biography conference last month.