I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story and could help track down a source.
The story bears some resemblance to the story about "turtles all the way down". In this story, told as an historical account about a particular mathematician's motivation for studying the three-body problem, the mathematician, perhaps Lagrange, perhaps d'Alembert, perhaps Poincaré, is over at a dinner party where he is the only mathematician. An older woman, perhaps a dean's wife, asks him if he knew about the mysterious planet sharing an orbit with the earth but always diametrically opposed from it, blocked from view by the sun. He tries to convince her that this is preposterous, and that we would know if there was such a planet by the effect on our own orbit. He can't seem to convince her, but--even worse--when he thinks about it harder at home after dinner he can't seem to quite convince himself either. This inspires the mathematician to study the three-body problem in full depth and to show rigorously that the kind of setup described by the woman would be unstable.
It is very possible that this account is apocryphal. Nevertheless, I would like to identify a source where it was told, or where it is attributed. Is there such a source?