One of the first name drop lines that comes to mind for me is always the one about the sunglasses in The Ghost Monument:
“Can’t remember who I borrowed them off now. It was either Audrey Hepburn or Pythagoras.”
To quote the Ninth Doctor: "I’ve been around a bit. I think you can assume at some point I’ve ‘danced’ "
I love this one from the Third Doctor in Day of the Daleks:
“Oh, quite right. Do you know, I remember saying to old Napoleon. Boney, I said, always remember an army marches on its stomach.”
Calling Napoleon “Boney” is such a Third Doctor thing to do
You can see some of the history of the Doctor with Harry Houdini here:
It is getting ridiculous how many Doctors met him.
Of course, with Isaac Newton, not only has the Doctor met him multiple times, he’s been involved in the discovery of gravity multiple times. Namely, one of the quotes I added for the fourth Doctor from the Pirate Planet was:
ROMANA: Newton? Who’s Newton? DOCTOR: Old Isaac? Friend of mine on Earth. He discovered gravity. Well, I say he discovered gravity. I had to give him a bit of a prod. ROMANA: What did you do? DOCTOR: Climbed up a tree. ROMANA: And? DOCTOR: Dropped an apple on his head. ROMANA: Ah, and so he discovered gravity. DOCTOR: No, no, he told me to clear off out of his tree. I explained it to him afterwards at dinner.
If it just gets used as a gag, it’ll get old. I have a feeling it might get tied into a season arc or some such, though. Like it was part of the damage to the fabric of reality causing things to get more supernatural and less sciency.