There’s a similar effect in actual genealogies. Almost everyone of Irish descent can trace ancestry to Niall of the Nine Hostages. Most people of German descent goes back to Charlemagne. And other than a few trace examples everyone of east Asian descent can go back to Genghis Khan.

Every time I look someone up in it and go back a few generations I always hit a really famous mathematicians (or physicists) like Gauss, Klein and Boltzmann. It doesn’t matter what area they work in, it always seems to go back to the same people.

Am I right to conclude that all doctoral supervisors from ~120 years ago were famous?

So here’s what I’d suggest, tailored to the applications in gauge theory: read “Gauge Fields, Knots, and Gravity” first. Then some more technical books to pick up the theory of fiber bundles (with an emphasis on connections in principal fiber bundles). Then go to a real physics book on gauge field theory (not one that purports to teach the math to physicists) and try to see the fiber bundles hiding behind the physicists’ prose.

I really don’t know of a book that would cover, say, the standard model aimed at a mathematician.

Galois: The book “Handbook of analysis and its foundations” by Eric Schechter is a general purpose reference for real analysis, but it’s particularly good for the set-theoretic underpinnings of each result.