The closest I will every get to something like an Erdõs number is that I can now claim the one and only female Abel prize winner was my Differential Equations teacher at college!
I missed taking a class with Steven Weinberg when I got to UT because he semi-retired the year before.
I felt very lucky to have had her for an experimental mathematical modeling course (M375) back around 2000. She was simply delightful as a professor, even for a mathematical lummox like myself. :) Encouraging, informative, brilliant ... we should all be so lucky as to have teachers and influences like her in our lives.
There is a story around UT that Weinberg heckled her during a lecture of his when she asked about the convergence of a series and promptly got a talking-to by the department chair. I hear he’s been much better behaved since.