I have conversations on (admittedly different) versions of these topics with my fellow math PhDs.

Gracie, May I recommend a few famous articles? Try Wigner’s famous essay on the unreasonable effectiveness of mathematics:

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html">https://www.dartmouth.edu/~matc/Mat... https://twitter.com/graciegcunning/status/1298804338727489536">https://twitter.com/graciegcu...

Then I’d recommend Paul Lockhart’s “A mathematician’s lament.” It is pretty good and should be even more widely known. https://www.maa.org/external_archive/devlin/LockhartsLament.pdf">https://www.maa.org/external_...

At book level, the short “A Mathematician& #39;s Apology” by G. H. Hardy is pretty terrific.

https://www.math.ualberta.ca/mss/misc/A%20Mathematician%27s%20Apology.pdf

As">https://www.math.ualberta.ca/mss/misc/... is Edward Frenkel’s “Love and Math.” Which is more contemporary. You can follow Edward at @edfrenkel. https://www.amazon.com/dp/0465064957/ref=cm_sw_r_cp_api_i_hUUsFbZFFQM6R">https://www.amazon.com/dp/046506...

But the bottom line is that there appears to be a world of mathematics that is rich, non physical, non-arbitrary and not socially constructed but whose investigation by us IS socially constructed. It is a bit of a mystery why it is there and so logically rich...but there it is.https://abs.twimg.com/emoji/v2/... draggable="false" alt="🙏" title="Folded hands" aria-label="Emoji: Folded hands">