Good evening. I am a current astrophysics undergraduate who is currently having a $10 bet with my classical mechanics professor (chemistry/mathematics background) over what the official curvature of the universe is. While my academic level of understanding is still not quite high enough to fully understand the various mathematical arguments involved, I often read books on the topic such as 'Cosmology' by Edward Harrison, 'The Fabric of the Cosmos' by Brian Green, and many other related books out of sheer interest and entertainment. Within these sources, along with several others including NASA, I've read strong indications that for all intents and purposes, the universe's curvature on the grandest of scales is approximately flat (according to the standard Big Bang/Inflationary Cosmology model). My professor claims otherwise; citing general relativity as a reasoning. I've brought up these several different sources I've mentioned above, but he wants a quantitative argument, rather than qualitative. If I'm wrong, I'd love to find out why. Does anyone familiar with the hardcore, in-depth mathematics of this topic have any recommendations they could point me towards where I could spend some time learning this? I'd love a good challenge.