To me it seems that the IUT Inter- Universal Teichmuller Theory and also the Scholze Langland's Program connection between Geometry and Algebra are important advances. But I do not have anything to say about either since I am involved in trying to study both. [That is even though recently I decided to quit the study of the Langland's program in order to have a bit more time to look into IUT.
Why is this important? u might ask. Answer: To Ibn Pakuda and the Rambam there is an aspect of math and physics which come under the category of "Learning Torah."
This is seen in Chovot Levavot Gate of Behina chapter 3, and in the Mishna Torah concerning the idea of dividing one's learning time into three parts. And right there the Rambam says "the things called Pardes [ field of fruit trees] are included in Gemara" and he defined "Pardes" in the first four chapters of Mishna Torah as Physics and Metaphysics. There however, it is possible to mistake his intension. But In the Guide for the Perplexed his intension is much more clear.
[I am starting to see that Shinichi Mochizuki's IUT is built on a lot of previous results that I need to work through.]]
