What is inter universal geometry?
It is a part of anabelian geometry. The term “inter-universal” apparently refers to the fact that the theory is meant to formulated explicitly in a way that respects universe enlargement, hence that it is universe polymorphic (IUTT IV, remark 3.1. 4, Yamashita 13).
Why are proofs important in geometry?
Geometrical proofs offer students a clear introduction to logical arguments, which is central to all mathematics. They show the exact relationship between reason and equations. More so, since geometry deals with shapes and figures, it opens the student’s brains to visualizing what must be proven.
How do you prove proofs in geometry?
The Structure of a Proof
- Draw the figure that illustrates what is to be proved.
- List the given statements, and then list the conclusion to be proved.
- Mark the figure according to what you can deduce about it from the information given.
- Write the steps down carefully, without skipping even the simplest one.
Who verified Scholze and Stix’s IUT?
In 2018, Scholze and Stix released the document to show the famous fatal flow, so did Mochizuki to show the validity of his work. In April, 2019, Fumihiro Kato, a Japanese mathematician who verified IUT, has published a book about IUT for non-expert Japanese audience.
Did Shinichi Mochizuki fail to fix fatal flaw?
This is very odd. As the Nature subheadline explains, “some experts say author Shinichi Mochizuki failed to fix fatal flaw”. It’s completely unheard of for a major journal to publish a proof of an important result when experts have publicly stated that the proof is flawed and are standing behind that statement.
Does Peter Scholze’s judgment have changed?
In the Nature article Peter Scholze states: My judgment has not changed in any way since I wrote that manuscript with Jakob Stix.