At 10:15 What Gowers suggest is precisely what is missing in many books and teaching. A definition is what "it does" and "does not" never what it is. Adding and removing constraints from a definition helps getting a proper grasp on it. Similarly ( dixit Polya) adding and removing from hypothesis or conclusion helps solving a problem/question/conjecture.
2:38 I am applying for PhD programs in math later this year. RIP me.
At 10:15 What Gowers suggest is precisely what is missing in many books and teaching. A definition is what "it does" and "does not" never what it is. Adding and removing constraints from a definition helps getting a proper grasp on it. Similarly ( dixit Polya) adding and removing from hypothesis or conclusion helps solving a problem/question/conjecture.
I was like what is Tom Cruise doing ?