Things are heating up on Terry Tao’s blog. In “If Math Is More Than Proof, We Need to Better Celebrate the Rest of It,” Grant Sanderson of @3blue1brown proposes “open exposition problems” -- rewarding the work of making math genuinely understandable.
https://t.co/zBOhhDNuNU
@ShadWonderguy@justinskycak "solve problems with [the] complex ideas" is not the only thing that matters. That's what frogs optimize for, and that's fine. But drilling too much engineering calculus may even be detrimental if your goal is to understand how algebra, topology, geometry, and logic fit together
@ShadWonderguy@justinskycak Spending one's finite time sharpening one's grasp of definitions, making one's own examples, drawing visualizations, connecting ideas across areas, covering more material, and seeing the same patterns again and again is also a way of getting enough reps
@ShadWonderguy@justinskycak The driving analogy captures well the development of skills that can be automatized by repetition in a limited setting. But math proficiency is broader and more diverse. Time is scarce and may be better spent on definitions, examples, visualization, connections, and covering more
It seems a nice idea to put in the center the country which is the main object of scrutiny in history and geography classes. The connections with the rest of the world from the pov from within becomes more apparent
@aryehazan Use WOP:
Choose the lexicographically first of the "uninteresting theorems". Clearly, it is interesting - it is the first "uninteresting theorem". Therefore, it should not be in in the set of uninteresting theorems ... and no theorem is uninteresting.
@TonyTheLion2500 Nice. I often jump from book to book, though sometimes I stay focused on one for longer. I switch topics like someone moving their attention among different pieces of a jigsaw puzzle as the underlying image slowly unfolds
@leecronin Fair! But in math, the base thing often becomes clear only by exploring its extensions. Distributions reveal functions. Schemes refine varieties. Complex analysis sharpens real. Understanding flows both ways
@TonyTheLion2500 They don't! Classes don't solve the paradox. Russell first solved it with type theory. Later, Zermelo solved it in set theory by replacing unrestricted comprehension with restricted comprehension. Classes came later so we could still talk about collections too large to be sets
@demystifysci I always wonder how can someone not have a mystical experience induced by math? How is it even possible to contemplate the infinity digits in the decimal expansion of pi and not immediately feel there is sth transcendental, mystical, reflected on it? Perhaps brain differences?
@TonyTheLion2500 @Maikh73 How exactly are the tutoring sessions? Are they like lectures? Or you just talk about what you feel like talking each day? I wonder if some tutoring could also help me