omg, how boring is topology?

you'd think you gonna see how coffee cup turns into a donut.

instead, you got a fiat “open set”. From there on, its set of sets, subset, empty set, union of set, intersection of set, complementary set, power set, super set, finer set, coarser set, and it's set all the way!

you'd think you gonna see how coffee cup turns into a donut.

instead, you got a fiat “open set”. From there on, its set of sets, subset, empty set, union of set, intersection of set, complementary set, power set, super set, finer set, coarser set, and it's set all the way!

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- +Xah Lee It may be your major handicap in understanding mathematics, since a lot of it is motivated and inspired by physics :-( Besides, not understanding physics is all in itself a major intellectual and cultural handicap :-(Oct 20, 2017
- +michael livshits in some sense, true, but oh no, we are veering into the land of philosophy!

tons of accomplished mathematicians know nothing of physics!

let's see, from top of my head,

Turing, alonzo church, J H Conway, Coxeter, poncelet, pascal (early projective geometers with synthetic methods)...

i probably got some wrong.

and basically, most practical physics are related to just analysis and differential geometry stuff. And half of math has nothing to do with physics.

the whole pure computer science branch (formal languages, computability, recursion theory...), entire branch of math under logic (math foundation issues), and most discrete or finite stuff (graph theory, knot, number theory, combinatorics, game theory, tiling theory, discrete geometry, linear programing...)

of course, lots connections among when advanced enough.

well, if can live again, i would some physics... but then again, i don't know biology, chemistry, neuroscience ... many of which i'd find interesting!Oct 20, 2017 - +Xah Lee It's true, many accomplished mathematicians know no physics, and it is a tragedy, for them, and especially for their students that major in natural sciences :-( Now I can see why you hate differential equations and why you have such a formalistic view of mathematics :-(Oct 20, 2017
- +Xah Lee - when someone says you don't know enough stuff and you should instantly cure that by reading a dozen more books, you have to tune it out. Nobody ever knows enough; the most important thing is to have fun. I love physics, and I think it's important, but I don't try to make people feel bad about not knowing it. Instead I spend time explaining it!Oct 20, 2017
- +John Baez says: "... the most important thing is to have fun." Well, not always, for example, I would not like to be operated upon by a surgeon who thinks this way. Very often being competent at what you are doing is more important than having fun. More to the point, presenting a distorted view of mathematcs as a "pure" brain game to the people mostly interested in applications may be fun, but it is not what they need :-(Oct 20, 2017
- +michael livshits

(long creative writing follows extempore! ☺ )

but if you look at the incredible advances in past 20 years, i'd say, it's mostly due to communication tech, namely, the internet!

and our daily life, online shopping, social network, cellphone, google maps, all, due to, computing! cryptology, digital transactions!

they, mostly, have nothing to do with traditionally considered respectable branches of math, namely, algebra, analysis, geometry. Those with lots

and due to the fundamental of this computing stuff, which, in my view, is propelling all other sciences. it allows physics to compute complex things that without computer is impossible. It advances math such as dynamical systems, and mostly, email, video chat, social network, allow mathematicians to talk outside of ivory tower. It allows, rockets and visions of traveling on mars SpaceX. ... and we have credit cards, ATM, uber taxi that requires a iPhone!

computing, in my opinion, is truly fueling the advances of all sciences of past 20 years. (not to mention the side effect of creating mega billionairs such as google facebook amazon founders, which in turn, changes society's structure and power structure (and the impending threat of censorship at scale))

not to mention the oncoming of AI, a term that we can now accept as here. Namely, that AlphaGo beat human go players, by far. Have you heard of the news just this week, that a new version, AlphaGo Zero, learned the whole go game by playing with itself, sans ANY human data, and in just 3 months or so, now it beats the previous alphago that beat human world go champion, 100 to 0. I think this, to me and many, is certain life time view changing event.

the science of AI, really have little to do with traditional math of academia. Rather, lots of computer science, and computer programing, computer engineering, and formal logic, and computer chips! (ok, and statistics, which also means, analysis.)

and those big telescopes, satellites, GPS, physicists's linear accelerator, all would be naugt sans advancement in computing.

and robotics.

and then, now on the horizon is quantum computing! Imgine it coupled with Artificial Intelligence!

On that note, physics is back!

it's quite interesting, that a practically useless theoretical physics stuff wakes and is about to have major impact of our world!

Like number theory to cryptography! and conic sections to moon trip!Oct 21, 2017

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