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AT&T does have a plan where any provider can sign up to pay for their customers' data use, which is different from waiving costs for certain large, established sites.

Wait, how is that different?

Panza’s Paradox 8 years ago

I always thought Russell's paradox was basically just a formulation of the Liar's paradox in the language of set theory at the time, and that this was no secret. Its significance was not that it shed light on fundamental questions of philosophy, but rather that it poked a hole in what was supposed to be a foundation to all of mathematics.

Perhaps for now, but the ubiquity of smartphones could also bring them back in new and interesting ways. The most recent runaway hit was Pokemon Go, and though it was clearly a fad, it may have had more staying power if the social aspects were stronger, e.g. direct PvP battling.

Caveat: Take what I say with a grain of salt; I've never built a game in my life.

Sounds like an effective filter to me. Where I work, this would be the first part of one of the interviews, with the second part being something more like "Given a list of calendar appointments, what is the maximum number which can be attended without conflicts?"

The natural numbers {0, 1, 2, ...} under addition are an example of a monoid which is not a group. Another example is natural numbers under multiplication.

An example which may speak to a programmer more: the set of functions which take a 32-bit int as argument and return a 32-bit int, where the operation is composition of functions. The identity is the identity function. Since not all functions are invertible, this monoid is not a group.

I would argue the concepts of monoid objects and the category of endofunctors on an object are simpler than that of monads, so this description does help. I come from a math background and had never seen this quote before, and I think it has given me a definition of (mathematical) monads that I can remember.

Haskell, unfortunately, is still quite opaque to me.

Tenured at Princeton, had already solved some fairly big problems in the field, and it helped that FLT had recently been "reduced" to proving a conjecture about elliptic curves which were already very much in Wiles's wheelhouse.

Not to take away from his achievement, but I think it is not stressed enough how much the proof depends on work from previous decades that a priori had nothing to do with Fermat.

I have asked 0 questions, given 0 answers, and reached 0 people, giving an overall Reputation of 101 (the 100 bonus coming from activity on MathOverflow).

That being said, I probably hit StackOverflow at least once a month for my job, and if I'm working on a personal side project it's probably more like once an hour.