fiforpg

Curiously, this review (and perhaps the book being reviewed?) makes no mention of the model of mathematics as a language. This seems to be a common idea among working mathematicians and physicists[1,2], and it is rather clear that the question of reality of a language is ill-formed. A rich enough language should be suitable for expressing both real and abstract statements. It is also interesting to think about mathematics from the point of view of programming language paradigms: is it functional (I think mostly), what is its type system, etc.

[1]: Galileo says that, roughly, the book of nature is written in the language of mathematics https://en.m.wikipedia.org/wiki/The_Assayer

[2]: A classical essay by Wigner on the "unreasonable effectiveness of mathematics" also brings up the language analogy. https://web.archive.org/web/20210212111540/http://www.dartmo...

> Traditional vector math gives the output of the cross-product of two vectors the same type. (That's why it's only meaningful in 3d.)

That is not really the reason. Relevant trivia: that cross product is defined only in dimensions 3 and 7 (not only in 3) has to do with existence of certain algebraic objects — division algebras — which only exist in dimensions 1 (reals), 2 (complex), 4 (quaternions), and 8 (octonions).

https://en.wikipedia.org/wiki/Seven-dimensional_cross_produc...

https://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(compositi...

You could say there is cross product in 1d by analogy, but of course it is always equal to 0.

This website is surprisingly useful. Recently I had to decide whether I could bring my ezpass transponder on the plane, and a quick search revealed a similar page answering exactly that question. Compare that to flying in Europe where afaik most airports won't have such detailed lists of ok/not ok items, to say nothing of the national differences.

> If you're promoting research into quantum gravity that doesn't respect special relativity, you're a crackpot.

Is there a short argument for why MOND cannot agree with relativity, at least on the relevant scales?

> Sometimes called "orals," "comprehensive exams," etc.

— other names I have heard people use for these: prelims, quals, ...

My first distracted thought upon reading this title on HN: cool, Terry Tao is finally getting his own army!

Jokes aside, Tao also has a nice write-up in AMS Notices on this experience and how it influenced his career:

https://www.ams.org/notices/202007/rnoti-p1007.pdf

Why "not supposed" to say out loud? Sounds simply as a problem of the only X on a team of Ys. Cultural (and other) differences can be hard, it is just a fact of life.

Think of it as being in the shoes of a lonely non-American in the country of Americans, if that is any consolation.

“I was poking around, Googling ‘how to download Library Genesis,’”

LG literally has this info on its front page. Researchers will research, I suppose.

A rather bizarre number, 2^8*5. Only two prime factors, but also not a pure power of 2.

Come on, prior to this people read Nocedal & Wright, which is still very much a standard text on nonlinear optimization, and there were well-known implementations of nonlinear optimization algorithms written by these people in Fortran. These are most likely hiding in any modern LBFGS library you are looking at, including Scipy etc.

It is rather that more people understand these algorithms now and more people wrote implementations or bindings for popular languages, so you don't need to use Fortran anymore these days, but only conveniently invoke your optimization library of choice. The entire optimization ecosystem has matured; any particular good book certainly has contributed to that, but so did any other particular good book.

Curiously enough, another painting by Bruegel, Hunters in the snow,

https://en.m.wikipedia.org/wiki/The_Hunters_in_the_Snow

is prominently featured in Tarkovsky's Solaris, which is discussed in another thread on the front page of HN today. Cultures and ideas move in mysterious ways.

The parts where the author is scandalized about the tasteless use of technology in religion read less as a critique of technology then that of religion. If anything, they demonstrate that the human-written sermons were just as robotic.

I know some people who seem to be able to push forward year after year after year, maintaining this extremely productive pace and having no apparent issues with burnout. I wonder what makes this possible, is it based in a healthy upbringing, some innate brain properties, or did they just luck out into a local equilibrium of life-work?