fiforpg

If not for AI, the project would have remained where it was born: in the author's head.

I do understand your sentiment, of course.

Arnold's principle (after Vladimir Arnold) says that no invention is attributed correctly to its true inventor. The principle applies to itself, of course.

To be fair, NSF grants for pure mathematicians were never as substantial as for applied sciences, but they would routinely reach 500k–1M territory. That's the amount going to a single proposal, and grant panels in, say, analysis would definitely spend millions per application season. NSF funding data is public and can be looked up.

I'm using past tense because iirc NSF has recently reduced their funding volumes, although I'm not following the situation very closely.

The use of computers in mathematics has been somewhat controversial from the very start.

There are of course all the computer-assisted proofs (see 4 color theorem), as well as the partially-assisted ones (see Viazovska et al on packing problems in dimensions 8, 24). But even finding a solution numerically, then rigorously verifying its properties can leave a lingering sense of incompleteness, of a gap in understanding. I like this one quote by (allegedly) Wigner that illustrates it well:

"It is nice to know that the computer understands the problem, but I would like to understand the problem, too."

On opening the article, I was somehow expecting a mention of the large deviations formalism, which was (is?) fashionable in late 20th century, and gives a nice information theoretic view of the CLT. Or something like that. There's a ton of deep math there. So having a bio statistician say "look, the CLT is cool" is a bit underwhelming.

Edit: see eg John Baez's write-up What is Entropy? about the entropy maximization principle, where gaussians make an entrance.

> much more performant compared to Linux alternatives is WinMerge

I have found Beyond Compare to be very good on Linux, even on large files/directories.

While you can certainly argue that some texts have more substance to them than these literary works, you cannot deny that most texts have worse prose than the books.

> abusive language/notation basically everywhere in math

In most cases it is not as much abusing notation as overloading it. If you think of the context of a formula (say, adjacent paragraphs) as its implicit arguments (think lambda captures in c++), then it is natural that curly braces can denote both a set and a sequence, depending on this implicit input.

Such context dependent use of symbols is actually rather convenient with a little practice.

Right, I did realize after posting that close to numbers of the form

1{hidden bit} + (1-2^-52){mantissa with all ones}

the relative accuracy — corresponding to the absolute accuracy of a single bit in mantissa — is about 2^-53. The hidden bit is easy to forget about...

In the context of double precision the article says

> the largest integer value that can be represented exactly is 2^53

— I am confused as to why it not 2^52, given that there are 52 bits of mantissa, so relative accuracy is 2^-52, which translates to absolute accuracy larger than 1 after 2^52. Compare this to the table there saying "Next value after 1 = 1 + 2^-52".

While the idea — of shuffling a societal system a little bit to prevent it from going stale — sounds important, I'm not convinced. Random shuffling leads to good results only when it is combined with a good fitness estimate (see: natural selection). And establishing a fitness test for a societal order seems to be a much harder issue than than that of an organized randomization.

Not necessarily—in 3d there are uncountably many non-lattice packings. They all have the same density as the FCC lattice though. To construct these packings, shift horizontal layers of FCC horizontally with respect to each other.

It is conjectured that in higher dimensions, the densest packing is always non-lattice. The rationale being that there is just not enough symmetry in such spaces.

That's true — time is a big place, and a lot of things are lost in it. I for one am rather more pained over disappearing of physical objects — genomes, books, art.

Plus, it is all the more exciting to think about what caused some languages to exist and thrive for so long, and the information about the past they retained.

If you like this kind of language archeology, check out David Anthony's The Horse, the Wheel, and Language — for how the people that spoke the Proto Indo-European language were located in time and space.

That paper by Wigner about mathematics really did originate an entire naming scheme for such texts, didn't it.