jcla1

Spoiler: there is a simple argument against the existence of such a lower bound.

Interesting follow-up question: What is the distance between the set of harmonic numbers and the integers? i.e. is there a lower bound on the difference between a given integer and its closest harmonic number? If so, for which integer is this achieved?

FWIW the import syntax is now part of standard JS, according to the ECMAScript 2026 specification:

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe...

And node seems to be used only as a dev dependency, to test, benchmark and build/package the project. If you'd be inclined you can use the project's code as-is elsewhere, i.e. in the browser.

Even today it is exceedingly rare to find a still-well-conditioned bottle of wine that has the capability to have aged for 117 years or so. Most often sweet wines are capable of this.

FWIW I was also sceptical, but just tried it from my phone network and it seems indeed blocked. Wouldn't be the first case of different ISPs using different block-lists. c.f. bs.to

Measure its volume by dunking it in a jug of water and compare its weight with its expected weight (depending on the density of gold).

There is a famous tale of Archimedes doing exactly this when posed with the problem of determining if a certain crown is made of pure gold.

Do not underestimate the urge to procrastinate (by still doing productive things, like learning Mandarin) while pursuing a PhD.

I am not sure if this will be the author's experience too, but pursuing a PhD will often leave you exhausted without any hope of ever finding "the final missing ingredient" to solve the problem you are currently tackling. So turning to entirely unrelated problems, however productive they may seem to outsides, suddenly becomes an attractive alternative in order to procrastinate.

You can get gcc to generate the blend instruction in the example given - you just have to 'force' it to use SIMD more aggressively by, for example, using -march=native.

I recon the general cosensus among mathematicians (as that is what counts) is that the ABC conjecture so far has _not_ been proven. Mochizuki (and his school around him) seem to be the majority of people that believe his proof is correct. As you point out, Scholze has identified a supposed flaw in Mochizuki's argument, but anyone not already at the forefront of IUT/NT/ABC conjecture is probably incapable of telling if this flaw is a true flaw or not. As Mochizuki refuses to elaborate (on this supposed flaw) consensus cannot be reached and thus the ABC conjecture remains open.

https://news.ycombinator.com/item?id=19781756

I think giving any more details than his three short posts would delve too far into the specific arguments of the paper to be valuable for a wide enough audience, subtracting those that are going to be looking at the pre-print anyhow.

Unfortunately the presented method only works for the most simple linear recurrence relations.

Tangentially: look up the master theorem if you're interested in at least estimating growth rates for recurrence relations that crop up in computer science.

Just because of the impossibility of an exact formula for the roots of a high-degree polynomial that does not rule out the possibility of figuring out, say, the distribution of roots of such polynomials. The question is not about any polynomial in particular (hence Abel's theorem is no barrier).

edit: Think of the following example: take a polynomial a_n x^n + ... + a_0, where the coefficients a_i are i.i.d. Bernoulli random variables. Even though the degree n might be large (> 4) I can say with confidence that such a polynomial has a real root (x = 0) with probability 1/2. Similar though more sophisticated arguments are at work in the linked question.

I do (I'm a mathematican). We are usually between 4 and 10 people marking an exam with anywhere between 50 and 600 participants.

This sounds like an organisational nightmare to be honest. You'd be going through the pile of exams multiple times (at least twice) and what do you do if there are multiple mistakes that are common in a single exam question?

Also: if you're sorting into "mistakes piles" for single exercises, how can you parallelise marking of separate and independent questions?

Regarding you last point: out of interest, what kind of venues were you thinking of? Be this personal blogs of said academics, just dumping it on a preprint server or actual ("formally published") publications?

There is no universal algorithm for solving integral.

Not that I want to dispute this, but depending on what you meant, there is in fact such an algorithm: https://en.wikipedia.org/wiki/Risch_algorithm

Though often it is not implemented because it is quite complex (its details covering two thick books) and many of the special cases it covers rarely crop up in the real world, so the effort isn't worth it.

The caveat of Risch's algorithm is that it only "works" if the function you are trying to integrate has an elementary antiderivative. Many of the problems that Mathematica can solve (but SymPy fails at) involved special (i.e. non-elementary) functions.

That is definitely not true - I have an analog wrist watch (and am under 30). Also, there can be benefits to the use of analog clocks: in some circumstances they're quicker to read the time off of.

http://www.mcld.co.uk/blog/2006/digital-vs-analogue-clocks.h...

I'd deem it useful, though unusable in practise, as GMail for example does not accept messages that contain multiple From addresses.

To clarify, I guess you mean "Captain in the navy", equivalent to a Colonel in other branches. A captain in the army is O-3.

I typically do a medium roast with no oily sheen to them and it serves me well.

I thought an oily/shiny appearance of coffee beans was due to them being roasted too long ago and then some of the coffee bean oils "leaking" out of the beans. Is this not the case, i.e. something that might even be controllable with the roasting process, even something desirable in some cases?

The difference is that in the Schrödinger case you're effectively 'turning' the solution (in the complex plane) which leads to the uncomfortable question of whether the solution to the heat equation you'd start with is still defined. When going from heat to Black-Scholes you're just rescaling in 'existing' dimensions which doesn't change the character of the PDE.

But pro-tip if you are being apprehended by police is to furiously click on the side button as the phone will require pin code after that.

Apparently that won't work on Android -- though there's a lockdown feature (that will disable biometric-unlock) that you can access after long pressing the power button.

This confusion is caused by the different notions of problem: there are "decision" problems and "functional" problems. What grandparent asked ("what is the shortest path?") is a functional problem in nature, whereas P & NP are classes of decision problems. A (more or less) equivalent decision problem version of above question would be "is there a path of length at most X?", which then is of course easy to verify if a potential solution is presented.

Not to be confused with the also very SQL-like Q language[1] from Kx Systems/Arthur Whitney.

[1] https://en.wikipedia.org/wiki/Q_(programming_language_from_K...

I never really got the point of (digital) self destructing messages, since the reader can easily just copy the text/data, i.e. destruct only means not available anymore after future point in time. So you're just relying on the receiver of the message to follow protocol -- as always.

It's not just that, i.e. you may be fooled if you read the script "in the wrong way".

https://www.idontplaydarts.com/2016/04/detecting-curl-pipe-b...

Previously: https://news.ycombinator.com/item?id=21364413

Introduction to Functional Analysis, R. Meise and D. Vogt.

Despite the name, that's nowhere near just an introduction, especially Part III.

Classical and Multilinear Harmonic Analysis, C. Muscalu and W. Schlag.

After reading the two volumes you will have a huge base of knowledge. The books can get quite advanced as well, containing previously unpublished results when being first printed.

This kind of thing isn't anything new... here's a similar system that is less geared toward vandalism, but more to pointing out structural and lexical flaws in the articles: https://github.com/jcla1/wikipedia_analyser

(Disclaimer: I'm the author)

It too uses neural-nets (and an up to 3-gram model) to detect flaws...