Infinitely many twin primes | Hacker News Reader

Infinitely many twin primes

arxiv.org

35 pointsColinWright19 comments

Well, a purely heuristic evaluation: this appears to be written in Word rather than LaTeX, it seems to be this person's first publication, it seems they're not affiliated with any institution, and it reads like an undergrad's homework rather than a paper. So I'm pretty skeptical.

While I agree with the overall sentiment here, on an unrelated note I noticed someone commented “If I saw Terence Tao’s name on it I’d assume it’s true” (I’m paraphrasing what they said)

That kind of assumption has actually bitten Mathematics in Academia in the past:

“ In the final sentence of the same paper, Gödel added:

In conclusion, I would still like to remark that Theorem I can also be proved, by the same method, for formulas that contain the identity sign.

Mathematicians took Gödel's word for it, and proved results derived from this one, until the mid-1960s, when Stål Aanderaa realized that Gödel had been mistaken, and the argument Gödel used would not work. In 1983, Warren Goldfarb showed that not only was Gödel's argument invalid, but his claimed result was actually false, and the larger class was not decidable. “

So although statistically assuming the proof is correct for a super famous “genius” mathematician isn’t a “bad” assumption since you’re “probably” correct in that assumption.

That’s not the same as certainty.

And before using that proof in further works

It’s very important for some others to go through and validate the proof as well.

Even the smartest humans are plagued by the simple fact that they are human and thus prone to mistake/error from time to time.

Source of the anecdote: https://math.stackexchange.com/questions/139503/in-the-histo...

I’m pretty sure you can tell this is nonsense by the second page. It uses elementary concepts in a way that doesn’t seem to make any sense. How do you form a group from the same number modulo different bases for example?

HN comments: Not LaTeX, must be invalid.

Fails test #1 of Scott Aaronson’s “Ten Signs a Claimed Mathematical Breakthrough is Wrong” (https://www.scottaaronson.com/blog/?p=304): it’s clearly typeset in Word with the Equation editor, not in LaTeX. As much as that is intended to be a joke, it really is true that the vast majority of high-quality mathematical work is typeset in LaTeX.

Also, it isn’t from anyone remotely reputable in the area of number theory, so the odds are very high that this is just a crank submission.

I see many red flags here:

- The author claims no academic affiliation.

- The title of the paper sounds a bit unusual, the gap is not a property of a prime, is a property of a couple of primes. Also, there's no need to specify 'exactly', that's number theory.

- In general the language used throughout the paper does not follow that of a mathematics paper.

- No LaTeX, extremely minimal bibliography.

These red flags mean nothing if the result is correct, and I would love it to be correct. I don't have time to check the proof, even if it seems to rely on elementary constructions.

> No LaTeX, extremely minimal bibliography.

I prefer TeX! And I've published applied math with just TeX, sent to Information Sciences, an Elsevier journal, and they handled the TeX source easily!

I prefer TeX because Knuth's book is shorter and easier to read than the books on LaTeX.

Yes, for TeX I wrote about 100 macros for table of contents, cross references, help with bibliographies, ordered, unordered, and simple lists, boxes around text, etc.

So, it's not all just LaTeX guys -- TeX is still darned nice!

Nothing comes between me and my TeX!

Give up TeX? It will have to be pried out of my cold, dead fingers!

I wrote my thesis in LaTeX, there was at least minimal support at our PhD office (minimal in the sense of they would accept postscript at the time). My choices were MS Word (in early 90s, so ... yuck) which I didn't have on any machine I had access to, or LaTeX. So LaTeX it was.

I wound up using some of the APS macros, and a number of things I wrote.

For me, the cool part of this is that my thesis was built using a multi-pass makefile. I ran it on all of my machines (SGI Indy, OS2 laptop) at the time.

Since then I've written documentation for 2 projects in LaTeX. It worked quite well, but then I was forced into using the dark side's tools (Word) as none of my colleagues were versed in the finer side of (La)TeX.

One reason I avoided LaTeX is that I was unsure just how my macros would conflict with what was in LaTeX.

I'm sure LaTeX has a lot of super tricky stuff that does really good stuff and was too much work for me to implement, but with LaTeX if something went wrong then I'd be stuck-o since I would not be able to debug LaTeX.

So, TeX it is. If there are bugs in my macros, then I fix the bugs.

Yes, I got around to TeX in about 1998 on OS/2. Now on Windows, It's my standard for all more serious word whacking, of course, especially for anything mathematical.

My TeX setup has a converter from TeX's DVI file type to PDF, and my Adobe Acrobat reader can print to FAX, and my computer has a FAX modem card I run my land line phone through. So, net, I can send letters from TeX to Congress!

"These are red flags unless this is correct in which case just kidding."

So why doesn't someone here verify the proof in itself rather than critique the author's typesetting?

Time. It takes time. There is a lot of quackery out there. Theoretical physicists deal with quacks all the time.

I wouldn't call it quackery. It's mad people doing proofs that sound good in their heads.

Or sometimes naive people doing the same.

Depends on how much you are hanging the definition of quackery on the presence of intentional fraud and charatanism.

I meant the usual inventors that claim to be on the verge of becoming miraculously rich after the miraculous achievment of building an unlimited energy or propulsion machine, but alas there is still some small issue.. I'd love to show you, but you'll need to sign this NDA first.

When an aquaintance of mine started doing this, trying to build a perpetual motor using magnets and suction pumps, and insisting I join his madness by signing a NDA, over and fucking over, refusing to get a job to support his family, feeding them dreams of riches that are born only of a psychological inadequacyand need to be special..

well pooh.

At least this proof didn't come with an NDA :-)

If you are interested in the problem, then only flaws in the logic are red flags.

If you are not interested in the problem, why did you click the link?

Disclaimer, I am not interested in the problem (but a bit interested in how the link get to the top here).

> then only flaws in the logic are red flags.

Sure, but the mathematics community knows that some red flags like the ones I pointed out, have an extremely high correlation rate with a wrong proof.

That's not enough to claim correctness or wrongness, and that's why I just spoke of "red flags".

> If you are not interested in the problem, why did you click the link?

I am very interested in the problem. However I am not interested in a thorough verification of the proof, which would take days.

Exactly as I am interested in some software projects, but I am not interested in performing a complete audit of their source code.

I'm not able to evaluate the paper but from what i can make out after a quick perusal the Twin Prime "proof" is showing that the probability of there not being a twin prime approaches zero?? That's an interesting approach (perhaps that's common, I don't know).

There seemed to be quite a lot of approximations in use; that approach prima facie seems shaky - surely the probability there isn't a prime above a particular integer could be anything non-zero and still leave the conjecture unproven.

I've probably misinterpreted it.

Will be interesting to see a proper teardown at a later date.

I've spoken with a maintainer of arxiv.org... anything in "General Mathematics" shouldn't be taken too seriously.

I was hoping to click through and see Terence Tao's name on the paper. Then I would assume it was correct. Agree with the other comments as it stands.

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