
Infinitely many twin primes - ColinWright
https://arxiv.org/abs/1709.09950
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Tenobrus
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.

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Divver
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...](https://math.stackexchange.com/questions/139503/in-the-history-
of-mathematics-has-there-ever-been-a-mistake)

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dullcrisp
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?

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netsec_burn
HN comments: Not LaTeX, must be invalid.

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nneonneo
Fails test #1 of Scott Aaronson’s “Ten Signs a Claimed Mathematical
Breakthrough is Wrong”
([https://www.scottaaronson.com/blog/?p=304](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.

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zakk
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.

~~~
graycat
> 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!

~~~
hpcjoe
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.

~~~
graycat
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!

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pbhjpbhj
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.

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

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JosephLark
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.

