
Statistician Proves Gaussian Correlation Inequality - tambourine_man
https://www.quantamagazine.org/20170328-statistician-proves-gaussian-correlation-inequality/
======
bglazer
> Not knowing LaTeX, the word processer of choice in mathematics, he typed up
> his calculations in Microsoft Word

...

> He opted instead for quick publication in the Far East Journal of
> Theoretical Statistics, a periodical based in Allahabad, India, that was
> largely unknown to experts and which, on its website, rather suspiciously
> listed Royen as an editor.

I couldn't help but laugh at this part. He proved a classic theorem in
statistics and then precision engineered the actual submission to be roundly
ignored.

Makes me wonder if there's a proof of P=NP with ClipArt illustrations that's
buried in the South Asian Journal of Mathematics.

~~~
jlg23
> I couldn't help but laugh at this part. He proved a classic theorem in
> statistics and then precision engineered the actual submission to be roundly
> ignored.

He simply did not care:

“I am used to being frequently ignored by scientists from [top-tier] German
universities,” he wrote in an email. “I am not so talented for ‘networking’
and many contacts. I do not need these things for the quality of my life.”

~~~
geezerjay
Sounds like a bullshit excuse. I don't understand why anyone would even argue
that they intentionally do a poor job presenting their work because they
somehow allege they are ignored.

The only reason why anyone would go through such pains to get ignored is if
they intentionally want to be ignored.

And this does not make any sense, particularly in a "publish or perish"
environment.

~~~
yomritoyj
I on the contrary find it perfectly reasonable. Academic publishing has its
own share of bullshit and I can well understand someone, specially a retired
person, wanting to give up on that kind of prestige in order to save time and
energy for actual science. For example, as far as I know, Grigori Perelman has
not published the work that won him an offer of the Fields Medal in any
journal.

------
digital55
A simple proof of the Gaussian correlation conjecture extended to multivariate
gamma distributions by Thomas Royen:
[https://arxiv.org/pdf/1408.1028.pdf](https://arxiv.org/pdf/1408.1028.pdf)

~~~
andreasvc
Mathematics has this funny habit of throwing around "it is easy to say that
...", or in this case, calling a proof that eluded mathematicians for decades
"simple."

~~~
cperciva
You just need to understand the language.

"Trivial" = "regularly covered in undergraduate courses"

"Easy" = "a good topic for an undergraduate honour's thesis"

"Non-trivial" = "a good PhD thesis topic"

"Distinctly non-trivial" = "a groundbreaking result which will establish a
professor's reputation in the field"

~~~
tnecniv
I had a professor who liked to talk about how "elementary" did not mean easy,
it just means "uses only the foundations."

This proof is a perfect example of that statement. Formulating the problem the
right way -- which is most often the hardest part -- was the real challenge
here, not the mechanisms needed to do the formulation or the proof.

~~~
huhtenberg
Not sure why, but this reminds me how we had a professor that would say

    
    
      Let y(x) = a*x^4 + b*x^3 + c*x^2 + d*x + e,
      whereby e is not _necessarily_ the base of 
      natural logarithm

~~~
cperciva
My favourite along those lines was "let epsilon be a small number which is not
necessarily greater than zero". Everybody who spent the preceding year on
epsilon-delta proofs did a double-take at that.

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d--b
The proof is hard to read for non-statistician. Is anyone willing to give a
short human-readable summary of how it works?

Also, the conjecture seems fairly simple, so it'd be great to understand what
made it hard to prove.

~~~
onuralp
Here is a blog post that I think clarifies why this conjecture had remained
unsolved: [https://almostsure.wordpress.com/2009/09/27/the-gaussian-
cor...](https://almostsure.wordpress.com/2009/09/27/the-gaussian-correlation-
conjecture/)

There is also a 'companion' article on arxiv that provides a clear
presentation of Royen's proof:
[https://arxiv.org/abs/1512.08776](https://arxiv.org/abs/1512.08776)

------
mrcactu5
terry tao has a great discussion of the entropy power inequality

[http://mathoverflow.net/questions/167951/entropy-proof-of-
br...](http://mathoverflow.net/questions/167951/entropy-proof-of-brunn-
minkowski-inequality)

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JorgeGT
From reading the article, it seems that his proof is _straight from The Book_.

------
darawk
> Imagine two convex polygons, such as a rectangle and a circle

Hrm....

~~~
georgecmu
You can think of a circle as an infinity-gon.

~~~
thaumasiotes
I like "infini-gon" :D

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meow_mix
I love stories like this one. Reminds me of the the twin prime story from a
little while ago. Well written article as well!

~~~
JadeNB
As someone who has been funded by them, I think that I am nonetheless not
being biased when I say that the Simons Foundation does a huge amount of good
for the sciences, not least by funding this kind of consistently quality
science journalism.

~~~
ISL
I'm not funded by them, and I generally think the Simons Foundation does great
work.

------
noobermin
Here's another data point in one of HN's favorite topics, how academia and
publishing are broken.

------
0xdeadbeefbabe
> “It is like a kind of grace,” he said. “We can work for a long time on a
> problem and suddenly an angel — [which] stands here poetically for the
> mysteries of our neurons — brings a good idea.”

Had he learned LaTeX, I wonder if it would be a matter of justice.

------
JCzynski
Could anyone explain why it is impossible for a Gaussian distribution to be
anti-correlated with a group of N other Gaussians? This proof clearly implies
that fact, but none of the discussion seems to remark on it. I can imagine a
distribution such that the "random seed" puts things closer to the tails based
on the measured variance of a group of other normal distributions. Intuitively
it seems like that ought to be able to be a normal distribution itself; I
don't follow why that is not true.

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openasocket
I seriously can't believe that a problem that has evaded mathematicians for
decades could turn out to have a 9 page elementary proof!

I don't know whether to be excited that, maybe, other hard problems in
mathematics could have such elementary proofs, or depressed that
mathematicians took so long to solve a problem with such a simple answer :)

~~~
noobermin
Or it was ignored because it didn't have an author from Harvard or Princeton
on it.

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huahaiy
This conjecture seems to be easily seen as true by intuition. It's surprising
that it took so long to find a proof.

~~~
vecter
Can you explain to me how this conjecture is intuitively true?

~~~
andreareina
Let's say A has a 0.7 probability, and B has 0.6, and are independent. The
compound probabilities are gotten by multiplying the individual ones:

Neither: 0.3 * 0.4 = .12 A, not B: 0.7 * 0.4 = 0.28 B, not A: 0.3 * 0.6 = 0.18
Both: 0.7 * 0.6 = 0.42

Now let's say that they're not independent; in fact, B absolutely requires A.
You'd get something like:

Neither: 0.3 (this is reduced to the chance of not A) B, not A: 0 (B can't
happen without A) Both: 0.6 (only other probability with B, has to make up the
0.6) A, not B: 0.1 (simply what's left to sum to 1.0)

Concrete examples of independent events: (fair) coin tosses -- the chance to
come up heads is always the same, no matter the prior result. Related events:
being dealt a face card in blackjack, and winning the hand -- whatever your
normal chance of winning a hand, the odds of winning that particular hand just
went up.

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a3_nm
Calling this a "famous long-standing mathematical conjecture" seems a bit of a
stretch. It gives the impression that this would be comparable to Fermat's
Last Theorem, the ABC conjecture, the Riemann hypothesis, etc. However, this
conjecture doesn't seem to have a Wikipedia page. The discoverer, Thomas
Royen, does not have a Wikipedia page either. The Loren Pitt paper
establishing a special case of the conjecture was cited only 50 times.

The only justification for the importance of the problem that I see in the
original article is that it was open since 1972 and someone is quoted as
having worked 30 years on it and knowing other people who have worked long on
it. That's something, of course, but it's not so much -- there are lots of
problems in mathematics that remain unsolved after some decades despite
serious efforts, and not all of them are famous ; it depends on how much
attention they have attracted.

~~~
infogulch
Citing the Wikipedia articles' existence is a curious argument to make when an
article titled "40% of Wikipedia is under threat from deletionists" [1] was
just on the front page.

[1]: [http://boingboing.net/2017/02/16/40-of-wikipedia-is-under-
th...](http://boingboing.net/2017/02/16/40-of-wikipedia-is-under-thre.html)

~~~
FrozenVoid
Obviously obscure content will not survive unless it somehow gains fans
willing to guard the page from these people, who pretend wikipedia is paper
encyclopedia with limited budget for "notable" topics. They have to defend
citations, perceived bias/neutrality and fight merge/deletion votes, gain
allies with admins once it reaches arbitration and explain the article
"notability" each time its questioned(and articles can lose "notability
status" once one of these pedantic autists start questioning every line and
word, deleting everything not following exact rules). In fact an isolated
article, with new content or very few backlinks will not even be accepted and
get speedily deleted before it gets worked into something acceptable to
wikipedians. There has to be an alternative to this.

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The_suffocated
The paper has only seven pages, but the actual proof is even shorter --- it
spans from p.3 to p.5. So, it's a three-page proof. Really well done.

