

Ten Signs a Claimed Mathematical Breakthrough is Wrong - gnosis
http://www.scottaaronson.com/blog/?p=304

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acangiano
One of the 'fun' aspects of running a math blog is that you get to see Word
documents containing "proofs" of unresolved problems or the existence of God
or Allah. A true glimpse into madness.

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nwhitehead
Using logic to "prove" God exists isn't totally crazy, just mostly crazy.
Gödel himself tried his hand at it [1].

[1]:
[http://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof](http://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof)

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tikhonj
Yeah, but Gödel was legitimately crazy towards the end of his life. He ended
up dying because he was too paranoid to eat!

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gertef
This is one of the bizarre comforts I feel when I acknowledge that I will
never be a math super-genius... the fact that there is a high correlation
between math super-genius and "overflowing" to insanity. Godel, Nash...

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amirhirsch
When I finally prove the Riemann Hypothesis it will be presented in HTML5 and
Javascript with interactive graphs.

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mikevm
Make sure to include a tl;dr, 'cause ain't nobody got time for that.

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derleth
> Make sure to include a tl;dr

You mean the Abstract?

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epochwolf
Yes but label it "TL;DR" instead of "Abstract"

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mahmud
Site is overloaded, so here is the Coral cache:

[http://www.scottaaronson.com.nyud.net/blog/?p=304](http://www.scottaaronson.com.nyud.net/blog/?p=304)

See also the famous Crackpot Index:

[http://math.ucr.edu/home/baez/crackpot.html](http://math.ucr.edu/home/baez/crackpot.html)

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Patient0
This is from 2008. Could you add (2008) to the title?

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archagon
I enjoyed the author's Beijing/Chinatown metaphor in point 10.

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thejteam
I probably disagree on the Tex one. I know several people with PhDs in
engineering and science disciplines who have never used Tex. Several of them
know enough math to at least make a reasonable stab at a few of the problems,
even if they are unlikely to be successful.

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jff
So what you're saying is that these non-TeX users are unlikely to successfully
solve P=NP? I'd say that sort of upholds his premise.

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GhotiFish
It would be reasonable to say users, in general, are unlikely to prove P = NP.
So I'd say it doesn't affect the premise at all. :)

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Sniffnoy
Note also signs 11 and 12 in the comments[1], and the later "Eight Signs A
Claimed P≠NP Proof Is Wrong"[2]. (OK, so there's a bunch of overlap.)

[1]
[http://www.scottaaronson.com/blog/?p=304#comment-8957](http://www.scottaaronson.com/blog/?p=304#comment-8957)

[2]
[http://www.scottaaronson.com/blog/?p=458](http://www.scottaaronson.com/blog/?p=458)

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wolfganglechner
Most of the points require reading the whole paper first, isn't it?

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jfarmer
No, not really. One thing that makes an expert an expert is their ability to
filter signal from noise. Sometimes they can prematurely bucket ideas into
relevant/not-relevant, but usually not.

Have you ever seen a novice programmer trying to find information on a
StackOverflow page? The answer might be staring them in the face, but they
still scroll past it once, twice, three times, etc. until I point it out.

A novice has no sense of what's important and what's not so they tend to think
everything is whereas an expert has a set of heuristics (like the ones in this
blog) which make them much faster. They'll look for familiar ideas, themes,
likely mistakes, etc. first before going into full-on, read-this-thing-line-
by-line mode.

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Havoc
>One thing that makes an expert an expert is their ability to filter signal
from noise.

Certainly, but will you be able to spot the breakthrough insight if all your
doing is filtering it against your notion of signal vs noise. Breakthroughs
tend to come at a problem from a totally different angle & generally it takes
a bit of time to understand why its brilliant rather than "noise".

~~~
jfarmer
Like I said, "Sometimes they can prematurely bucket ideas into relevant/not-
relevant, but usually not." I wrote that hoping to preempt your exact
response. Alas! ;)

Even if I grant your premise (which I don't), just because a breakthrough is
likely to be written in crazy-talk doesn't mean something written in crazy-
talk is likely to be a breakthrough. At that point it becomes a question of
opportunity cost, which is exactly where heuristics come in.

In fact, what you said could be true and it could still be true that

    
    
      P(breakthrough | does not seem crazy) > P(breakthrough | seems crazy)
    

So, if I were on the hunt for breakthroughs I'd still be better off ignoring
the crazy-seeming things.

Regarding your premise, can you name, say, ten mathematical breakthroughs
since the Enlightenment that came about the way you described?

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Havoc
Pretty sure we're talking past each other, but I'll give it a shot anyway.

>Even if I grant your premise (which I don't), just because a breakthrough is
likely to be written in crazy-talk

Who said anything about "crazy talk"?. My point is simply that your
signal/noise filter is by necessity driven by information derived from the
status quo. The status quo part being a really big problem if you're hunting
for something _new_.

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tjr
I wonder if there is a context in which preparing a document in TeX would be a
strong indicator that you _don 't_ know what you're talking about?

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solarmist
Maybe history. Or another of the humanities. :) But TeX takes time to learn to
use properly and only people that expect to use it regularly go through the
trouble I'd expect.

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sillysaurus
Are mathematicians going to be using TeX in a hundred years? Two hundred? Five
hundred? Two thousand?

Math is timeless. TeX may be, but it's too soon to say. It's a recent
invention. It's only been around for 35 years.

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cschmidt
It wouldn't surprise me if they still use it in a hundred years. It just fits
thinking in math. By then TeX will be on version number
3.1415926535897932384626433832795028841971693993751 :-).

~~~
adamgravitis
IIRC, it's supposed to be set exactly equal to pi upon Knuth's death.

