
The 3n+1 conjecture: Terry Tao has some thoughts ... - ColinWright
http://terrytao.wordpress.com/2011/08/25/the-collatz-conjecture-littlewood-offord-theory-and-powers-of-2-and-3/
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gjm11
A couple of remarks.

1\. For those who don't know of him already: Terry Tao is a very, very smart
mathematician. (One indication: he has a Fields medal.)

2\. He is not claiming to be anywhere near having either a proof or a
refutation of the conjecture, nor a plausible way of getting near to either.

3\. The main contribution (novel, so far as I know) of what he's done is the
observation that there's some connection between the conjecture and
transcendence theory. (Transcendence theory is an important and quite well
explored field of mathematics. A number is "algebraic" if some polynomial with
integer coefficients evaluates to zero at that number, "transcendental"
otherwise; almost all numbers are transcendental but proving them so is
generally difficult; transcendence theory is concerned with methods for
proving that numbers are transcendental and quantifying how transcendental
they are in various senses.)

The point of Tao's observation here is: as if we didn't already know, the 3n+1
problem probably isn't easy; an easy resolution of the problem would imply not
only that people working on the 3n+1 problem have missed something simple
(always possible since it's mostly of interest to amateurs) but that people
working in transcendence theory have missed something simple (less likely
because lots of really first-rate mathematicians have worked very hard in that
field).

~~~
tzs
Or as Paul Erdös put it: "Mathematics is not yet ready for such problems".

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X4
There's a way to benchmark NoSQL Databases with the 3n+1 conjecture.

[https://docs.google.com/View?id=dd5f3337_12fzjpqbc2&pli=...](https://docs.google.com/View?id=dd5f3337_12fzjpqbc2&pli=1)

I've submitted that to ycnews, but it didn't appear. I've no idea why.
<http://news.ycombinator.com/item?id=2919371>

~~~
huhtenberg
I used Collatz conjecture as a part of an anti-cracking scheme in one of my
projects. There was an obfuscated .exe consistency check, but it was not run
until few other parts of the code (mostly rare event handlers) iterated a very
long Collatz sequence down to 1. I figured if a cracker knew about hailstorm
numbers, I was cool with him messing with my stuff ... and if he didn't, at
least he would learn about it :)

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mingyeow
WOW: His father told the press that at the age of two, during a family
gathering, Tao attempted to teach a 5-year-old child mathematics and English.
According to Smithsonian Online Magazine, Tao taught himself basic arithmetic
by the age of two. When asked by his father how he knew numbers and letters,
he said he learned them from Sesame Street.[4] Aside from English, Tao speaks
Cantonese, but does not write Chinese.

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mturmon
My "Formal Methods in CS" prof dropped this conjecture into a problem set
without naming it or remarking on its heritage.

Pre-google, you had no way of knowing what you were dealing with.

~~~
tzs
Maybe he was hoping one of you would be the next George Dantzig.
<http://www.snopes.com/college/homework/unsolvable.asp>

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MostAwesomeDude
There are lots of things one can say about Collatz which would seem to affect
the problem but really don't. My favorite: All natural numbers belong to a
Collatz graph containing {4, 2, 1} if and only if all natural numbers _not
divisible by 2 or 3_ belong to that Collatz graph.

