The 3n+1 conjecture: Terry Tao has some thoughts ...

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).

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

https://docs.google.com/View?id=dd5f3337_12fzjpqbc2&pli=...

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

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.

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.

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.