Comments on: Simons Lecture I: Structure and randomness in Fourier analysis and number theory

By: The Beauty of Bounded Gaps | sladisworld

The Beauty of Bounded Gaps | sladisworld — Thu, 23 May 2013 14:18:37 +0000

[…] (A few suggestions for further reading for those with more technical tastes: Number theorist Emmanuel Kowalski offers a first report on Zhang’s paper. And here’s Terry Tao on the dichotomy between structure and randomness.) […]

By: E.L. Wisty

E.L. Wisty — Thu, 16 May 2013 09:49:31 +0000

Reblogged this on Pink Iguana and commented: Look up Simons lectures and David Donoho

By: Hugh

Hugh — Tue, 11 Jan 2011 13:35:51 +0000

My attempt at a twin prime proof, for anyone who is interested…

http://barkerhugh.blogspot.com/2011/01/twin-prime-proof-compressed-version.html

By: Arnie Dris

Arnie Dris — Fri, 29 Oct 2010 05:29:32 +0000

Dear Professor Tao,

I have some number-theoretic investigations going on at http://arnienumbers.blogspot.com. (e.g. the last 3 blog posts)

Please do take a look when you get the time.

Cheers,
Arnie

By: Terence Tao

Terence Tao — Fri, 03 Sep 2010 17:59:48 +0000

2 and 3 are the only primes that are not adjacent to a multiple of six. Note that the converse statement (all numbers adjacent to a multiple of six are prime) is certainly false, with 25 being the first counterexample.

By: Ana

Ana — Fri, 03 Sep 2010 15:55:43 +0000

As stated above: Primes are all adjacent to a multiple of six (with two exceptions). I found that one is for n=20. What is the other exception?

By: Math/Stat

Math/Stat — Mon, 15 Feb 2010 21:58:30 +0000

[...] (about string theory and enumerative geometry), the Szemeredi Festival (where we went through Terry Tao’s The Dichotomy between Structure and Randomness, Arithmetic Progression, and the Primes), [...]

By: Dan

Dan — Sun, 06 Dec 2009 21:16:52 +0000

Primes do have a distributive pattern althought very complex they
are associated with Mercenne triangle numbers and all 2^n and the
Fermat triangle numbers in a unique way as you will see below!

My studies of triangle number factoring where the addition and negation
of this series below produces no primes.

Except for the very beginning of this summation and negation there is an
actual pattern that can be observed disproving any sort of randomness
or psudo randomness to the primes.

9+3+2+1
+3+2
-2
+4+3+2
-6
+5+4+3+2
-11
+6+5+4+3+2
-17
+7+6+5+4+3+2
-24
+8+7+6+5+4+3+2
-32
+9+8+7+6+5+4+3+2
-41
+10+9+8+7+6+5+4+3+2
-51
+11+10+9+8+7+6+5+4+3+2
-62
…
You will note the negation is predicated on a natural progression
after each set of summations and negation of just (3) from the previous
set of summations and negation. After the negation the value will
allways be congruent to 0(mod 3).

This simple series does not produce any primes but does produce
all odd composites and even integers except for the special even
integers below.

A few even integer exceptions also are not produced such as –
Where n = 1,2,3,4..n then all 2^n are not produced.
Also all even Mercenne triangle numbers–
6,28,496,8128.. are not produced. Also known as even perfect numbers.

Also not produced are all even Fermat triangle numbers of the form –
When n>1 then ((2^(2^n)) +1)= prime then –
when n = 2,4,8,16 then Fermat t(n) = (2^(n-1))*(2^n)+1) =
10,136,32896,2147516416

There are other integers other than primes as I show above that are
not produced but they are all even or prime (2). So Just observing all
odd integer only odd composites are produced in the above sumations
and negations.

The primes shurely have a complex distribution but still a complex
ordered distribution by not appearing in the above summations and
negations.

Taking all integers that are not produced as being the primes and the special cases of the other even integers that also do not get produced
from this summation and negation sequence, is there a orderly reversal
of my sum and negation that will produce the primes and all the special
evens that are associated with the primes?

It would make the case for the not so complex distribution of the primes.

Dan

By: AJ

AJ — Wed, 02 Dec 2009 22:55:44 +0000

Professor Tao:
I think your explanation assumes “the universe” as a mathematical object is representable.

By: Structure and Randomness: Pages from Year One of a Mathematical Blog « Abner’s Postgraduate Days

Sat, 30 May 2009 21:55:08 +0000

[...] Simons Lecture I: Structure and randomness in Fourier analysis and number theory For instance, from the Siegel-Walfisz theorem we know that the last digit of large prime numbers is uniformly distributed in the set {1,3,7,9}; thus, if N is a large integer, the number of primes less than N ending in (say) 3, divided by the total number of primes less than N, is known to converge to 1/4 in the limit as N goes to infinity. Fourier analysis is an essential feature of many of these problems from the perspective of the dichotomy between structure and randomness, and in particular viewing structure as an obstruction to computing statistics which needs to be understood before the statistic can be accurately computed. [...]