Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Mathematics is beautiful. Many numbers are interesting such as

1729 = 13 + 123 = 93 + 103

Please list out the interesting numbers and reasons to make number interesting

share|improve this question
4  
numbergossip.com –  Qiaochu Yuan Jul 28 '10 at 7:10
    
Great link Yuan –  pramodc84 Jul 28 '10 at 7:12
    
    
1729 is also a Carmichael number. –  starblue Jul 28 '10 at 7:25
    
Start another thread called un-Interesting threads on Mathunderflow... –  user126 Jul 28 '10 at 7:59
add comment

closed as not a real question by Jamie Banks, Akhil Mathew, Larry Wang, BlueRaja - Danny Pflughoeft, Ben Alpert Jul 30 '10 at 2:30

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

4 Answers

up vote 14 down vote accepted

All positive integers are interesting. Suppose they weren't. Let k be the lowest non-interesting positive integer. That is an interesting property. Therefore contradiction. Generalisation is left as an exercise to the reader.

share|improve this answer
7  
All rational numbers are interesting, for the same line of reasoning. To say that all real numbers are interesting you need the Axiom of Choice, unfortunately. –  mau Jul 28 '10 at 7:33
1  
"Calculus III is left as an exercise for the reader." –  Vortico Jul 28 '10 at 16:57
    
@mau: only if there's something interesting about your particular choice of well-ordering for the reals. –  Simon Nickerson Jul 29 '10 at 22:07
    
Maybe it would be fun to suggest the smallest positive uninteresting real. –  marshall Dec 8 '13 at 16:51
add comment

$196883$ is interesting because it's the smallest dimension of a faithful complex representation of the Monster group. Roughly speaking, a group is a collection of symmetries of something. A simple group is a group which can't be decomposed further into smaller groups; to borrow a phrase, it's an "atom of symmetry." There is a classification of these atoms with several infinite families and 26 exceptions, and the Monster group is the largest of these exceptions. And the simplest way to write it down is using $196883$-by-$196883$ matrices.

$196883$ was crucial to McKay's discovery of Monstrous moonshine, which began with the observation that the j-invariant, an important function in number theory, has a Taylor series in which $196884$ appears. The story of this discovery is explained in Mark Ronan's wonderful book Symmetry and the Monster, which I highly recommend.

share|improve this answer
    
There is a faithful representation of dimension one less (196882) over F_2, and matrices for this representation have actually been computed. –  Simon Nickerson Jul 29 '10 at 22:03
add comment

$163$ is interesting because it's the largest Heegner number. This means that it's the largest positive integer $d$ such that the ring of integers in $\mathbb{Q}(\sqrt{-d})$ has unique factorization. If you don't know what that means, two other elementary consequences of $163$ being a Heegner number are that

$n^2 + n + 41$

is prime for $n = 0, 1, 2, ... 39$ and that

$e^{\pi \sqrt{163}}$

is extremely close to an integer.

share|improve this answer
add comment

I always liked 23 (or more precisely, -23) because Q adjoin the square-root of -23 is the first quadratic imaginary field whose class number is not a power of 2; in fact, it's class group is of order 3.

share|improve this answer
add comment

Not the answer you're looking for? Browse other questions tagged or ask your own question.