Mathimoto's Real Complaint

My real complaint is I haven't been able to post more.

Alack, alack, alack. And the real victims are you good folk. But even Mathimoto needs a job, and rest assured once the job situation is stabilized, posts will come once more!!!

But in lack of that, let me give you a little play with number, related by the way, to some secret math speculation I'm doing.

If you want to find if a number is divisible by:

2, check if it's even. (Simple enough)

3, add all the digits and see if the sum is divisible by 3, if it is then the actual number is divisible by 3. (That's one of the cooler tricks)

4, if the last two digits are divisible by 4, then the whole thing is divisible by 4.

9, add the digits, and if the sum is divisible by 9, then the actual number is divisible by 9.

Do you see the suggestion here? Maybe there's a relation between numbers and their base 10-representation. Maybe... and maybe I'm getting close to it... maybe...

But what we do know for sure (to quote my good friend Kendrick), is that numbers are awesome.

NUMBERS RULE!!!!!!!!!
WOOOOO!!!!!!!!

Let me hear you say math... MATH!!!

A friend of mine once noted that it's a shame that math theory is becoming too complicated for normal people to play with.

But I don't think that it's a necessity, I think mathematicians just accept that this is the way the world must be, and thus refuse to take any effort to simplify mathematical theory.

And perhaps more importantly, new areas in math theory which might be more accessible to amateur innovation aren't being explored as vigorously as they should, largely because mathematicians are starting to forget what math is really about...

Playing with numbers.

Because numbers rock.

In that spirit, look at a list of squares
1
4
9
16
25
...

If you look at the differences between consecutive squares, you'll see a pattern and if you play with that pattern a little, you get...

n^2 = Sum from i=1 to n (2i - 1).

Think about it...

Primes, they aren't just for Transformers

It has to be said.

There is just something magical about primes.



I mean they are numbers that represent something basic. Multiplicatively, they can't be broken down and they end up becoming the special cases upon which every mathematical theory must be tried. And yet once you throw them into the world of math theory you get all sorts of weird math facts, that are just undeniably cool.



Like the fact that (p-1)! + 1 is divisible by p, if and only if, p is a prime.



Dude, like awesome.



And yet primes remain mysterious. It was only a few years ago people learned how to test if a number was prime within polynomial time (see here), people still can't prove that there are an infinite number of primes where p and p+2 are prime. And there's the fact that as you go to infinity, the number of primes approaches the function x/ln(x). Zuh?!



I say zuh not because prime numbers are hard to understand, although sometimes they are, but because their wonder and bounty are just mind-boggling.



So let it be understood then, primes are awesome.



And since primes are awesome, math is awesome.



Of course, this is but one of the proofs of math's awesomeness, which are as numerous as prime numbers themselves, and thus proven to be infinite.