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Hey hey, folks. This is directed to anyone here who is good at maths: a member of the plebeian class wishes to learn more about mathematics because of his first real experience of mathematical beauty, and because it will give me something to do when I'm bored. Can anyone here give me some help there? I know at least one genius mathematician -ad a physicist- was almost completely self educated; while I sincerely doubt the ability to reach his skill, I'd like to know more to at least gain more ability to appreciate the beauty of numbers.

Note on combinatorics example: The question of writing 4953 as a sum of smaller positive integers such that repetitions are allowed and order does not matter is known as a Partition problem in number theory. It devolves into calculation p(4953) where p(n) is the partition function. Since exact results are a bit difficult to calculate I originally used the Hardy-Ramanujan approximation to derive an eyeball result but that was replaced with (I think, could be wrong) is a wrong answer based on an assumption which I didn't understand. Now I've decided to use the result provided by an online calculator you can find at