Who decides how may Bitcoins are available? Is it the number really 100% fixed?

As the title says, how is it guaranteed that Bitcoin will always have a fixed supply? Is this 100% certain? Who is in charge of this?

Background: I'm more or less a block chain newb, but I have a background in mathematics, so I'm not a complete moron. I have a small amount of BTC. I'm thinking of buying more. Are there answers for skeptics?

Edit: I'm getting some very detailed and rigorous responses. I sincerely appreciate the help, and I recognize that this is maybe an annoying question at this stage (although education will be key if more people are to addopt this). I'm going to take some time to read the white paper and square it with some of the responses.