Well, pretty much everyone expects mathematics to be the same everywhere, since at its root mathematics is nothing but a logical construct. An extremely useful logical construct, mind you, but a construct nonetheless.
What you may have heard cosmologists and science popularizers blathering on about in recent years is the so-called “string theory landscape”. This is the idea that there are other regions of the Universe, causally disconnected from ours, in which the laws of physics are completely different. In such a region you could have different ratios of the gravitational to the electromagnetic constant, different strengths of the nuclear forces, different particle masses, even fundamentally different forces and particles that don’t map neatly on to the fundamental particles that we see here in our vicinity.
This isn’t quite as absurd as it might sound. There’s a phenomenon in solid-state physics called the “Curie temperature”: if you heat up a block of iron, and then let it cool back down below a certain temperature, you’ll find that on a microscopic level the iron has thousands of little regions (called “domains”) which act like little magnets. The “poles” of each domain are pointing in a different direction, and so there’s no net magnetic field for the whole block, but within each domain there’s a preferred direction to the magnetic field.
The analog, then, is that the Big Bang “heated up” the Universe, and as it cooled down there were certain “domains” that were created. Instead of having different magnetic fields in the different domains, though, you have different fundamental constants. If, like the string theorists, you believe that all of the fundamental constants (or at least most of them) and other stuff like the particle content of the Universe are determined via some “higher-energy” theory that we can’t easily investigate, then pretty much anything is fair game.
Oh, and once you start tinkering with the fundamental constants of physics, anything goes as far as chemistry and biology are concerned. Tweak the fundamental constants so that the neutron no longer exists, and all of a sudden you can’t have any atoms heavier than hydrogen — so no chemistry and probably no biology either. Tweak them slightly differently, and the periodic table could look completely different. Evolution via natural selection would still apply to any Universe with imperfectly self-replicating systems, but other than that all bets are off.
You might find The Anthropic Cosmological Principle, by John Barrow & Frank Tipler, interesting reading in this regard. While their conclusions are still very much a matter of debate, there are many, many, many calculations therein that show that “life as we know it” would not exist if the fundamental constants of the Universe were tweaked very much at all.