I don’t think it counts as “faith” if it demonstrably works to produce useful results.
Also, “the universe came from nothing” is not generally what physicists and mathematicians think. It’s often presented like this—especially by Christians attacking science. But it’s more accurate to say that physicists believe “the universe has always existed.” (You know, sort of like how Christians believe God has always existed.)
Either that or “they don’t know what’s up with the beginning of the universe.” That also describes the feelings of many scientists.
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To answer your second question, one of my favorite paradoxes in math is the paradox of infinite sets, or more specifically/narratively, the “Grand Hotel paradox.” Wikipedia has a good explanation here:
http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel
Of course, it turns out that the answer to this paradox is logical, but for the longest time people didn’t realize it.
Infinity is weird.