is big crunch explainable by todays mathematics? is there any end to the universe?
Whether or not the universe ends in a big crunch is a question of physics, not mathematics. Current physics theory does not have a definite answer. As far as can be ascertained, the expansion of the universe is accelerating. Continuing in that direction leads to a completely open universe. However, we don't know enough to say things won't change in the future.
Also depends on how you want to define "end of the universe". A Big Crunch would be a definitive end to be sure, but there are other possible "ends" such as Heat Death where nothing interesting ever happens again. (setting up for a joke here...)
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