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Proofs. Axiomatisable structures. Functions (maps). Continuity. Sets.

But that's highly subjective, as any answer on your question has to be.

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Q: What are the most important concepts in mathematics?
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Marin Mersenne (1588-1648) was a monk in France who studied science, especially mathematics. He made some important discoveries in mathematics and musical theory. Some people suggest that his most important contribution to science and mathematics was his correspondence with other scholars. His work on prime numbers of the form 2n-1 resulted in their being known as Mersenne primes.