[dbyte]

For their website:

  mpmath internally uses Python's builtin long integers by default, but automatically switches to GMP/MPIR for much faster high-precision arithmetic if gmpy is installed or if mpmath is imported from within Sage.

With gmpy you rely on C libraries. Faster but those are still arbitrary precision computionations.

[adrianN]

Yes, that's for the numbers, but the algorithms are Python. Computing eigenvectors or complicated stuff like that in Python probably takes a lot longer than using a library written in Fortran.