Final answer:
Karl Weierstrass rebuilt calculus after Cauchy's modifications by reformulating it based on limits and providing the field with a more rigorous foundation.
Step-by-step explanation:
After Cauchy's contributions to calculus, it was Karl Weierstrass who further developed the foundations of calculus. He did so by rigorously reformulating calculus in terms of limits and eliminating the notion of infinitesimals that had been used previously.
Whereas Newton and Leibniz were the original co-inventors of calculus, and Euler made substantial contributions to the development of mathematical analysis, Weierstrass is known for giving calculus a more rigorous logical structure which is still the basis for calculus today.