Within pure mathematics, the evolution of calculus has been a story of crossbreeding and its benefits. Older parts of math were invigorated after they were crossed with calculus. For example, the ancient study of numbers and their patterns was revitalized by an infusion of calculus-based tools like integrals, infinite sums, and power series. The resulting hybrid field is called analytic number theory. Likewise, differential geometry used calculus to shed light on the structure of smooth surfaces and revealed cousins they never knew they had, unimaginable curved shapes in four dimensions and
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