Certain types of mathematics were called "calculus" as far back as the ancient Egyptians, but calculus as we know it today was established by Gottfried Leibniz and Isaac Newton, each independently, in the late 17th century.

Harvard University was founded in 1636, first as Harvard College, to ordain ministers.

Therefore, as jeff_the_nurse said on Reddit, Harvard is older than the creation of calculus.

While Harvard is the oldest continuously operating university in the United States, it isn't even close to being the oldest one in the world. That would be the University of Al Quaraouiyine in Fez, Morocco, established in 859.