From today’s vantage, it comes as a surprise to learn how slow the American academy was to embrace the practice of original mathematical research. It was at Harvard that the pursuit finally gained a foothold in the 19th century, and the history of the university’s mathematics department tracks well with the rising regard for mathematics in America. Steve Nadis and Shing-Tung Yau trace these developments in A History in Sum: 150 Years of Mathematics at Harvard (1825-1975), which they introduce below.
These days, the importance of math is widely recognized. The ongoing revolution in computers and communications devices, to take a familiar example, owes to advances in information theory, solid-state physics, and other disciplines that are, themselves, rooted in mathematics. Our country considers mathematics education a priority (even though existing programs often fall short of our goals). In terms of understanding the world around us, many people realize that the physical laws that govern our universe are—in their clearest form—mathematical statements. As Galileo Galilei once said, “Mathematics is the language with which God has written the universe.”
Isaac Newton’s law of universal gravitation is summed up in a simple mathematical expression that accurately describes the motions of objects in our solar system. Newton’s law has since been subsumed into Albert Einstein’s broader theory of general relativity, which encapsulates the workings of gravity in ten linked equations. String theory is more ambitious still, attempting to explain the particles and forces of nature (including gravity) through the geometry of tiny, hidden six-dimensional spaces. Carnegie Institution researcher Daniel Kelson, who hunts for distant galaxies, claims that his work in astronomy is “100 percent” mathematics. MIT astrophysicist Max Tegmark goes even further, suggesting that the universe we inhabit is, in itself, a “mathematical structure.”
Americans, however, have not always valued mathematics in this way. When Harvard College, the nation’s first institute of higher learning, was founded in the 1630s, “arithmetic and geometry were looked upon … as subjects fit for mechanics rather than men of learning,” the historian Samuel Eliot Morison wrote. In those early days, students did not need to demonstrate any proficiency in mathematics to gain admittance to Harvard, nor did they receive any training in the subject until their third and fourth years of school. The training they did receive was often far behind the times. Algebra, for instance, did not make its way into the Harvard curriculum until the 1720s or 1730s—roughly a century after René Descartes introduced modern algebraic notation. Calculus instruction began in the 1720s as well, more than 50 years after Newton and Leibniz put the discipline into a form that’s recognizable today.