It is almost impossible to graduate at Cornell without having engaged in some interaction with the Mathematics department. Whether it be taking a distribution requirement in Arts & Sciences or a core class as part of the College of Engineering, almost every student has interacted in some way with it. Since it is so influential, it should be held to strict scrutiny, as it plays a key part in every undergraduate’s initiation into society. And while the department does a lot well, such as with the quantitative and problem-solving skills conferred to students, which are crucial, it is the way in which the historical and cultural context of these discoveries is presented that is needing reform.
Students may say that they don’t wish to learn such things in their math courses; Cornell has Departments of Comparative Literature, Classics and Government for a reason after all. But this argument fails to appreciate the depth of the subject at hand. For centuries, mathematics has been the principal driver in all technological and scientific advances. Thus, gaining proficiency is not only about knowing how to solve an equation or plot a graph, but understanding the logical innovations that have allowed humanity to build up to all manner of progress. Essentially, it is the University’s most discrete lesson in human history.
This is where the principal problem lies. Those having taken a calculus course at Cornell will have heard any number of names important in mathematical spheres of influence: Newton, Euler, Riemann, and Taylor. There is no contesting the contributions these people have made to our modern scientific understanding of the world, but the homogeneity in their backgrounds and identities paints an illegitimate picture of how mathematics has been constructed throughout history. Even if the sudden sparks of innovation that brought such study to the forefront of scientific progress were spawned by the major European thinkers of the time, the contributions of many other cultures that created the conditions ripe for such breakthroughs lay hidden. In a sense, mathematics seems to be a totally European conception, where other cultures copied and followed. This is categorically untrue.
200 years before Taylor or Newton were even born, Madhava in Kerala discovered the polynomial expansions for the sine and cosine functions. In the 10th century, 800 years before Gauss, a Persian named Al-Karaji proved a formula for the sum of the first 100 natural numbers, as well as the first descriptions of the binomial theorem. Another 200 years before that, Al-Khwarizmi theorized solutions to quadratic equations. All these theorems and discoveries are foundational to the modern study of mathematics, especially when it comes to its applications in science, economics and engineering; however, they are now referenced to euphemistically through omission of the original author’s name, or, even worse, attribution to a different mathematician. Currently, the only way to fully interact with these names is to take Math 4030: History of Mathematics, offered every two years and barred by the entry fee of two 3000-level mathematics courses. Almost no undergraduates, except those within the Math major, will ever learn how diverse and multifaceted the development of the study has been.
Naturally, some may argue that this is simply not how math is supposed to be learned. Students will, of course, only have so much patience for learning the names of so many different people, especially in a subject as challenging as mathematics. Additionally, breaking away from how the textbook presents ideas could be incredibly difficult for some, leaving them confused as to what actually needs to be learned, especially if an unfamiliar name mentioned in lecture appears nowhere in the written material.
This is a disingenuous perspective, as it ignores the many ways such instruction can be rendered accessible, as well as the numerous liberties Cornell professors often take in teaching their lectures for the benefit of students. Providing both possible names to every theorem, or correctly attributing authors to certain ideas, are the small steps needed to encourage the broad changes needed in teaching mathematics, such that it remains true to its global origins. Giving students additional context to the material they learn, at the cost of a couple minutes in lecture or an additional sentence on a slide, is an infinitesimally small price to pay compared to the benefits gained. The ultimate goal of a Cornell education is to prime young adults for their introduction into actual society; as one of the foremost academic institutions in the nation, the University plays an essential role in giving each student sufficient perspective and knowledge to make them diverse and reasonable thinkers. Thus, it is every department and professor’s responsibility to pursue and promote this message, allowing the real depth of every subject to surface to the forefront of the education provided.
Ayman Abou-Alfa is a second year student in the College of Arts & Sciences. His fortnightly column Mind & Matter delves into the intersection of culture and science at Cornell University. He can be reached at [email protected].