The importance of theoretical research
Why the pure sciences are essential to humanity
I was prompted to write this article by a recent column in The Tech. There, the author discusses why he believes that MIT spending one billion dollars to create a College of Computing is a bad idea. I have opinions on the broader message he was trying to convey, but this will not be the topic of this article; instead, I will object to a few sentences used by the author. As a remark, my broader opinions on this subject are shared by a friend of mine, Shreyas Kapur, who has written a response to the cited column which addresses these broader concerns.
My opposition to this column stems from a few very generalized, but still troubling, statements. In particular, the subtitle reads “we should do things not because they are hard, but because they are important.” Perhaps it is a little unclear as to what exactly the author means by the word “important”; this is clarified a few paragraphs down, where he says “but as an institution that seeks to better humanity through the sciences, our mission should not be to solve hard problems; it should be to solve pressing problems.”
These statements are concerning; they seem to be suggesting that the so-called “pure sciences” are not worth studying, since (by definition) the questions studied have absolutely no applications to solving pressing problems. I'm not sure if that is what the author intended to convey, but I believe that it is still important to argue that the pure sciences are very important to humanity. This is, in part, a defense of my interests. However, more generally, these generalized statements have surely been uttered to almost anyone who works on something theoretical.
Before making any claims, I will have to address what I mean by the “pure sciences.” I don't really want to provide a precise definition, so I will let Randall Munroe illustrate what I mean. Certainly, therefore, if I could argue that pure mathematics and theoretical physics are important, then it would be possible to use similar arguments to claim that all of the pure sciences are important.
So why are pure mathematics (which I will just refer to as “mathematics” from now on) and theoretical physics important? One could argue that mathematics and theoretical physics are important to work on now because somebody will find some application in the future. Take, for example, Einstein's work (a very cliché example; sorry!) on general relativity. Back when he was working on developing this theory, there was no application for his work. His work, for example, clarified the precession of the perihelion of Mercury: stuff that is utterly useless to society! But today, you need predictions made by general relativity to make corrections to GPS satellite clocks, and nobody would deny that anything having an impact on GPS technology is useless.
While this is a good defense of theoretical research, and one that probably has appeared in numerous grant letters, I don't think this is really why theoretical research is important, or why theoreticians do what they do. I believe that people do theoretical research for a much deeper reason, one that isn't appreciated by a lot of people today because of the numerous problems existing in today's world.
Humans are not unique in creating tools to solve problems: there is a long Wikipedia page cataloguing examples of animals using tools. While tool-use does require some cognitive sophistication, it is certainly not representative of the limit. What, then, differentiates humans from other animals? I don't want to claim that humans are in any way superior to other species, but one possible answer is our ability to approach abstract problems. For example, we can plan out the construction of a skyscraper, say, using pure thought, without having to make multiple attempts and fail numerous times in order to learn the right method.
Using this unique ability to only build tools that will be useful to society seems short-sighted. This power to imagine and play with abstract concepts means that we could be thinking about things that have never been studied before in the history of life on Earth. That’s a grandiose statement, so let me translate this into a claim that is less pretentious. Mathematics, and more generally any pure science, studies hard problems simply because they are challenging, so studying something like mathematics is essentially understanding the way the human mind thinks. Mathematics, for example, is a very “clean” subject.
Unlike subjects like biology, chemistry, and any engineering subject, one does not need to have anything other than a brain and the relevant training in order to understand math. One does not have to worry about their code not compiling because they accidentally used Python 2 instead of Python 3, or that they do not know the coefficient of friction to five significant figures. As long as one is willing to spend time and energy ruminating on concepts and ask for, and provide themselves with, clarity in exposition, anybody can understand mathematics. Any proven statement is indubitably true, and there is no way anyone could contest its truth. Of course, one could still make mistakes in a proof, but a mistake is created not because someone messed up entering values onto a computer, or because they did not account for air resistance; rather, it is because they have an error in their logic. It's horrifying to make a mistake, because when you do, you realize that you have a misunderstanding of something as fundamental as logic, and that you haven't grokked something well enough. And that's the whole purpose of mathematics: to understand things as well as possible and to solve hard problems.
I approach mathematics as a sort of very large and complicatedly intertwined graph. I don't think I've understood something until I can zoom into this graph arbitrarily well and explain every step taken to deduce a final result. When I do have a statement along with a correct proof, it is exhilarating because I know that I have come across a fundamental, irrefutable truth. I wouldn't trade that feeling for anything.
So far, I have only addressed why one should study something like theoretical mathematics. While the reasons mentioned above are also applicable to the other pure sciences, there are other reasons more specialized to fields like theoretical physics. Sure, theoretical physicists might revel in their ability to stretch the barrier of human thought, but the reason they are physicists and not mathematicians is because they love the thrill one gets when thinking about the way the universe works.
Take, for example, things like Bell's theorem and quantum entanglement, which both (very roughly) say that quantum mechanics is nonlocal. These theories tell us important facts about the way physics (or, more generally, the world) works at small scales. These sorts of results are rather inconsequential for everyday life, and certainly do not help with humanity's impending climate-change-induced doom — but they are still absolutely vital to humanity, by showcasing mankind's unique ability to understanding the “inner workings of the world.”
I certainly believe that the non-pure sciences are equally important to humanity. Although we obviously need to address issues that plague us today, we should also be very hesitant to claim that the pure sciences are not as fundamental as the applied sciences. It would be very shortsighted to abandon studying such subjects or look down upon them in disdain: we would lose a major part of what makes us human.
Sanath Devalapurkar is a member of the MIT class of 2020, studying mathematics (Course 18) and physics (Course 8).