Math vs English: on hard vs soft subjects
Why math isn't intrinsically harder and what that means for us
Is math difficult?
Your first answer to whether mathematics is difficult is probably a resounding and unwavering yes. Hard subjects — mathematics, physics, statistics, computer science, engineering, and possibly chemistry — strike fear in the hearts of high school students. They cause adults long away from the narrow fray of academia to shudder. Math anxiety is a depressingly well-researched field.
In contrast, subjects such as art, political science, and economics — what I call the soft subjects — are perceived less rigorously and even abjectly. Art, management, and English students are studying art, management, and English because they aren’t smart enough and can’t handle more difficult subjects, with the difficult thing usually being quantitative shape-rotating ability.
The reason hard subjects are hard is a self-reinforcing myth driven by two predominant factors. Firstly, hard subjects require consistent hard work. Secondly, objective merit is easier to measure in hard subjects. These factors act in unison to toughen competition in hard subjects relative to soft subjects, which makes these fields appear harder than they are. More intellectually ambitious students select the hard subjects, reinforcing the apparent difficulty of mathematics.
Math isn’t intrinsically harder
Hard subjects aren’t intrinsically harder. Firstly, rigour doesn’t guarantee difficulty. I like this quote: “the reason economics is harder than physics is that the atoms we study actually think”. In that sense, sociology or literature is even “harder”: the lack of quantifiability in sociology proves the difficulty in understanding the multifaceted nature of humans that the subject itself isn’t even possibly quantifiable using mathematics.
Is this a simplified view? Maybe our minds weren’t made for mathematics, but there’s minimal evidence for this. As the science writer Elizabeth Landau argues, no evidence suggests that our brains aren’t for math or numeracy. Rachael Meager argues that the hard subjects are difficult because they “requires lots of dedicated, focused attention to learn and thus resolve it”. But this problem isn’t exclusive to hard subjects — one can imagine devoting a lot of time to interpreting the confusion that is Foucaultian philosophy as well!
Secondly, our definition of subject difficulty is too narrow. There’s a distinction between the difficulty students face in learning a subject and the challenge of making significant contributions to it. According to Bloom’s taxonomy of learning: the highest level of learning involves original creation. Hard subjects have an edge here: with the exceptions of pure mathematics, it seems easier to create original knowledge in chemistry or physics than in soft subjects. For instance, academic papers in the sciences are cited, scrutinised, and analysed, but the same cannot be said for law, the arts, or the humanities. All good criticisms of Hobbesian philosophy or Shakespeare may have already been explored, but there is still much scientific progress to be made in the supposedly hard subjects. Under this definition of difficulty, soft subjects edge out the hard subjects.
So, why do we think of math and the hard subjects as harder?
Math is more hard work
Math appears harder because it’s a lot of hard work. The rewards of studying math are more closely linked to hard work. More formally, the returns to effort are higher and less volatile in math. In mathematics, the grading distribution ranges widely from 0–100, and the costs of not studying are drastic. In comparison, the grading distribution is tighter in English: you’re guaranteed an unremarkable but sufficient grade if you put something on the page that shows a semi-decent understanding of Shakespeare’s Othello.1
Math is difficult in high school because it’s about your ability to follow a precise set of rules built on top of each other. You need to know the rules of algebraic manipulation to understand differentiation or trigonometry. When some students are inevitably behind or get poor teaching for one year, it’s a lot harder to catch up. The same problem doesn’t exist for soft subjects.
There's also a peculiar cycle in play with hard subjects like mathematics and chess. Students with higher general intelligence (g-factor) often opt for these fields, influenced by the societal perception that they are challenging and prestigious. This, in turn, heightens the competition, reinforcing the idea that these fields are inherently difficult.
Math is more meritocratic
Hard subjects such as mathematics are more meritocratic. The International Mathematics Olympiad (IMO) and Putnam Competition capture the brightest mathematical talent. Math and physics are fields laden with geniuses. Borrowing a mathematical term, merit is well-defined in hard subjects. Extending this to the grading system, a B in math is different from a B in English.2 The signal from a B in mathematics probably means you did fairly well on an exam. Grade B in English is much more confusing: it could mean “decent essay!” to “I am bored reading the 35th essay on the use of colour in Romeo and Juliet, and you are a mediocre writer, but it was sufficient.”.
Let me further elicit this point. A computer science student who is told that they’re performing at the 70th percentile might feel bad about their programming abilities. Your mathematics skill level seems so set in stone. In contrast, an English student who is told that they’re at the 70th percentile might disagree with this assessment. Just think about the history student who receives a poor mark on an essay and thinks to themselves: the teacher graded my paper wrong… they had the wrong views… they’re biased… hmmph! And they wouldn’t be wrong! Feedback loops in soft subjects are less fruitful — at the very least, feedback in the “easily accessible” subjects is noisy due to the belief that we are more entitled to comment, disagree, and disobey in the humanities.
This is why competitions such as the Putnam or the IMO are so prestigious. These competitions reliably and legibly speak to intellectual ability in a way that’s valid for everyone from our mothers to the Harvard admissions office. In contrast, a high school student who successfully publishes their literary critique in a quality magazine might be well-respected and admired, but may also be perceived glitzy, facile person who only knows how to lambast poetry. They may be advised to get a real job or skill instead!
A game of chess and poker
Comparing hard and soft subjects is similar to comparing chess (hard subjects) vs poker (soft subjects). A game of chess is highly deterministic: betting against Magnus Carlsen would not be a good idea. In a game of poker, results are noisier. Your wins are occasionally down to skill, but your self-assessment of your actual skill level is intermingled with luck.3 In chess, you know that you probably won’t ever be the best chess player. In poker, there’s just that slim possibility you could be the next Daniel Negreanu.
This thinking affects how we think about talent distribution and what to do with our lives. If you were a 95th percentile child in school, you know that you aren’t the original engineer or the genius mathematician. But you may very well be the best writer, salesperson, or sociologist because there are more unobserved elements of succeeding in these soft fields. Your options set is bounded in the hard fields: there are only so many correct answers, rational chess moves, and solvable mathematical problems. But in a soft field, or in a human game of poker, your creativity, mind, and soul are the only natural bounds on your limits. The competition in hard subjects is tougher and more meritocratic. But the subject itself isn’t necessarily harder.
Writing vs interpreting the rulebooks
Overall, the most intrinsic element of hard subjects is the existence of absolute truths. Soft subjects are soft in part for their relativity due to the consistently evolving viewpoints of scholars and the changing nature of our world. When we’re students, following and using the rulebook well (hard subjects) is harder than making your own rules (soft subjects).4 But figuring out the rules of the rulebook (research in hard subjects) is easier than understanding what makes for good rules (soft subjects).
Our perception of math and hard subjects as harder is justified by social mythology. Hard subjects demand rigorous work. Merit is clearly defined. But this doesn’t make the hard subject itself more difficult than the soft subject — if anything, soft subjects are easier to access but harder to master. The true tragedy of all this is the people who live in unjustified fear of rigour or numbers because of the way that we’ve been conditioned to think about numeracy. Addressing this problem head-on is pivotal for flourishing in the 21st century, an era that demands both the supple nuance of the humanities and the fact-based precision of mathematics. — MC
Another interesting argument: is it that the content in hard subjects is more difficult than soft subjects? History classes focus on the most interesting and accessible parts of history, which for most people are the two world wars and the inter-war period. English classes focus on similar easily accessible seminal texts that have been analysed to wit’s end. Maybe the soft subjects are too easy?
The notable exception to this is for standardized tests such as the SAT, ACT, GMAT, and GRE. But these tests examine one’s ability to manipulate, understand, and write the English language, which is very different from one’s ability to interpret, evaluate, and synthesize ideas in the English language, which feature much more significantly in the academic study of literature and philosophy.
This, in part, is why people pick poker over chess when considering which game of strategic choice they would like to try and get good at. You can Dunning-Kreuger yourself into thinking that you’re good at poker and chess, but the effect lasts much longer in poker.
By the way, this partially criticizes the free-verse new age Instapoets in the 21st century. The reason these poets are so often the target of ridicule is because their writing shows no understanding of rhythm, structure, or meter. In other words, they never learned the subtle but necessary rules of poetry so thoroughly mastered by the old and dead masters of poetry. It’s an argument for mastering the sonnet before writing in free verse.