I recently saw some typical projections about what college majors were drawing the highest compensation three years out from graduation. It looked pretty math-heavy to be sure. I’ve looked into it further and found that while there’s no official dataset that tracks pay exactly three years after graduation, the closest are the New York Fed’s early-career figures (grads aged 22–27, roughly 0–5 years out) and Department of Education data covering about four years out. Both tell the same story: engineering and computing dominate. The highest early-career median pay by major (New York Fed, latest release) are: Computer engineering ($90,000), Computer science ($87,000), Chemical engineering ($85,000), Aerospace engineering ($85,000), Industrial engineering ($83,000), Electrical engineering ($82,000), and Mechanical engineering ($80,000). That’s well below the $200,000+ numbers I was seeing for applied mathematics and statistics. Finance is the only major on the list that isn’t engineering or computing. Liberal arts and humanities majors typically earn about half what engineers do.
When I went off to Cornell in 1971 I had scored much higher on the math SAT than on the verbal SAT and my strengths and preferences ran to both math and sciences (now called STEM), so I applied to and got accepted to the engineering school. That’s where I met up with calculus for the first time since my foreign prep school education had not included what most U.S. AP high schools were already offering students…a pre-calculus course. Calculus knocked me flat. You see, calculus, while a branch of math, in unlike arithmetic (numbers and operations), algebra (unknowns and equations), geometry (shapes and space), statistics and probability, and even number theory, as it deals with change and accumulation, and it has two core ideas: Derivatives measure how fast something is changing at a given instant, like a car’s speed at one moment or how quickly a stock’s price is moving, and Integrals that add up infinitely many tiny pieces to get a total, like the distance traveled given a changing speed, or the area under a curve. Newton and Leibniz developed calculus independently in the late 1600s. It builds on algebra, geometry and trigonometry, which is why it usually comes at the end of the high school math sequence. But calculus requires a different form of thinking. It’s actually a shift in thinking more than a different kind of thinking, and it’s the same shift that shows up in all higher math. Calculus is just where most people meet it first. Where the thinking changes is from procedures to processes. Arithmetic and algebra are mostly about following steps to get an answer. Calculus asks you to reason about what happens as a process unfolds, such as a gap shrinking toward zero or a sum growing toward a total. You have to picture something in motion, not just compute. It takes things from finite to infinite. Intuition built on everyday quantities breaks down. Adding up infinitely many pieces can give a finite answer, and a quantity can approach a value forever without reaching it. Getting comfortable with that takes deliberate rewiring. It takes you from exact answers to approximation. Calculus essentially says: approximate, then make the approximation better and better until the error vanishes. That’s a different mindset from “find the right number.” You think in functions and rates rather than single answers.
What’s funny about me hitting the calculus wall as I did was that calculus actually figures quite prominently in econometrics and since I shifted from engineering to the Arts College to study economics and government, I wasn’t entirely escaping it by running away from engineering. What’s even funnier is that while finance is very math-heavy, the place where calculus really starts to come in strongly is in the areas like contingent claim analysis that developed in the 1980s into the forward markets and the development of the derivatives market. Being the guy who was trying to avoid calculus makes it particularly funny that I was one of the guys who led the charge in the development of the derivatives business and that, in many ways, formed the basis of much of my advancing career on Wall Street. It plays to one of my themes that when you try to avoid a specific beast, it tends to sneak around behind you and bite you in the ass in some other way eventually.
I am hardly alone in my love/hate relationship with math. I really do love simple math and while calculus is clearly one of my boogeymen, I even embraced what I needed of it to become a derivatives major domo. But America is even more conflicted over math. U.S. math performance peaked around 2013, slid for years, and then the pandemic knocked it down further and it hasn’t recovered, just as the world is shifting from the Information Age into the math-intensive AI Age. The data show that among high school seniors, average math scores were the lowest since 2005, when the assessment framework changed significantly. 45% scored below the “basic” level, five percentage points more than in 2019. Only 22% reached proficiency or above. Testing officials estimate that 33% of the class of 2024 was ready for college-level math, down from 37% in 2019, even as more students said they intended to go to college. On the 2022 global math tests, the U.S. ranked 28th in math. Scores dropped for all but the highest performers, and the gap between high and low performers widened. The top students are holding steady while the bottom is falling away. This does not bode well for wealth disparity since we see that the highest paying jobs have the highest math orientation. The leading explanations for this include that states have had more flexibility in setting their own metrics, and schools have shifted focus toward mental health, attendance and digital devices and away from math. The timing of this sharp decline in math scores matches the rise in social media usage, though this is hard to prove. Students in 2024 were less likely to report taking pre-calculus, so it isn’t likely to get better any time soon.
I just this morning read a Paul Krugman article about Trump’s recent deal with Russia for diesel fuel. Trump announced that he was buying 300,000 tons of Russian diesel. From a legal standpoint he’s not allowed to do this since sanctions set by Congress prevent the purchase of Russian oil by law, but since when have laws stopped Trump from doing anything. So the big issue is that Trump isn’t even hiding the fact that he is supporting Putin and his war of aggression against Ukraine (kinda makes him look like he’s is, indeed, Putin’s patsy, as has been suggested and litigated over the past decade). But that’s not the most interesting point…unfortunately. When I read about 300,000 tons, the first thing I wondered is why it was being shown in tons rather than the normal barrel designation. It turns out that 300,000 tons of diesel fuel is a bit over 2 million barrels. America consumes approximately 4 million barrels of diesel and heating oil every day. As Krugman put it, Trump is betraying our embattled democracy, demonstrating our faithlessness to the whole world, seriously damaging whatever is left of America’s leadership in the world, for the sake of maybe 12 hours’ worth of diesel. He is obviously counting on the fact that Americans can’t do even simple math, or, worse yet, his acolytes in these policy discussions themselves cannot do simple math. WTF?!?!?!?