Hi, this is Ray.

Here's a story I've been embarrassed to tell for about two decades. When I was 17, I quit math. Not officially. I kept showing up to class. I kept turning in homework. But somewhere around the start of pre-calculus, I made a quiet internal decision that math just wasn't for me. I was a "language person." I was a "creative person." Math was for the kids who were good at it, and I was clearly not one of them, so I would do the bare minimum to get through the requirements and then never touch it again for the rest of my life. Adios, equations. Vaya con dios, calculus. We had a good run.

For about 15 years after that, I was a proud non-math-person. I'd tell people, with a sort of mock-rueful smile, that I "didn't have a math brain." I'd dodge any conversation that involved statistics. I'd accept any explanation involving numbers without checking the work. I'd build entire businesses without understanding the financial math behind them, which (looking back) was less charming and more a slow-motion disaster I was lucky to survive.

Then, around age 32, I started learning some basic statistics for a project. Not because I wanted to. Because I had to. And something weird happened. The skill I was acquiring (the actual math part) was useful, sure. But what really surprised me was that learning math seemed to be making me better at learning OTHER things. Things that had nothing to do with numbers. My ability to parse a complicated argument got sharper. My ability to evaluate claims I read on the internet got better. My capacity to hold multiple variables in my head while thinking through a problem expanded. The math wasn't just teaching me math. It was teaching me how to think.

Today's newsletter is about whether this experience generalizes… whether learning math actually makes you better at learning OTHER things, or whether I just happened to be growing up in general during the same period and gave the math credit. The research on this is more interesting than I expected, and the honest answer is: probably yes, but with important caveats. Let's get into it.

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Let me start with the controversy, because there is one. The popular claim that "math teaches you how to think" is older than your grandparents and has been treated by the educational establishment as basically self-evident for generations. It's printed in university brochures. It's used to justify math requirements. It's the reason you had to take algebra even if you never planned to use it.

The catch: when researchers actually started TESTING this claim experimentally, the picture got a lot messier than the brochures suggested. A 2020 study published in PLOS ONE titled "Does mathematics training lead to better logical thinking and reasoning?" laid out the issue bluntly. As the researchers framed it, psychological research has been empirically investigating the concept of transferability of skills since the early 1900s, and points quite oppositely to reasoning skills as being highly domain specific… therefore, support for claims that studying mathematics engenders more than specific mathematics knowledge is highly pertinent, and yet largely absent. Translation: a hundred years of research suggests cognitive skills tend to stay within the domain you trained them in. Learning math makes you good at math. Whether it makes you good at OTHER things is much less clear than the brochures claimed.

A major 2014 paper by the Centre for Curriculum Redesign concluded, after reviewing the research, that there is not sufficient evidence to conclude that mathematics enhances higher order cognitive functions, calling for a much stronger cognitive psychology and neuroscience research base on the effects of studying mathematics. That's a pretty strong statement against the "math teaches you how to think" narrative. It's also more honest than most pop-science treatment of this topic.

So is the whole premise of this newsletter wrong? Should I tell you all those people pushing math classes were just gatekeepers running a 100-year hoax?

Not quite. Because the research has gotten more nuanced over the past decade, and the picture is more interesting than either "math is magic for the brain" or "math doesn't help anything else."

Here's what the more recent research actually shows. Math training doesn't make you generally smarter in some vague global sense. But it does seem to develop specific cognitive habits and skills that DO transfer to other learning, when those skills are similar enough to the math skills you trained.

A 2022 study examining mathematical achievement and cognitive ability in primary school children found a reciprocal relationship between math learning and general cognitive abilities. According to the researchers, Cowan et al. found that learning mathematics improves general cognitive abilities, and indicated that the relationship between general cognitive abilities and mathematics learning is reciprocal, at least between the ages of 7 and 9. The math wasn't just sitting in a sealed compartment. It was both drawing on and feeding back into broader cognitive development. Specifically, math learning during this developmental window was tied to improvements in planning, evaluation, and the ability to interrelate spatial images and verbal propositions. Those are cognitive skills that show up in basically every other subject too.

The interdisciplinary learning research is even clearer about transfer. A 2020 study on transfer of learning between mathematics and science at the university level emphasized that in order for successful transfer to occur, a learner selects appropriate previous skills and knowledge, applies them to new problems, and monitors the appropriate general and specific cognitive processes to solve them, and metacognitive strategies are used in transfer. Math training, when done well, builds a particular set of metacognitive habits… planning your approach, monitoring your progress, evaluating your answer, debugging when something goes wrong… that DO transfer to non-math domains. The transfer isn't automatic, but it's real when the conditions are right.

The research on math difficulties tells the same story from the opposite direction. A systematic review of children with mathematical difficulties found that some general cognitive domains are compromised in children with mathematical difficulties… specifically executive functions, attention, and processing speed. Kids who struggle with math often have broader cognitive deficits in areas that affect ALL their learning, not just math. The relationship between math and general cognition is genuinely entangled. You can't have rich math skills without strong executive function, working memory, and attention… and developing those skills in the math domain seems to support them generally.

Let me get concrete about what skills math actually develops, because "math makes you smarter" is too vague to be useful. Here's what the research suggests math training specifically builds:

Working memory under load. Solving a multi-step math problem requires holding multiple pieces of information in your head simultaneously while manipulating them. This is the same cognitive resource you use to follow complex arguments, plan complicated projects, or navigate any subject with multiple interacting variables. Math gives you reps with this capacity in a way that few other activities do.

Precise definitions and the discipline of being exact. Math forces you to be specific in a way most subjects don't. The difference between "approximately" and "exactly" matters. A small error compounds. Precision is non-negotiable. This habit of mind, once developed, transfers to fields like law, programming, philosophy, and science… any domain where exact specification of what you mean is part of the work.

Sequential reasoning with consequences. Each step in a math problem follows from the last, and an error in step 3 invalidates everything after it. This trains you to check your reasoning, to track logical dependencies, and to feel the seriousness of being wrong about something foundational. People without this training often build elaborate arguments on shaky premises and don't notice the foundation is rotten until it collapses.

Abstraction. Math is the practice of moving from concrete examples to general patterns. "Three apples plus four apples equals seven apples" becomes "x + y = z." This skill (seeing patterns underneath surface differences) is the engine of expertise in basically every field. Programmers, scientists, lawyers, writers, engineers, musicians: they all rely on the ability to extract general principles from specific cases. Math is one of the most reliable training grounds for that skill.

Tolerance for difficulty without giving up. Real math problems require sustained effort against initial confusion. You don't get them on the first read. You have to wrestle with them, try things that don't work, refine, and try again. People who have learned to tolerate that productive confusion in math are usually more comfortable with productive confusion in other domains. The "I don't know what to do here, but I'll figure it out" muscle is what math builds. That muscle works in many places.

Here's the angle I think gets undersold. You don't need to become a mathematician to capture most of the benefits we've been discussing. Even modest math literacy (statistics, basic probability, comfort reading a graph, the ability to do simple arithmetic in your head) has outsized benefits for everything else you learn.

Why? Because the modern world runs on quantitative arguments. Every news article cites statistics. Every business decision has financial math underneath it. Every health claim involves probability and effect sizes. Every scientific finding is reported with confidence intervals. Every policy debate includes economic numbers. If you've quit math, you've effectively quit your ability to evaluate any argument that uses numbers, which is approximately all of them.

I felt this directly when I started learning basic statistics. Suddenly I could read research papers and understand what was actually being claimed. I could spot when a news headline was misrepresenting a study. I could evaluate financial decisions based on actual math instead of vibes. The world hadn't changed. My ability to engage with it had. The cost of math illiteracy is enormous, and most of the people paying it don't even know they're paying it.

This isn't about being "good at math." It's about being able to think clearly when numbers are part of the picture, which is everywhere. As one analysis of cognitive transfer noted, mathematics skills are associated with future employment, well-being, and quality of life. The correlations aren't because math makes you a better human in some mystical way. They're because math literacy unlocks your ability to engage with a world that's increasingly quantitative.

A short rant before we get to the practical part. The single biggest barrier to most adults benefiting from math isn't difficulty. It's identity. Decades of telling yourself "I'm not a math person" creates a self-fulfilling prophecy where you avoid math, never develop the skills, and confirm your initial belief.

The research is pretty clear that mathematical ability is much more like a skill (trainable, improvable, sensitive to practice and instruction) than like an innate trait. The "math gene" is largely fictional. Most people who think they're bad at math had a few bad teachers, hit a wall they couldn't get past with the available support, and concluded that math wasn't for them. The wall was real. The conclusion was wrong.

If you've been carrying around the "not a math person" identity, please consider that this is an expensive belief. It's costing you cognitive development, it's costing you the ability to engage with quantitative arguments, and it's likely costing you opportunities professionally. The good news is the identity can be revised. Adults learn math just fine when they're motivated and patient with themselves. It just takes shedding the story before you can build the skill.

Okay, practical part. If you've been convinced that some math practice is worth doing, here's how I'd actually approach it:

Start with the math you'd actually use. Statistics is high-leverage for almost everyone… it changes how you read news, evaluate research, and think about uncertainty. Personal finance math is high-leverage if you have any money to manage. Basic probability is high-leverage if you make any decisions under uncertainty. Pick the math that maps to actual situations in your life. You'll be more motivated, and you'll get the benefits faster.

Use the resources that exist. Khan Academy is free and genuinely excellent. 3Blue1Brown's YouTube channel is the best math explanation content humans have ever produced. Coursera and edX have rigorous math courses, often free to audit. Books like "Naked Statistics" by Charles Wheelan or "How Not to Be Wrong" by Jordan Ellenberg make math accessible without dumbing it down. The infrastructure for learning math as an adult is better than it has ever been. The bottleneck is not resources. It's commitment.

Practice problems, don't just watch lectures. This is the failure mode of most adult math learners. You watch a video, the explanation makes sense, you feel like you got it, you move on. Then a week later you can't do anything because you never practiced producing the work yourself. Math is procedural. You learn it by doing it. Aim for 70% practice, 30% explanation. Suffer through the problems. The suffering is the workout.

Be patient with yourself. You're rebuilding cognitive muscles you haven't used in years or decades. The first few weeks feel awful. Things click slower than you remember. This is normal and it passes. Six months of consistent low-intensity work will produce dramatic results. Six weeks of intense work followed by burnout produces nothing. Tortoise. Hare. We've discussed.

Notice the transfer. As you build math skills, watch for the carryover into other parts of your life. Are you reading articles more carefully? Pushing back on claims that don't add up? Following arguments more cleanly? The transfer isn't automatic. Noticing it makes it stronger.

Here's what I want you to take from all this. The "math teaches you how to think" claim is partially true and partially overstated. Math doesn't magically make you smarter at everything. But math training, done well, develops a specific bundle of cognitive skills (working memory, precision, sequential reasoning, abstraction, tolerance for productive struggle) that show up across many domains. And math literacy, even at modest levels, unlocks your ability to engage with a world that increasingly speaks in numbers.

If you've been carrying the "not a math person" identity, please consider letting it go. Not because you have to become a mathematician. Because keeping it costs you more than you realize. The real benefit isn't becoming good at math. It's becoming someone who isn't shut out of every conversation that involves quantification, which means most important conversations.

I quit math at 17 and spent 15 years paying for that decision in ways I didn't even notice. I picked it back up at 32 and have been quietly grateful ever since. The brain you have at 22, 35, 50, or 70 can still learn this stuff. The opportunity cost of not learning it is much higher than the discomfort of the learning curve. Trade up.

Even Gandalf had to count rings.

Keep learning (and consider learning some math),

Ray