I've been working in systems for years, and there's something tutorials never say out loud: all of this is undergraduate math running at industrial scale. Remove linear algebra and no "AI" remains. You're left with an expensive GPU with nothing to do.
Today the PISA 2025 results came out, and Mexico once again stayed where it has been for twenty years: at the bottom of the OECD in math. I want to connect these two things, because from my perspective they are not separate topics. They are the same problem seen from two ends.
Computing is math with electricity
I'll start with what I see every day.
A language model is, at its core, matrix multiplication. Attention, the mechanism that made GPT, Claude, and Gemini possible, is written in one line:
Three matrices, one product, one normalization. Repeat that billions of times and you have a chatbot. NVIDIA GPUs are worth what they are because they are factories for multiplying matrices and nothing else. When we quantize a model so it fits on a cheaper server, we are deciding how many bits to give to each entry in those matrices. That is numerical linear algebra.
The embeddings I use in any retrieval system are vectors of 768 or 1,536 dimensions. Searching for "the most similar document" is calculating a cosine similarity—a normalized dot product. pgvector, which is what I run in PostgreSQL for that, indexes with HNSW, an approximate nearest neighbor graph whose recall depends on how distance behaves in high-dimensional spaces. If you don't understand norms and projections, you cannot reason about why your index returns garbage.
Training is calculus. Backpropagation is the chain rule applied with discipline: you calculate the derivative of the loss with respect to each weight and take a step in the opposite direction of the gradient. Adam, the optimizer almost everyone uses, is gradient descent with first and second moment estimates. A poorly chosen learning rate diverges for reasons explained by a Taylor series. No one trains anything serious without understanding that, even if PyTorch hides the derivatives.
Video games and 3D graphics are pure linear algebra. Every frame, the engine takes each vertex of every model and multiplies it by a 4x4 matrix that combines model, view, and projection. Rotating a character by an angle $\theta$ on the Z axis is applying
to each point. When composite rotations lock up (the classic gimbal lock), engines switch to quaternions, which are an extension of complex numbers. Unity, Unreal, and Blender do this millions of times per second. Lighting is a dot product between the surface normal and the light direction. Without trigonometry, there is no Minecraft.
There is more, and I'll list it quickly because the list is long:
- Cryptography. TLS, the browser padlock, relies on modular exponentiation and elliptic curves. It's number theory, the branch that for centuries was considered the most useless of all.
- Compression. JPEG, MP3, and any video call use the discrete cosine or Fourier transform. Your Zoom call is signal analysis.
- Routing. Google Maps, or the CDMX transit planner I built a few months ago, run Dijkstra or A* on a graph. PageRank, the algorithm Google was born with, is the eigenvector of a giant matrix.
- Statistics. Every machine learning model is a disguised probability distribution. A poorly done A/B test costs you a product. Bayes lives in every spam filter.
- Optimization. Linear programming decides how packets are routed, how shifts are assigned, and how a supply chain is planned.
- Logic. Your processor's circuits are Boolean algebra, and the compiler translating your code is automata theory.
There isn't a single well-paying area of computing that isn't standing on mathematics. Those who "just code" are gluing together pieces that someone with math designed.
Why this matters for Mexico
I already wrote about the country's technology gap. I'll summarize: we have young demographics, a border with the largest market on the planet, and a wave of nearshoring that is giving us an opportunity we won't see twice. The question is which part of that wave we capture. We can be the country that assembles, or the country that designs.
Assembly pays assembly wages. Designing chips, training models, building simulation engines, doing cryptography, optimizing logistics networks: that pays ten times more and stays. And it cannot be imported. You can bring in a factory in two years; you cannot bring in a generation of engineers. You have to form that generation, and the formation starts at six years old with fractions, not at twenty-two with a Python course.
Language models don't fix this. They make it worse, in a sense. Now anyone can generate code that compiles, and the value has moved to those who can verify if that code is correct, if the model hallucinated a formula, or if the metric the dashboard reports means anything. That verification is mathematical judgment. A country without math will have millions of AI users and very few who build or even understand it.
What PISA said today
PISA is the test the OECD applies every three years to 15-year-old students in dozens of countries. It measures if a young person can use math, reading, and science to solve real problems, not if they memorized formulas. The 2025 edition was published today, September 8, 2026.
Mexico scored 388 points in math. The OECD average was 469. That is an 81-point difference, and the OECD itself calculates that about 20 points are equivalent to one school year. Our 15-year-old students are about four school years behind the average in math. In reading we scored 408 against 461; in science, 414 against 482. Compared to 2022, we lost seven points in math and seven in reading.
The percentages are worse than the averages. Only 30% of Mexican students reached level 2 in math, which the OECD considers the minimum to function in adult life. In the OECD, 65% reached it. Seven out of ten Mexican 15-year-olds cannot, for example, convert a price to another currency or read a simple graph. On the other end, 0.1% of Mexicans reached the high levels (5 and 6) in math. The OECD average was 8%. One in a thousand against eighty in a thousand. That's where the designers come from; we produce almost none.
91 countries and economies participated. In the full math table, Mexico ranked around 65th, tied with Jordan and just above Costa Rica. But the comparison that matters is with the 38 OECD member countries, the club Mexico chose to join, and there we ranked 36th in math and 37th in reading and science. The sample was 7,843 students in 297 schools, and here is another fact almost no one mentions: those students represent about 69% of the country's 15-year-olds. PISA only evaluates those enrolled in middle or high school, so the other 31%, mostly kids who have already left school, don't even appear in the results.
And the country almost didn't participate. There were months, between 2023 and 2024, when the SEP did not confirm if Mexico would go to PISA 2025. After the previous government eliminated the INEE in 2019, PISA is practically the only external and independent measurement we have left. Without it, we would be flying without instruments.
Twenty years below the line
What bothers me most isn't today's number. It's the full series.
Eight measurements, eight times below average, and never close. Our best year was 2009, with 419 points, and even then the distance was 83 points. Since then we've had 16 years of slow decline: 413, 408, 409, 395, 388. Today we are below the 2006 level.
Someone will say the OECD average also fell, and it's true: it went from 502 in 2003 to 469 in 2025, with the pandemic and phones as the usual suspects. But falling from 502 to 469 is not the same as falling from 419 to 388. They lost an advantage. We lost the little we had. The gap closed between 2003 and 2009, when Mexico was still rising, and since then it has stayed between 81 and 88 points only because the OECD is also going down. We are "approaching" the average in the same way a parked car approaches one that is in reverse.
A bad streak doesn't last twenty years. This is a system that produces this result in a stable and predictable way, under governments from three different parties.
What I believe can be done
I am not an educator. I am someone who hires, trains, and works with engineers, and from that place I see three concrete things.
The first is to measure. A country that eliminates its evaluation institute and hesitates to participate in PISA is choosing not to know. In engineering, that's called turning off monitoring because the alerts are annoying. We need to go back to having independent evaluation that is published and comparable year by year and by school.
The second is the teacher. The 15-year-old student who cannot read a graph had a primary school teacher who probably didn't feel comfortable with fractions either. The 2022 curriculum diluted math into broader "formative fields" at the exact moment the rest of the world is going in the opposite direction. Training and paying math teachers well is cheaper than any other policy, and it takes ten years to see results. That's why no one does it.
The third is on us. The technical communities in this country, MexicoDev included, have spent years teaching frameworks. We should teach the bottom layer: linear algebra with NumPy, probability with real data, why the gradient points where it points. The resources exist and are free: Khan Academy in Spanish, 3Blue1Brown, MIT open courses, the Mexican Mathematics Olympiad which finds talent every year in places where no one looks. There is plenty of material. What's missing is the decision to treat math as infrastructure and not as a subject to just "pass."
I'm going to do my part with what I know: content, open source, and this community. But I won't lie to myself about the size of the problem. A country where seven out of ten young people don't reach the basic level of math will not design the chips or models of the next decade. It will buy them. And it will pay the full price.