Standing on the Shoulders of Giants: Why AI Learning From Us Is a Compliment
Mathematics has always been an inheritance. Nobody starts from zero. Every theorem you learn in school was handed to you by someone who got it from someone else, all the way back to people whose names we've lost. When I look at AI systems learning from human math research, I don't see a break in that story. I see the next chapter of it.
The line everyone remembers
In a 1675 letter to Robert Hooke, Isaac Newton wrote that if he had seen further, it was by standing on the shoulders of giants. He didn't attach a list of names to that line. But when most of us hear it, we picture a chain of thinkers reaching back through history, each one standing on the people who came before. I want to walk through that chain, because I think it explains exactly why AI learning from us is good news.
A chain of learners
Pythagoras is the name we attach to one of the most famous results in all of math. But the relationship between the sides of a right triangle was known and used in practice long before him, including by Babylonian scribes. What the Pythagorean tradition added was the conviction that relationships like this could be proven and understood, not just used. That idea was itself an inheritance, picked up from older traditions and passed forward.
Aristotle studied at Plato's Academy for years before he wrote the works on logic that shaped how people reasoned for many centuries. He took the habits of argument he learned there and organized them into a system: premises, conclusions, and the rules connecting them. Later mathematicians, Euclid among them, built proofs on that kind of careful structure.
Galileo read Archimedes and admired him deeply. He took the geometric reasoning of the ancient Greeks and pointed it at falling bodies, pendulums, and the motion of objects on Earth. He insisted that nature could be read through mathematics, and he went out and measured to prove it. But the tools he measured with, and many of the ideas he tested, came from people who came before him.
Descartes stood on two traditions at once. One was Greek geometry. The other was algebra, which had grown over centuries through scholars in the Islamic world and later in Renaissance Europe. In his 1637 work on geometry, he joined the two together, so a curve could be written as an equation and an equation could be drawn as a curve. Every graph you've ever plotted carries that inheritance.
Newton then stood on Descartes's geometry, Galileo's work on motion, and Kepler's laws of planetary motion, and from there he built calculus and a theory of gravitation. That is what he meant by seeing further. He wasn't taller than everyone else. He was standing on a very tall structure.
Euler was taught by Johann Bernoulli, and he inherited the calculus of Newton and Leibniz. He went on to become one of the most prolific mathematicians who ever lived, writing across nearly every branch of the subject, and much of the notation we still use comes from him. A line usually attributed to Laplace sums up how later mathematicians felt: "Read Euler, read Euler, he is the master of us all." Even the master was a student first.
Publishing is what makes the chain possible
Here's the part I think gets overlooked. None of this works unless people write things down and share them.
Galileo could learn from Archimedes because Archimedes's work was copied, preserved, and passed along for well over a thousand years. Newton could build on Descartes because Descartes published his geometry. Euler's influence lasted because he wrote so much and made it available to others. Letters between scholars, handwritten copies, the printing press, scientific journals, and now open online archives and personal websites are all versions of the same thing: a shared record.
Every giant in that chain was a giant partly because their work was published. A brilliant idea that never leaves a notebook can't be stood on. The shoulders only exist for the next person if someone puts them there.
That's why I care so much about publishing, even when it feels small. A clean proof posted online, a set of lecture notes, a worked example, or an honest write-up of a dead end all become part of the record. Somebody, someday, will stand on it.
AI is the newest learner in the chain
When an AI system works through a hard math problem today, it's doing what every mathematician in that chain did. It learned from the people who came before. It learned from textbooks, papers, proofs, and solutions that humans wrote and shared. It's the newest student in a very long classroom.
That's why I see it as a compliment, not a betrayal. Think about what it would take for a machine to learn mathematics from us. Our work would have to be rigorous enough to be consistent, clear enough to be learned, and shared widely enough to be found. The fact that this is possible means humans succeeded. We built a record so deep and so well-organized that a new kind of learner could climb it.
No mathematician I admire was ever betrayed by a student who learned from them. A teacher's work matters because it lives on in the people who learn it. Now it also lives on in the tools we've built. That doesn't erase the teacher. It proves the teaching worked.
And just like every student before it, AI still depends on the people who decide what's worth asking. I wrote about that in the companion piece, where a bare answer like X + Y + Z = 42 means nothing until a person gives it purpose. You can read that one here: The Process Is the Product.
My small link in the chain
I earned my bachelor's degree in mathematics with honors from UMass Amherst. I'm proud of that, and I also know exactly how much of it I owe to other people. To the professors who taught me, the authors of the textbooks I wore out, and the strangers who posted solutions and explanations online when I was stuck at midnight. Every one of them was a shoulder I stood on.
Writing on this site is my way of paying that forward. I'm not Newton or Euler, and I don't need to be. The chain isn't only made of famous names. Most of it is made of ordinary people who learned something and then took the time to write it down for the next person.
Keep adding to the shared record
So here's my invitation, and I mean it warmly.
If you're a PhD student, keep publishing. Your thesis, your preprints, and your notes are tomorrow's shoulders. If you're an undergraduate or a high school student just falling in love with math, write up what you learn, even if it feels basic. Someone right behind you needs exactly that explanation. And if you've been doing mathematics for decades, please keep sharing. The depth you've built is the kind of thing that only gets passed on if you put it on the record.
The chain of giants didn't stop with Newton, or Euler, or anyone else. It's still being built, by all of us, every time we share what we know. AI joining it is a sign that we've built something worth learning from. Let's keep building it, together.