Mathematics is not a museum
I dropped out of a mathematics degree after four years, but I never stopped loving and studying mathematics. For me, mathematics is the most meaningful thing in the world. I like mathematics because you can apply it to anything: from physical motion to computations. When I talk about math, people often say it's complete — that there's nothing left to research or create. Schools give the impression that mathematics ends at trigonometry, logarithms, statistics, and algebra — that everything beyond is done. And only when you study mathematics seriously do you realize — no, there is so much mathematics that it's just crazy to think that there's nothing more. Mathematics is not a museum. It is a frontier.
There is not yet enough mathematics
Even so, there is not yet enough mathematics. We need to mathematize real-world systems — not to reduce them to numbers, but to build mathematical structures — with their own rules and properties — that model how these systems actually work.
How we got here
In ancient times, mathematics was valued for its applications: measuring land, calculating star movements, doing taxes. Nothing has changed since: mathematics is valuable because of its applications. Mathematics was so powerful that it was eventually applied to logic itself, giving logic a mathematical foundation. And mathematical logic led to computers, one of the defining themes of the contemporary world. You cannot imagine the 21st century without computers. This is how mathematization changed the world once. Now we need to do it again — for the domains that remain unformalized.
The gap
Computers make things easier. I can't imagine life without my phone, without the internet at my fingertips. Computerization is an important aspect of the world, but what about mathematics? Do people do mathematics in the era of computers? When we computerize books, transport, medicine — even intelligence (though I don't consider LLMs to be true AI) — is there still a place for mathematics? Many non-mathematicians say there isn't. But mathematics is behind these systems. It is behind computerization itself. So you need mathematization to back up computerization. We already have the machines. We don't have the mathematics. That's the gap.
A place of endless novelty
Mathematization is the next step. We need to mathematize everything. To do this, mathematics needs people. People who study mathematics and then create new mathematics where we need it.
We can model emotions, formalize creative spaces, give structure to thought. The possibilities are endless. We don't need to apply existing math to these domains. It's hard to imagine how calculus can capture emotions. We need new structures. We can invent new math. It can be something we haven't imagined yet. We can develop a mathematical theory of any idea, any concept. Applications follow understanding. First we need the mathematics. The applications will come.
This is not about flattening the human experience. It's about taking it seriously enough to give it a rigorous language.
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