Math has undeniably escaped the human mind and implanted itself in nearly every corner of the world. Over the past 75 years, as computers became commonplace and grew in power, what once amounted to mental arithmetic has become something else entirely. It’s not just math; it’s “Big Math,” too large for the human brain alone.
Big Math’s offshoot algorithms, the step-by-step sets of instructions and rules used to perform calculations, now undergird much of the technologies we take for granted in modern life. They organize your addictive TikTok feed, compress your Netflix shows from terabytes to gigabytes so you can stream seamlessly, help you locate your lost iPhone with Apple’s Find My app, and manage the logistics of your Amazon purchase, among many other functions.
Disassemble these algorithms and what you will see are numbers. Lots of numbers. To the untrained eye, they might seem random, meaningless. But discernible patterns emerge in these digits. While mysterious, they can be demystified.
When math became Big Math
That’s what Cornell University mathematicians and “office neighbors” Steven Strogatz and Alex Townsend ably do in their forthcoming book, Big Math: The Hidden Codes That Run Our World. As they told Big Think, that aim is increasingly urgent. Why? Because Big Math isn’t merely augmenting and improving our lives; it’s increasingly determining them.
Will you get a credit card? Be granted a loan? Accepted into college? Considered for a job? Algorithms are making more and more of these vital decisions. And, of course, algorithms provide the foundation for the artificial intelligence models driving the modern economy and altering how we live and work.
“In the democracies of the world, where people still have a choice and can participate, how can they participate meaningfully given how uncomfortable most people are with math?” Strogatz wondered during our conversation, adding that comprehension of these key Big Math advances shouldn’t be hoarded by tech titans.
“We wanted to write a book for anyone who is curious and wants to be part of this moment and who has felt left out.”
Too big to understand?
In Big Math, Strogatz and Townsend excel at explaining the optimization functions that make Amazon fulfillment centers hum, the compression algorithms that shrink down your images and videos, and the Markov chains that, through Google Search, effectively sort the internet. Furthermore, they share stories of great mathematical advancements that render their field — regularly stereotyped as intellectually impenetrable — humanly relatable.
Importantly, they do not conceal an uncomfortable truth: As AI models have advanced at breathtaking pace, their operations defy understanding.
“We don’t know why these models work so well. No one does,” Strogatz and Townsend write. “This is the unnerving moment we’ve reached in Big Math. We are surrounded by systems that perform astonishingly well, yet they defy our attempts to understand them.”
During our conversation, Townsend further explained what that means: “We understand what [AI models] are made of. We understand the mechanics that go into them. We understand … the learning process they undergo. What we don’t understand is how they learn the things that they actually learn.
“We understand the pieces, but not the whole.”
When Big Math came for mathematicians
Mathematicians also don’t fully understand how the AI models, which they helped birth, are now churning out remarkable math proofs at a bewildering pace, upending their entire field.
In early September, OpenAI announced that 88 of their agents solved the Navier–Stokes Millennium Prize Problem, one of math’s “holy grails” (though the highly intricate proof still awaits official verification). A month later, the company released solutions to 372 more problems, each highly sought-after in its own niche of mathematics.
Clearly, their book’s publication was impeccably timed for the moment, and Strogatz and Townsend have since been publicly grappling with the potential ramifications for their field. Notably, in an article in The New York Times, they fretted that using AI as a solution factory for math problems deprives humans of the insights that arise when mathematicians struggle through mind-boggling problems.
One recent OpenAI proof dealt with a problem Townsend himself had been working on. The proof was just 13 pages long, but dense. Using an AI assistant, Townsend expanded it to 150 pages and spent four or five days deciphering it line by line. He told Big Think he now has a close sense of what’s been accomplished.
“There’s been a couple of times when I’m reading it, I go, ‘Wow, that is such a fantastic idea.’ If a human did that, I’d say it was beautifully elegant. It’s been teaching me how to think about matrix/matrix multiplication.”
Mathematicians are now confronting an uncertain future: Their careers as explorers surmounting soaring mountains of arithmetic may be coming to an end. They’ll no longer be heroes foraying into the cognitive unknown to solve epic problems, then teaching others what they’ve discovered. They might all become forever students to AI teachers.
Both Townsend and Strogatz expressed the most concern not for themselves, but for the young, rising mathematicians whose futures have suddenly been thrown into profound doubt. Will there be problems to solve? Will there be careers available? Not just in academia, mind you, but as statisticians, actuaries, cryptographers, and more.
Townsend and Strogatz are also lamenting the potential loss of a less well-known aspect of mathematics. Contrary to the stereotypes, it’s a remarkably social discipline.
“You see in the media that there are all these lonely people that spend ten years on a problem. This is not the reality of most mathematicians,” Townsend said. “Most math is a collaborative, social activity. It’s a rare few that do their own thing in their office. Most papers have many co-authors with many people collaborating and coming up with ideas. We’d like to keep that in the future.”
The bigger picture
But again, while AI advances have for the moment focused the limelight on mathematicians, Strogatz and Townsend seek to broaden it.
“This is not just about us; this is about all of us. What does Big Math mean for you as a person, and what does Big Math mean for all of us in the world?” Strogatz told Big Think.
He noted that Big Math fundamentally underpins more controversial technologies: data centers, surveillance systems, cyberweapons, drones, and military targeting systems. The public, not just technocrats, CEOs, and venture capitalists, must shape regulation of these technologies. Mathematical literacy can help people feel empowered to join the conversation and decisions we need to make, Strogatz said.
Such literacy doesn’t mean excelling at geometry and matrix/matrix multiplication; it means having a basic understanding of Big Math’s reach and effects. Then anyone can take action.
To that end, Strogatz and Townsend offered five empowering tips in their book for surviving our algorithmic era. Whenever you encounter Big Math, in any of its myriad forms, intervening in your life (and that’s pretty often), ask yourself:
- What’s being optimized? So much of Big Math is about efficiency and balancing different outcomes, but that goal can leave you, and others, out in the cold. “That’s mathematical thinking as quiet skepticism, asking what goal — and whose goal — the math is serving,” Strogatz and Townsend write.
- Are there feedback loops? “Your behavior trains the models that shape your behavior,” they remind us. “The first step toward freedom is noticing that the loop exists. That’s how mathematical thinking restores a measure of control.”
- What’s missing? Is something being left out of the data? Systems are only as capable as the data they are fed.
- Is it interpretable? “A model that can’t be explained shouldn’t be trusted blindly,” Strogatz and Townsend write. If a model is messing with your life in some way, say at a bank or doctor’s office, don’t hesitate to ask for an explanation.
- How uncertain is it? Remember probability isn’t a promise, especially in a single moment. “Whether it’s a medical test, a weather forecast, or an election poll, uncertainty is built in,” they write.
Too often today, Big Math is behaving more like Big Brother. But unlike Orwell’s Nineteen Eighty-Four (1949), this story hasn’t been written yet.
“Every mathematical invention begins and ends with human choices,” Townsend and Strogatz write. “We might never fully understand the oracles we’ve made, but we can decide what to ask of them, and why. We can remain the conscience behind the code.”
This article We built our world on “Big Math.” Now we no longer understand it. is featured on Big Think.