Mathematics for humans

The threat from AI is not that it will gain self-consciousness or a soul. The threat is that we will destroy ours—that, bewitched by the appearance of AI-consciousness and AI-souls, we will lose interest in cultivating and honoring our own. In doing so, we will cease to produce students capable even of cheating intelligently, let alone of writing coherent papers themselves. At the same time, we will cease to produce teachers capable of telling the difference....
To maximize the chance of not having their jobs replaced by machines, students need to learn how not to think like machines....
AI is not going to make human intelligence obsolete; on the contrary, it is going to make human intelligence more necessary than ever. But human beings might well let AI make them stupid enough to believe that their own intelligence is obsolete.
– Kate Epstein, We, Robots
I am much more concerned about the decline of thinking people than I am about the rise of thinking machines.
– Derek Thompson, You have 18 months

The 20th-century computer scientist Edsger W. Dijkstra famously compared the question of "whether computers can think" to that of "whether submarines can swim." I find this analogy excellent: it does not deny that the machine can accomplish certain tasks more effectively than an unassisted human, nor that humans must learn to use the machine to remain relevant; but it also makes clear that the machine does not replace human ability. If your submarine breaks down in the middle of the water, you better hope you still know how to swim.

Today's computers are much more capable than those of Dijkstra's era, but his point remains equally valid. If this distinction between human thinking and "AI" eludes many people, perhaps it is because most people do very little thinking anyway.

[AI] is only using statistics and pattern recognition to generate predictable responses to my inputs. But isn't that what many people are doing? We go through our days responding to prompts, like robots, and much of what we say and do is as banal and formulaic as AI slop.
I recall observing, well before AI was a thing, that most of the work students produced for the "creative writing" workshops I attended could easily have been generated by a computer program. People weren't writing stories and poems so much as they were generating material that sounded like what a story or poem is supposed to sound like. If they had anything truly fresh to communicate, they were doing a very fine job of hiding it....
With AI cranking out predictable content free of charge and at lightning speed... I can't get away with thinking and writing like a robot. I must write like a real person. I must do the fun but difficult work of conducting fresh research, making my own connections, drawing my own conclusions, and articulating them in my own words. In 2022, I could get away with the occasional cliché or warmed-over observation. In 2025, that's an open invitation for the robots to eat me for dinner.
– Anne Kadet, What I Learned From My New AI Friend
"AI"s are certainly artificial, having been made by human hands. But they are not intelligent. To call them "artificial intelligence" is to accept, not just a fiction, but a lie. It is to misconstrue both the nature of machines and of man. It is to give in to the ways in which chatbots threaten to atrophy our humanity, and, in extreme cases, even drive us to madness.
In lieu of "artificial intelligence," I propose a more accurate, ethical, and socially responsible name: "pattern engine."
– Nathan Beacom, There is No Such Thing as Artificial Intelligence

The distinction between human and computer is especially stark in mathematics, because mathematics is the science of logical thinking. For two decades I have taught mathematics students who struggled to fake their way through math problems by searching the Internet for similar questions, throwing together words and equations that seem related, copying a number from the back of the book, and confidently drawing a box around it. But only now do I have a name for what they have been doing: behaving like an AI.

If we humans are to remain employable in the age of AI — and, more importantly, if we are to retain our humanity — we must learn how not to behave like an AI, how to behave instead like a human. This, then, should be the primary goal of a university education. But in fact, it always has been the goal of a university education. The only difference now is that we have a name for it, and an increased urgency to achieve it.

An old professor of mine, in my freshman year, once said something wise and important to a seminar I was in when one of my classmates observed that "I know what I think, I just can't get the words down on the page." My teacher responded: "Well, you don't actually know what you think, then. The act of writing the thing is the same thing as the thinking of it. If you can't write it, you haven't actually thought it."
Which is to say that writing and reasoning are effectively identical activities — and for many years now, writing has been the way we have taught young people how to reason....
Generative AI thus presents a double threat: first it tempts you by offering to unburden you of your need to reason, the tedium of organising your thoughts. But, almost as bad, it also scrapes the brain of human civilisation of all information and all learning ever and then, apparently, reduces it all to unvariegated mush, spitting out to you its tawdry imitation of thinking — insipid, composite accounts that I would say are written at a 10th-grade level but for their uncanny alien quality that is not quite like anything human at all.
– Aaron Maclean, A warning to the young: just say no to AI
The worry is that we, as a society, will become innumerate, not just illiterate. A.I. appears to be exacerbating an alarming trend in which our basic education is failing our young citizens. And that crisis is aimed at the most basic elements of that education: reading, writing and arithmetic.
My advice to young students today is to study language and mathematics. When you talk to a chatbot, you're using everyday language to talk to a mathematical system that, in turn, talks back to you. Technical skills won't be enough to deal with the unpredictable results in markets, so a broad-based knowledge of math and language will be the only way to adapt. And while jobs might disappear in one sector, we will always need humans who can make sense of A.I.
– Leif Weatherby, A.I. Killed the Math Brain

For all of these reasons, I design all the courses I teach to inspire, guide, and support students in learning how to behave like a human rather than an AI, in the context of mathematics. Below I have collected some additional recommended readings on the subject of AI.

Michael Shulman
Professor of Mathematics
University of San Diego