Acknowledgments and AI Disclosure: No ai was used. In exchange for coffee, I lured my colleague Edward Bryden (a human!) into my office to check my text. He generously corrected it and made suggestions that resulted in a definite improvement. I have left some of my spanish influenced mistakes for expository proposes and to, again, keep writing human!
We have all witnessed how the arrival and display of power of a foreign technology, to be found a few years ago in Philip Dick novels, has forced us into a healthy and long due discussion about the purpose and future of our doing as mathematicians. The range of answers and public reactions has been rather motley, yet at times elitist and riddled with moralizing considerations on our shared responsibility. One hears from some that we are to maintain the human aspect of mathematics at all costs and from others that we have to accept the reality as it changes and keep mathematics engaged in a world where artificial intelligence dominates larger territories of human intellectuality. All voices come from our shared love for mathematics.
I am writing not to offer an alternative point of view, I am much too slow of a thinker to form an articulated standpoint regarding artificial intelligence in the middle of this very loud maelstrom. My mind goes immediately to Quino’s genius expressing what many of us feel now.
My intention here is to contribute to the discussion of an aspect of mathematics which I believe is under threat and has been forgotten in the rubble of this ongoing earthquake: the mystical aspect of mathematics. I am aware that using the word “mystical” in the mathematics community comes with some risks; yet I will try to defend it, because I think that this is one of the crucial aspects of human engagement with mathematics. Not only has it been there all along, certainly for the several thousand years of recorded mathematics, but it is in urgent need of protection from the settlers and their powerful machines.
We have fallen too easily into the comforting belief that science is a societal response to the human need for understanding the world, and that mathematics, as such, will never disappear. Even when the settlers and their machines are capable of answering all our questions, proving all our theorems, perhaps even formulating the questions, embarking on homeric research explorations and explaining their findings with soft patience and exemplary clarity, we say to ourselves, as long as we are humans, mathematics will not disappear because it comes from one of our defining ways to be in this world: trying to understand it. Our ways of doing mathematics might change, and perhaps the type of mathematics we do in the future will be reshaped, but our need for engaging with mathematics will always be there. As a warm someone in this blog offering comfort said: we can always take joy in the beauty of mathematics, independent of its creator. I agree with all this. Yet, just as our personal and communal relationship with the world is much more complex and mysterious than simply trying to understand it, the same is true for mathematics. In my eyes, it is a fatal mistake to cling to this optimistic premise and, to use the language of the settlers, wait until the sea is calm again and the machines open the way to a new era of mathematical research.
One could argue that the only other universal product of human culture present throughout our history that distinctly uses symbolism as much as we do in mathematics is our myths. Religion being the most prominent example. Although mathematics and myths use symbols in very different ways, it is not a coincidence that it is in these two places that we can find them sprouting from every branch. Religion accepts its relationship to the mystery, and it is perhaps because we want to mark some distance that we ignore the mystery in our doing.
We are not always aware of this, but whenever we write “Let X be a ” we are doing something much deeper than just fixing a name for a mathematical object; we are spelling some form of life to a mind-conceived object, and once it has been spelled, we can observe it interact with us and with its peers. This points directly at our anemic, yet desperately human power of creation. This permeates our work, from leaders in our fields conceiving game changing mathematical constructions to small decorations on a lemma intended to help us overcome a harmless obstacle.
Creativity covers a large portion of our relationship to the world. We place creativity in the realm of intuition; reason and understanding are only there to shape, order, and filter, as clothes that wrap around them, giving shelter and warmth. Understanding comes after creating, yet both are needed, both drive us to do mathematics, and both are a deep and unavoidable response to our awe at being thrown into this world. The discourse that it doesn’t matter what creates new mathematics, as long as we as humans engage in appreciating and understanding it, is a fallacy. If it is not us the ones breathing life into our delicate, glacial, and often beautiful objects, then human mathematics dies. Maybe not in a decade, maybe not in a century, but eventually our creative pulsion will take us somewhere else.
We all know that academia has its fair share of big egos, but for the overwhelming majority of mathematicians, conjectures are there not to find heroism in solving them. They do play a central role in helping us orient ourselves and our research communities in our explorations of the ever growing landscape of mathematics. But this is not their only role. They also help us stay in contact, as a community, with the fact that we are part of a living mystery, and that no matter how far we go in our explorations, darkness, the unknown, the mystery is always around us. Conjectures are attractive and grounding because of this.
If you think about it, most of our time is spent in the unknown. Our most common state of mind is confusion, disorientation, and at times desperation. The goal of this never ending doing that we call mathematics is never to find comfort in the questions answered. We are almost allergic to that comfort. As soon as we get there, we move on as quickly as possible, we find the next mystery, we jump almost as a reaction into the darkness again. Why do we do this? I don’t think it is because we hopelessly suffer from the fever of “progress”, whose premise is that reality as it is needs to be changed as fast and as radically as possible. No, we have been doing mathematics for much longer than the rampant pandemic of progress. We do this because of our human need to collectively and individually stay in touch with that ancestral awe that made science and mathematics possible, to remind us that our place in this world is not under the encandilating light of answers, but rather under the dim light over the space between the answers and complete darkness.
Someone please tell the settlers to use their machines for something else!
Ignacio Barros,
September 29, 2026.
Received 29 September 2026.
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