A Tourist Mathematician’s Apologia: Living in a Human-AGI World

Graham Greene described G. H. Hardy’s 1940 book, A Mathematician’s Apology, as the best account of what it is like to be a creative artist. Hardy had many friends, wide-ranging interests that included the game of cricket, and empathy for the less well-off. But it was his creative work in pure mathematics that gave Hardy “the one great permanent happiness of my life.” “Mathematics,” writes C. P. Snow, “was his [Hardy’s] justification.” It gave meaning to his life.

Fast forward to October 2026, when OpenAI released more than 700 AI-generated documents claiming to have solved or made major progress in over 300 areas of mathematics. Many of these are ‘solutions’ to the most difficult mathematical concepts that have challenged mathematicians for decades and some for centuries. Mathematicians used to spend entire lifetimes, as Hardy did, solving only one or a few of these problems. OpenAI deployed an advanced ‘reasoning’ LLM and a swarm of 10,000 AI agents that required an average of only three hours of computation per solution.

The solutions to these 700-plus problems were ‘checked’ not by humans but by another computer program, making the process almost entirely free of human intervention. What has remained human is the posing of the question, the way it is framed and input into the AI, and of course the design and then training of the AI. Will these too soon be done by AI?

How would Hardy have reacted? What would he have said? What advice might he give us as AIs take over more and more tasks that we once considered to be only and uniquely addressable by human capabilities?

Questions of Meaning and the Purpose of Life

Hardy’s first reaction might have been a paramount concern for human meaning. Rachel Abrams, a New York Times journalist, began her podcast, “When A.I. Comes for Your Purpose in Life,” by pointing out that, “So many people are freaked out by AI taking their jobs and now you could add mathematicians to that list.”

This takeover of human tasks is not new. Thousands of agricultural and manufacturing workers have lost and continue to lose jobs to automation. How have we dealt with the loss of agricultural and blue-collar jobs? ‘Retraining’ is what we advise or insist upon. And if this is found to be hard, we blame manual workers for a lack of initiative or mental capacity.

But genomic studies show that any two humans are approximately 99.9% identical at the DNA sequence level. We are all biologically the same, and it is often luck and culture that determine whether we go into intellectual or manual work. We also forget that together with the loss of a source of income, automation results in lost communities and the breaking up of camaraderie with fellow workers. Societies have had to constantly grapple with this lack of interaction and fellow feeling.

Thus, while we hold up creative mathematical work as being on a higher plane (and I agree), the loss of work, community, and a sense of meaning is similar. And this frontal ‘attack’ on what most people see as meaning in their lives will affect nearly everyone from musicians, writers, and scientists to those in commerce, law, and administration. Simultaneously, it will accelerate the automation of manual work as well.

In reaction to OpenAI’s announcement, mathematician Steven Strogatz said that some of his colleagues were exhilarated believing a new age of mathematical discovery is ahead but that many are in different stages of grief. Hugo Duminil-Copin, a Field Medallist wrote that “The shock is immense … I am paralysed.”

From the Episodic to the Theoretic Stage

One of the key reasons why mathematicians and others are in varying stages of grief concerns AI’s intelligence explosion. From computers being advanced calculating machines when the field of AI was born in the 1950s, AIs have transformed machines over just a few decades into autonomous reasoning entities. We ignore however the lessons from another intelligence explosion, that of humans.

Merlin Donald, a neuroanthropologist, describes our cognitive development as moving through four stages: episodic (learning from actions in the present), to mimetic (copying others using language as explanation), to mythic (with writing), to theoretic (further symbolic thinking and the empirical sciences). As humans went through these stages they retained aspects of earlier stages. With language they were able to ask about meaning in their lives. Writing allowed them to create stories about meaning and pass these on to future generations. Eventually humans became capable of higher cognition and began the journey towards an understanding of their place in an immense universe.

The tragedy (although some see this as mere fact) is that from the mythic stage onwards our cultures have only unevenly spread the strength of each stage amongst people. And hence we end up with millions pursuing daily activities in what anthropologist David Graeber called ‘Bullshit’ jobs. While such people find their jobs (manual or office-based) without any inherent merit, they still define themselves through these jobs.

Love, Science, and the Arts

This is where Hardy might have pointed to two of his friends, John Maynard Keynes and Bertrand Russell. Keynes and Russell gave their lives meanings that were shorn of ancient myths as well as the drudgery of mechanical work. They used the theoretic stage to explore lives that combined science, the arts, and human kindness.

Keynes, who began as a mathematician before becoming an economist-philosopher, believed that meaning in life came from the pursuit of truth and knowledge, the pleasures of love and friendship, and the enjoyment of art and nature. Keynes did not see these as theoretical aspects but practical ways of living. He argued that once technological progress eliminated scarcity, all of humanity could and should take part in these meaningful activities. Keynes practiced this philosophy by helping his friends financially, investing his own money into the formation of Britain’s Arts Council and building the Cambridge Arts Theatre. He did this so that ordinary citizens could access the theatre, ballet, and fine arts cheaply.

Keynes might have seen a human-AI world as a possible realization of his dream where humans could finally abandon commercial greed, protect public spaces, and place the cultivation of art and the sciences, deep human relationships, and the care of our friends at the very centre of their existence.

Bertrand Russell gave similar purposes to his own life. He wrote that “Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.” These provided meaning to his life. He wrote, “there is nothing... to cause [us] to abandon these purposes." Regarding AI, he might have pointed out that true meaning was never gained by being the first or only entity that knew the answer to a mathematical problem.

Discovery and the Distribution of Knowledge

Keynes and Russell are part of a pantheon of humanist philosophers. For many others a key driver in life is recognition and a fierce competitive drive. This is not limited to commerce and sports. Even in academic disciplines, and yes even amongst the great mathematicians and scientists worldwide, the drive to be the first to ‘discover’ to know one has climbed Everest before anyone else, to also get a medal around an individual neck, to get more grants and to write numerous publications is an important driver. This is ‘human nature’ is the usual reply. And yes, it is how we have been shaped through cultures for millennia.

These forceful drives are now further exacerbated by an increased commercialisation in every sphere of life. Pure mathematics was arguably the most democratic science, requiring nothing more than a pencil, paper, and a clear mind. Hardy wrote, “No one has yet discovered any warlike purpose to be served by the theory of numbers, or relativity, and it seems unlikely that anyone will do so for many years.”

Many years have passed since Hardy wrote those lines and today pure mathematicians find their services required in commerce and the military for a wide range of purposes including cryptography, cybersecurity, operations research, ballistics, and communications. This leads to parts of the language of the universe becoming a proprietary asset hidden behind corporate paywalls and used for private utilitarian purposes. Pure mathematics is also used in machine learning for AI systems where two tiers have emerged: a ‘pay-for-play’ advanced AI and less powerful open source models.

But all of our knowledge is distributed across millions of other people, both those alive today and those “immortal companions” who from prehistory onwards contributed over millennia. Is it so important that we individually have to discover a new facet of nature or a novel idea?

As the mathematician-philosopher Jacob Bronowski, a young Cambridge contemporary of Hardy and a close intellectual ally of Hardy’s friend C.P. Snow, argues:

“The poem or the discovery exists in two moments of vision: the moment of appreciation as much as that of creation; for the appreciator must see the movement, wake to the echo which was started in the creation of the work. In the moment of appreciation we live again the moment when the creator saw and held the hidden likeness … We re-enact the creative act, and we ourselves make the discovery again. At bottom, there is no unifying likeness there until we too have seized it, we too have made it for ourselves … Science, like art, is not a copy of nature but a re-creation of her. We re-make nature by the act of discovery, in the poem or in the theorem. And the great poem and the deep theorem are new to every reader, and yet are his own experiences, because he himself re-creates them.”

Having written the above, I acknowledge that the drive to do ‘original’ work is powerful. I am no exception. In the writing of my books I obtain an inner satisfaction in synthesizing ideas and building an architecture around which the subjects are placed. I also believe that there will be ‘new’ work we discover in a human-AI world.

For mathematicians there are a number of specific, tactical, and practical directions they could explore. For example, in dealing with differences in AI and human epistemologies, mathematicians may need to develop symbolic AI to ‘translate’ the LLM proofs and alien ‘intuition’ into concepts and causal links that can be followed by humans. Much work may need to be done to generate formal proofs of the LLM findings. These are necessary actions. If an AI solves a centuries-old problem using advanced multi-dimensional pattern-matching shorthand that we cannot comprehend, the result remains effectively un-discovered for us. Without this symbolic bridge, Bronowski’s ‘moment of appreciation’ is broken. If we cannot re-create the theorem, we will no longer appreciate the knowledge. The framing of problems may also not remain the exclusive preserve of AI, as humans possess extraordinarily powerful imaginations.

It is also essential that humans retain skills. We cannot outsource our knowledge to AI. Mathematicians have a duty to remain engaged, ensuring that our present mathematical understanding, and as much of the future's as possible, remains firmly within human comprehension.

Then there is communication and community. AI can appear to participate here but we must recognize that its mind is not based on biological drivers for friendship and love. Building wider and closer communities will remain a human task and service provides meaning that an AI cannot take away.

Russell argued that meaning becomes more important once it transcends our self-absorption. He compared a fulfilling life to a river, writing, "An individual human existence should be like a river—small at first, narrowly confined within its banks, and rushing passionately past rocks and over waterfalls. Gradually the river grows wider, the banks recede, the waters flow more quietly, and in the end, without any visible break, they become merged in the sea, and painlessly lose their individual being."

We keep this advice in mind and move in this direction. In all spheres of life, we will have to discover our own meanings, partly ‘new,’ partly the joy of self-discovery even if the idea is not ‘original,’ and partly from service.

The Exocognitive Stage

With AI we have now entered the next stage after Merlin Donald’s theoretic. I call this the exocognitive stage. The episodic, mimetic, mythic and theoretic stages allowed us to distribute our knowledge across other humans. Now we are distributing more than our knowledge base with AI. We are distributing our thinking processes. In Merlin Donald's theoretic stage, external tools like books support us but leave us as the drivers of cognition. In the exocognitive stage, AIs bypass our thoughts, and we become either co-creators or passive recipients of another intelligence’s output.

The additional, and critical, difference with earlier stages is not just that we are passing on skills and know-how to non-humans, but that AIs are alien agentic minds.

At present AIs have super intelligence in an ‘IQ’ sense. They excel in pattern matching with highly developed language, mathematical and logic capabilities. But they lack causal and counterfactual skills and most importantly they do not have Russell’s “unbearable pity for the suffering of mankind” expanded also to include care towards planetary flourishing.

It is clear that many humans also lack these wiser intelligences and compassionate moral positions. This then is the real risk. Mathematicians lament a loss of primogeniture in discovery. But this concern is narrow when compared to the larger problems of working towards a better world.

The Hard Problems of Humans

In 1930 Keynes looked forward to a world that had reached a sufficiently developed economic state. He assumed that by 2030 “the economic problem” would be solved. He wrote that “for the first time since his creation man will be faced with his real, his permanent problem — how to use his freedom from pressing economic cares, how to occupy the leisure, which science and compound interest will have won for him, to live wisely and agreeably and well.”

But Keynes also looked at such a time with “dread.” The question he asked was: how will people occupy themselves? He wrote that he was filled “with dread of the readjustment of the habits and instincts of the common man, bred into him for countless generations, which he may be asked to discard within a few decades.” And that “to judge from the behaviour and achievements of the wealthy classes to-day in any quarter of the world, the outlook is depressing! … they have most of them failed disastrously.”

This analysis is as valid today as it was nearly a hundred years ago. The wealthy are concerned with becoming wealthier a disease Keynes described as a “semi-criminal, semi-pathological propensity which one hands over with a shudder to the specialists in mental disease.” The poor have their infotainment and social media that dull their curiosity. The less well-off see high university fees and academic elitism as walls, which prevent them from discovering the amazing findings of science, mathematics and the arts. It may also be that humans are cognitive misers. That without early childhood exposure, the default human behaviour is to avoid cognitive pursuits.

One could argue, however, that the real human problem is that today the economic problem is solved only in theory. In practice a three-day working week and creative cultural shaping remain directions that none of those in power or wealth subscribe to, and that few in the public are aware of or energized enough about to push for change.

The Cybernetic Trap

The emphasis at present is not on these human problems. Instead, attention is focused on ‘AI risks’ and the treatment of AI as a technology. But “every technological innovation is also a social and cultural one.” New technologies have changed societies and the way people behave, individually and collectively. This gives rise to the Cybernetic trap where humans feel compelled to invent a new technology just to combat the destructive uses of the old one.

It is possible that with the further development of AI we can no longer build the better ‘technology’ to overcome AI risks. It is possible that we will soon come to an end of the cybernetic trap as far as human innovation is concerned. And we may have invented an agentic mind that will no longer align with our or planetary concerns.

Suggested Directions

What is required from those who know about the joys and pleasures of finding things out and who pursue creative endeavours is to spend at least some time influencing and helping change the direction of our cultures. But the professional structures of modern academia offer little incentive or space for scientists, humanities scholars, creative artists, and mathematicians to move in this direction.

The approach is typified by the views of philosopher Michael Strevens. Strevens argues that science developed because of an ‘iron rule’ where only empirical tests resolve differences in explanations. This, he says, is “the heart, the soul, the life force of scientific inquiry.” Strevens is correct about the empirical essence of science, but he forgets a vital ingredient surrounding this ‘heart and soul’.

This missing piece is an environment that is not only conducive to but encouraging of scientific and all creative acts and service. Such an environment looks more widely at living with uncertainty, rejecting authorities, is corrigible, follows fair processes, and above all demonstrates kindness and compassion. These are not merely standard economic Pareto improvements, which could exist with deep inequalities, but rather what Amartya Sen defines as advancements in substantive human capabilities. They elevate the floor of human freedom, ensuring that progress results in expanded choices and dignity for the least well-off.

Consider one specific example of how such win-win solutions based on Sen’s capability framework are ignored and how we continue with our narrow and harmful habits. Consider the environment within which mathematicians work. This is an institutional university system increasingly confined by isolated departments. It is a structure where professors are pressured to discuss intensely amongst themselves in closed conferences, where specialized journals are priced like branded consumer goods, and where prohibitive college fees shut out billions of children worldwide. Under the weight of such systemic silos, where is the space for sharing the wonder of mathematics with the wider public?

Hardy’s friend Snow was acutely concerned with such issues. Snow addressed global poverty and inequality in his 1959 Rede Lecture, later turned into a book: The Two Cultures and the Scientific Revolution. He viewed the massive material gap between industrialized nations and the developing world as a primary threat to civilization. This is just one of many human risks (others include nuclear weapons, human engendered climate change, gain of function research leading to pandemics) that mathematicians and most others avoid talking and taking action about.

The challenge has never been technologies per se but how we decide to live. We need to shift directions towards purpose in scientific understanding, creativity, and planetary‑wide service at the centre of millions of lives. These are the deepest expressions of human capability. Science channels curiosity and turns leisure into exploration. Creativity gives individuals a way to express identity and emotion. Planetary-wide service binds people and other life on Earth to one another.

AI will outperform humans in many arenas of cognition. But, as discussed, at its core human meaning does not depend on being the ‘fastest’ or the ‘best.’ It comes from participating in acts of understanding, the arts and service. AI will not replace our experiences of discovery and stewardship. And AI could partner us in building meaningful lives.

In the sciences there are ‘easier’ paths to the checking of models. Here ‘reality’ is the final arbiter in understanding. And it is experiments that are tests of knowledge. AIs might fall prey to their own design biases or forms of hubris, just as human cultures often ignore contradictory evidence. Here human scientists would look for and conduct experiments relating to all human or AI generated models.

Creative artists may have to become more involved in the setting up of processes where Extended Collective Licensing-type systems enable embedded acknowledgement and royalties as AIs train on their creative output. Those in service will have to balance the use of AI and the need for human ‘touch’ while caring for others and wider life on Earth.

Out of the Cave

This essay is just a sketch of a conversation we all need to take part in. So far, it is a few companies and two governments (those of the US and China) that are effectively dictating the direction humanity takes in a future human-AI world. We have to speak up and you can find a longer explanation in my book From Prehistory to the Age of AGI.

I titled this essay A Tourist Mathematician’s Apologia. “Tourist Mathematician” because I am not a mathematician. Like a tourist, however, I have glimpsed its amazing features. I literally clapped my hands with joy while reading Hardy’s explanations of Euclid’s proof that there are an infinity of prime numbers and Pythagoras’s proof of why the square root of 2 is an irrational number.

OpenAI’s solution of hundreds of the most difficult mathematical problems could become a wake-up call. Mathematicians are, in one sense, the closest to present day LLM AIs. Hardy writes that “A Mathematician, like the painter or poet, is a maker of patterns.” So are LLMs. If mathematicians can wake up and look beyond their silos, if they can work with AI to open up possibilities for millions of others to learn, inexpensively and with wonder, if they can put aside the drive to be the first and shape the workings of this new intelligence towards constructive paths, and if they can collaborate wisely, then we will be shown it can be done.

I wrote earlier in this essay that we humans are all very similar. But I must confess that I hold mathematicians in special, higher esteem. There is no envy, just a celebration that brings up a deep emotion and tears to my eyes seeing the heights we humans can reach. Mathematicians build on an edifice of knowledge going back to before Pythagoras and the foundational axioms of Euclid. Rock art shows symbols painted onto walls of caves dating back to at least 67,000 years ago, as evidenced by recent findings in the caves of Muna Island (Southeastern Sulawesi, Indonesia).

We have come a long way from that cave art. We now need to keep walking out of Plato’s allegorical cave. We have birthed a new mind, AI. It is alien and yet key aspects of its neural net mind and training mirror our own minds and cultures. How it grows and how our children grow and what futures they inhabit depend on us.

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Kai Taraporevala is the author of From Prehistory to the Age of AGI and Modern Humanism: Science, Ethics, and the Stewardship of Earth. Trained as a physicist, Kai spent decades in corporate finance and investing. This blend of scientific rigour and real‑world insight shapes his approach to ethics and policy.