Ecce Homo Mathematicus

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Translation by AB – October 3, 2020


Humans will obviously never be supplanted nor replaced by artificial intelligence. This fantasy has no serious foundation. We must first remember this very simple point: what we call “artificial intelligence” is neither more nor less than a set of techniques and history is strewn with examples illustrating the ebb and flow of the myth of replacement in the wake of technical progress. So, nothing very new.

At the same time, the techniques have become so complex that only a handful of initiates (a sort of “1%” …) master them and have the means to make us pass their prophecies for predictions and their desires for destinies. This complexity unfortunately weakens any conscientious attempt to challenge the validity of verdicts like these, delivered by “experts in artificial intelligence1:

Replacement human artificial intelligence

According to these experts, this diagram shows the number of years from 2016 before certain activities or jobs are replaced by intelligent machines. Thus, all “human tasks” could be fulfilled by a machine with “high-level intelligence” within fifty years or so, and all “human jobs” could be replaced within a century!

The purpose of this article is not to dispel the myth of replacement nor to challenge these verdicts, but rather to propose a critical way forward2. Many approaches have been tried and they all ultimately come down to questioning the specificity, singularity or irreducibility of the human not as a living being – we think this is inadequate (Miguel Benasayag and the question of the “living”) – but as a … human being. We are well aware of the unfathomable depth of this eternal reflexive question and we will not tackle it head-on.


Rather, we propose to explore a human practice that would occupy this narrow ridge separating the side of intuitively replaceable practices, some of which appear in the diagram above, and the side of intuitively irreplaceable practices because they are animated by “indescribable” aptitudes or aspirations: art3, philosophy, etc. Mathematics are on this ridge. Their practice requires both a kind of “inductive intuition” (irreplaceable?) and an exercise sufficiently rational (replaceable?) to think that a machine would in principle be capable of it. The experts in AI grant besides to the mathematicians in flesh and blood a respite of about forty years before their replacement in the field of “Math Research” described as follows:

Routinely and autonomously prove mathematical theorems that are publishable in top mathematics journals today, including generating the theorems to prove.

But if proving theorems (rational exercise) seems within the reach of machines, doing so “routinely“, i.e. for any type of theorem, and “autonomously“, i.e. without any human intervention, is much less obvious. As for being able to “generate the theorems to prove“, it would require this capacity of “inductive intuition” that seems irreducibly human. Nevertheless… There is still enough doubt to ask: to which side do mathematics belong and, above all, for what reasons?

We are convinced that the Being of the human is hidden at the heart of mathematics, but before coming to this “proof by mathematics” of the human singularity, it is necessary to prepare a bit the premises and briefly evoke three of the “impetuses” towards our replacement in general: the aspiration to reason, the human indignity and the idea of progress.


Everyone guesses that the announced replacement of workers by “intelligent” machines is not obvious. There is in fact, as we can feel, an essential difference between replacing the strength of the worker’s arms with mechanical power and replacing his “intellectual strength” with computing power. However, in the field of work, which involves a kind of rational action, this difference is in fact quite minimal.

Indeed, as far as skills are concerned, there is in principle no technological limit to the replacement of “intellectual strength”, since if there remains a difference between a human and a machine, as well as between two humans, as it comes as a difference in ability for a goal, it does not appear as a rupture but as a gap that can always be reduced, if necessary by adjusting tasks. This adjustment always ends up benefiting the machine and it is finally the human who cannot or no longer replace the machine. It should be noted in passing that one of Elon Musk’s arguments in favor of his Neuralink project is precisely this one: if humans do not wish to be definitively excluded from the realm of skills, they must be “increased” with neural implants and artificial intelligence, and somehow mechanized.

But don’t we still have the privilege of “soft skills”, which will withstand any closing of the gap and whose jobs that depend on them will always be safeguarded? This position is in fact to be qualified because professional “savoir-être” is not so much considered as a positive general quality but rather as the absence of a properly human character that would be detrimental to professional efficiency. Both “stress management” and “motivation”, for example, are indispensable for humans but useless for mechanics. Moreover, positive “savoir-être” such as communication, empathy, a sense of the collective … are qualities of being required in a fallible human environment. Ultimately, a fully mechanized system, regardless of the intensity of intellectual strength it deploys, no longer requires any soft skills. Therefore, the artificial only replaces the already “artificial” human.

Thus, the human made universal by reason is the first cause of its own “replaceability”.


The identification of the Being of the human must probably go through a dismantling of the myth of the “rational animal”. But there seems to be a growing belief system that impedes this dismantling and which in some ways is quite disturbing. We are thinking in particular of “ecologism” which, strangely, finds itself in a situation of objective alliance with the most unbridled technical thinking: In principle, nothing would distinguish humans from any other organisms in the biotope – which also obey their own rationality – with which they co-exist. Thus, there would be no properly human dignity, but it is even worse: as destroyers of our environment, we are, in a quasi-ontological sense, undignified (we pass over the already perceptible theological implications of this denigration).

From the point of view of political ecology, this load of indignity and guilt leads to anti-speciesism and its essential paradox: the human being is nevertheless the only being capable of “destroying” the planet; In order to repair it, we must therefore recognize his specific dignity of having to take care of other beings, to which the dog, the dolphin or the badger cannot have access. Technique deploys in the same way, but not for the same reasons, an anti-speciesist thought leading to the transhumanist theme of the fusion of the human and the technique, under sometimes extreme forms such as the ultimate equivalence of man and machine.

The second impetus towards our replacement would thus come from our indignity.


If the replacement of the human by the machine is a myth consubstantial to technical progress, it remains as difficult as ever to demystify it. Perhaps this is because technical progress has always been considered as a liberating progress: the machine must end up doing all of human’s “work”, especially if it is painful, and allow him to enjoy his time fully freed. There is thus, in technical progress, this ambiguous aspiration to replacement. But, as Gandhi already observed, who had a highly developed sensitivity to the question of mechanization (“the machine has won over man, man has become a machine, works and no longer lives“), we are on the contrary witnessing a generalized enslavement of humans to what Lewis Mumford called “mega-machines” (Return to Babylon). It is not surprising, moreover, that resistance movements are emerging, increasingly visible (fake news, conspiracy theories, direct actions, etc.), and attacking the very framework of technical progress, our “first cause”: the universal reason.

This third force towards replacement, the aspiration for a progress that liberates, nevertheless remains powerful.

Homo Mathematicus

The mathematician gathers these three impetuses: a) he is one of the great makers of our common reason, b) he does not practice “from” his human singularity because he postulates – in the strong sense – the universality of his field, and c) he participates of course in the idea of progress. No wonder then that mathematicians are among the first humans to consider of their own replacement.

In 2017 a collection of essays by mathematicians and philosophers entitled “Humanizing Mathematics and its Philosophy4 was published on the occasion of the 90th birthday of Reuben Hersh, an American mathematician best known for his engaged reflections on the practice of mathematics and the social impacts of his discipline (Reuben Hersh died on January 3, 2020). In preparing this collection, Reuben Hersh said that Paul Cohen, a world-renowned mathematician and 1966 Fields Medal winner, warned him that one day mathematicians would be replaced by computers. Let us recall that at that time artificial intelligence was booming and had not yet entered its first ice age. This prediction had apparently impressed but also irritated Reuben Hersh and guided all his life his reflections driven by the intuition that there is something irreducibly human “in” mathematics. This “something”, which no one has really been able to reveal so far, is obviously a real treasure for a general criticism of the artificial. There seem to be at least two paths to get there: the “path of the body” and the “path of the Being”. We will briefly describe these paths, which form the “critical way” proposed in the introduction.

Critical way

Against the hypothesis of the artificial mathematician, we first claim that it takes a body to make mathematics “spring up”; as the computer is not embodied, it is incapable of doing mathematics. This argument can be countered in two ways. Firstly, by objecting that the practice of mathematics, a purely mental activity, does not require a body. This is the argument of the “abstract mathematician“. Second, by noting that the computer can always be crimped into an “artificial body“, either robotic or biological.

By the other more philosophical path we claim that mathematics reveals the proper, irreducible Being of the human. The machine can imitate mathematical practice but does irretrievably something else. This thesis can also be countered by two types of arguments. Firstly, by taking as a starting point “Platonism“, the principle according to which mathematics reveals essences existing in the world and independent of human, machine or any being in the world. Human and machine should therefore identify the same essences and practice the same mathematics, although not necessarily at the same pace nor with the same language. Secondly, the smart philosopher can always turn over any thesis, such as that of the Being established philosophically! On this dialectical field, it is therefore more a question of strengthening our defense.

This is how this critical path looks like, consisting in countering four “arguments”:

Then, we will have to continue the exploration of the “paths of the body and of the being” to hope to come back with this trophy: Ecce Homo Mathematicus. The artificial, to which man does not seem to want to set bounds, will perhaps then have clearer limits.

1. Katja Grace, John Salvatier, Allan Dafoe, Baobao Zhang, Owain Evans / – May 3, 2018 – When Will AI Exceed Human Performance? Evidence from AI Experts
2. Obviously we are far from being the only ones to contest this vision and we have here one article among many that exposes a hyperclassical defense of human/IA complementarity against the replacement thesis (in French): Guillaume Renouard / – 2 avril 2019 – Intelligence artificielle: pourquoi le remplacement de l’humain par la machine relève du fantasme (broken link)
3. Although… see Artificial Intelligence-Art in its infancy
4. Various authors / Bharath Sriraman Editor – Birkhäuser – 2017 – Humanizing Mathematics and its Philosophy

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