Abstract: We present a theoretical framework to understand our field, and the disruptive effect of AI in mathematics. Treating mathematics as an economy, we borrow ideas from the labour theory of value to uncover the hidden dynamics of prestige, attribution, and the job market.
Disclosure: The following text was written by a human. The text might reflect human thoughts obtained through the human experience.
The arrival of a new actor to mathematics has prompted us to philosophise about our field. Dealing with the disruption of the technology in mathematics requires deep conversations about many aspects of our jobs. It is however apparent that most of us have never set the grounds for such a conversation to happen.
Some say mathematics is being born, some say it is already dead. For David Bessis it is in crisis: «we are seeing the fall of the theorem economy». Although evocative, the analogy between theorems and currency is limited. Similarly, neither the quantity of papers nor citations alone determine the quality or employability of a researcher.
What is it then, that defines the value of a mathematical paper? What is it that elevates some of the members of our community to high standing and high regard?
I will attempt to frame mathematics as a pseudo-capitalistic system, basing my analysis on the theory of value1.
1. Before we start
There is no clear reason why mathematics, as a socio-cultural phenomenon, should be understood in an economic framework. However, I invite you to lean into this perspective. For me, personally, it has served as a good starting point to understand certain aspects of our field in new and unexpected ways.
2. The theory of value
In the labour theory of value, it is crucial to distinguish between the different values of a commodity.
- The (true) value of a commodity refers to the socially necessary labour time to produce said commodity. A bad worker might need more time than a great expert to produce the same commodity; the value of the commodity is the abstract amount of labour that society agrees an abstract average worker needs to invest in its production.
- The use value refers to the tangible properties of a commodity that satisfy a given human need.
- The exchange value of X with respect to Y is the amount of X that can be exchanged for a unit of Y. If a society has currency, then the price of a commodity is the actual quantity of money that was used in a purchase of the commodity.
The role of exchange value and price in the analysis of capital is to realise the value and use value of a commodity in a measurable and concrete manner. Departing from the usual labour theory of value2, I’ll call the result of this transformation realised value.
3. The values of mathematics
When applying the theory of value to mathematics, we need to begin by finding what defines the mathematical economy. In what follows, we ignore that mathematicians in Universities have responsibilities beyond research3.
A commodity in mathematics is any atomic piece of mathematical literature: a definition, a lemma, a theorem, a proof, a proof technique, a conjecture, a literature review, an analogy, a historic framing of a different commodity, an example, a counterexample, a computation, an algorithm, etc. are all commodities.
3.1. True value
The (true) value of a commodity remains being defined by socially necessary labour time to produce said commodity. The measurement of this value is hence inherently social.
Factors that contribute to the value of a commodity are the density and the length of the ideas necessary in their production, as well as their originality. Indeed, less original works (such as known proofs, straightforward generalisations, etc.) can be produced at a higher speed, and therefore have less impact in the research community4. It is understood, in the contrary, that original ideas require time to arise, and it is this abstract average time which an abstract average mathematician needs to produce a new original commodity that gives it value.
3.2. Use value
Given that our discipline is highly abstract, the use value of a mathematical commodity is also abstract, unlike in the analysis of capitalism.
In mathematics, the use value is typically realised via the appearance of the commodity in subsequent mathematical works. Each time a commodity is cited it contributes to the creation of a new commodity. It is this new contribution that gives use value to the original commodity.
Moreover, the use value of this new commodity continues to affect the use value of the original commodity further. For instance: a definition in paper A is used in a key manner in paper B to prove a difficult theorem. This theorem from paper B is highly cited, gaining use value; this use value retroactively trickles down to paper A.
Eventually (more commonly in applied mathematics), the commodity can escape the mathematical literature and enter other disciplines. The use value of the commodity continues to increase as it does so. In some instances, the commodity can reach the “real world” and be used in the development of a certain technology. At this moment, the mathematical commodity enters the capitalist system, and provides capital use value to the real commodities that it helps produce.
Some commodities are conceived with pre-existing true value and use value. When a conjecture is proven, part of the use value of the conjecture is transferred to the new commodity (the proof). Often we justify the importance of a conjecture by making reference to the amount of years passed since its conception. This is because the longer a conjecture is open, the more use value it is able to accumulate. (It is possible, of course, that the conjecture is instead forgotten, in which case it does not carry any additional use value just because it is older.) The person making the conjecture is often also given as a measure of its true value: if this person has previously produced high-true value commodities, it might mean that they are able produce commodities above the usual rate of production (since value is socially necessary labour time), and this in turn gives extra true value (but not use value) to the conjecture.
3.3. Realised value
Mathematical commodities aren’t exchanged but rather openly gifted. Moreover, they are non-fungible (unique and not mutually interchangeable).
However, there are still ways in which their values are realised. These appear in a dialogue between the commodities themselves, their author, and their institution (universities, research institutes, or certain private companies)5.
- A group of commodities (a paper) realises its true value through positive referee reports, publication in journals, being accepted to a conference, certain prizes, etc.
- An author has accumulated wealth, which is the sum of the true values of all commodities produced by this author. This wealth can be realised through letters of recommendation, grant awards, invitations to conferences, awards, job offers, tenure, editor positions in journals, etc.
- The institutions also gain a form of accumulated wealth as the aggregate or the average of the accumulated wealths of their members. This accumulated wealth is realised in national and international rankings.
As I said before, these are in constant dialogue. Commodities’ true values contribute to the wealth of their author, but the wealth of the author also gives true value to the commodity (see the paragraph on conjectures). Similarly, an author gives wealth to its institution, but the institutions’ wealth also gives value to the commodities produced by the author, which then contribute to the wealth to the author.
There are two phases to the realised value. On its first phase, it is a purely social concrete realisation of the values of a group of commodities (invitations to conferences, publications, job offers, etc.). Some of these realisations are standardised processes: for instance, candidates to certain positions may be ranked with a point system that tries (often controversially) to capture their intangible and abstract accumulated wealth. On the second phase, the realised value of mathematical commodities transcend the mathematical economy and enter the capital economy (in the form of grants, salaries, funding, monetary prizes, etc.).
The disparity between the true, the use, and the realised values of a group of commodities is a source of tension. The former two are purely social constructs and inherently subjective. The latter is an attempt a concrete realisation of the same, that is never able to capture the nature of the former.
4. The machine
The irruption of LLMs in our field cheapens mathematical commodities.
In a very apparent manner, the true value of a mathematical commodity (as socially necessary labour time) is immediately reduced if a commodity could have been produced faster by an LLM (or rather, if we as a community allow for such discourse to become predominant).
In the past, computer algebra systems cheapened examples and counterexamples, whenever these were found by known algorithms and run in computers that were not particularly powerful. The 4-colour theorem faced us for the first time against the devaluing of a proof, and thus sparked its own controversy at the time.
Regarding LLMs, different commodities are affected differently. Technical lemmas and counterexamples seem to be singularly devalued by the current frontier models. Correct contextualisation or explanation of a result, for instance, remain uniquely human commodities (but it is hard to know if this will be the case in the future).
LLMs also cheapen the use values of commodities. The models are known for hiding their true sources and the origin of their ideas. The companies behind them are notoriously mischievous. The reason is simple: not everyone is a mathematician, and the training data comprises millions of documents which are not held to the standards of attribution which we expect in mathematical texts. As per the companies themselves: they do not care about our standards.
Finally, the palpable fear among the new generations is the cheapening of the realised value of mathematical commodities (funding, positions, prizes, etc). The sentiment that is replicated throughout is that «we must adopt the technology to remain competitive».
The cycle described by Marx is as follows: the worker helps in the developing of a new technology, which gets adopted into a new machine; the skills of the worker become transferred to the machine, and the worker remains as a dead appendage to the latter. This is a process of deskilling.
5. The ghost of the capitalist
In capitalism, the deskilling cycle is only perpetuated because it benefits the capitalist who owns the factory. When the introduction of a technology first cheapens a commodity, the true value of the commodity (as socially necessary labour time) remains unaffected. Until all factories adopt the new technology, the first ones to adopt it are producing commodities at a cheaper cost, but selling them at the same price as before. Once all factories adopt the new technology, the value of the commodity falls (and eventually so might do its price).
In the mathematical economy, however, there is no capitalist: we are the ones that realise the value of a commodity. We referee, we are the editors, we sit in hiring committees, we decide who gets a prize, we write the letters of recommendation and we read them. We are asked by institutions whether we believe they should grant some funding to another group.
The competitive fear which we have is ill-founded. Or, it could be.
There is no incentive for us to recommend AI papers for publication. There is no incentive to hire or concede prizes to the AI prompters6. There is no incentive to grant them any money7.
The academic community has more soft power than it realises. We may face challenges regarding funding or labour conditions. But in Marxist terms: we remain largely in control of “the means of production” of the mathematical commodities.
6. Conclusion
My goal is to be descriptive, not prescriptive. Please take your conclusions yourself. I am by no means an expert in Marx, so please excuse me if you think that he wouldn’t have agreed with my analysis.
My hope is that some theoretical framework can help us have deeper conversations. For instance, reading philosophers’ analysis the original luddite movement might help you understand your neo-luddite student, when they start feeding an LLM with thousands of pages of nonsensical pseudo-maths to poison AI. Or, it might help you respond to your colleague when they announce they’ll be leaving academia and joining an AI company.
- I am basing most of the essay in Marx’s Das Kapital (volume I). That doesn’t mean that the essay projects a communist or revolutionary lens to this text, but rather that it is framed in dialectical materialism. Also: Marx would have spent thousands of pages expanding on these ideas. I won’t. ↩︎
- The main contribution of Marx to the theory of value is to neatly separate the different natures of these values to properly analyse their relationships. Rejoining two of these into one category is thus against the spirit. It is enough for this essay. ↩︎
- Awards and other honour distinctions are rarely based on the teaching or administrative capacities of the mathematician, even if these comprise most of their working time and often all of their contracted salary. Teaching experience affects your employability, but the quality of your teaching does not help you get tenure in a prestigious institution. ↩︎
- Except in expository texts, which are treated differently to research papers. Here, I’d argue that the effort of synthesis is what takes labour and hence gives value to the text. ↩︎
- The inner workings of this dialogue are complicated and could be analysed in much greater detail. This is beyond the scope of a blog post. ↩︎
- Except, when the rules of the institutions are too stiff for us to introduce any amount of nuance in the process. ↩︎
- Especially, given that they can get their money from AI companies. ↩︎
Received 24 September 2026, revised 5 October 2026.
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