Editorial
The author's opinion, if anyone cares.
The stakes are not abstract
In 2021 the University of Leicester moved to make all eight of its permanent pure mathematics staff redundant, offering to replace them with three teaching-only positions; ten members of the School of Informatics working on theoretical and foundational topics faced the same threat. Administrators justified it by citing demand for AI and data science — the exact fields the Ledger keeps finding downstream of the mathematics being cut. The London Mathematical Society condemned the decision. Timothy Gowers campaigned publicly against it from January of that year. Alison Parker, an external examiner at the University of Leeds, resigned her position over it and donated her examiner's fee to the resulting legal fund. A petition, “Mathematics is not redundant,” drew 8,500 signatures. None of it changed the outcome: three staff were dismissed outright, three were moved into teaching-only roles, and the rest took early retirement or severance. The University and College Union called for an international academic boycott.
I bring this up because the myth isn't only a historical curiosity about mathematicians being wrong in print. It has a live version, and the live version costs people their jobs. Nobody at Leicester argued, the way Hardy did, that a specific branch of mathematics would never see practical use. They argued that pure mathematics had no near-term institutional value next to AI — the same AI that runs on linear algebra, optimization, and probability, built on results that were once dismissed exactly the same way. (This account is drawn from a detailed, widely circulated contemporaneous record naming the people and organizations above; I haven't independently re-checked it against primary university or LMS documents this session.)
Who the empirical case is actually for
The Ledger runs on named dates and cited applications on purpose. That kind of evidence works on readers who aren't naturally comfortable reasoning in the abstract — and, in my experience, the readers who are comfortable reasoning in the abstract are not likely to call for funding cuts to mathematics departments. They don't need the course-correction. The dates and citations are for everyone else.
Why a theorem outlives its first use
Abstraction is the extraction of invariants; generalization is the weakening of assumptions; rigor is what makes conclusions transportable. A concrete solution settles one problem. A rigorous abstract theorem settles every problem, known or unknown, that realizes the same structure.
The case for rigorous abstraction does not depend on predicting particular applications. A theorem proved from abstract assumptions is valid in every realization of those assumptions, including realizations not yet discovered. Generalization enlarges that space of possible realizations by identifying which assumptions are genuinely necessary. Pure mathematics therefore creates a stock of logically certified, semantically portable results. Its future usefulness is not an accidental exception to its abstraction; it is a consequence of abstraction's ability to separate reusable structure from the circumstances in which that structure was first noticed.
It's bloody obvious that it is more efficient for those with skill and momentum to build the machinery before it is needed
It's more efficient to build abstract machinery on top of existing abstract machinery than to wait and extend the stock of mathematical results only when some applied problem happens to need the next piece. The alternative — add to the body of abstract truths strictly just-in-time, incrementally, whenever an application demands it — assumes the person standing there with the need has the background, the ability, and the drive to produce the result themselves. The odds of that are strictly less than unity. Not zero: applied work supplies plenty of its own impetus, and none of this is written to deny that. Just reliably less than one. Maintaining a standing supply of general-purpose structure, built ahead of demand, is the efficient policy. Waiting for exactly the right person to need exactly the right result at exactly the right time is not.
The name is doing the opposite of its job
“Pure” sounds like an indulgence — a luxury version of mathematics, done for its own sake, maybe at the expense of something more useful. But “pure” is close to a synonym for efficient, or non-duplicative. Call the field Efficient Mathematics, or Non-Duplicative Thinking, and nobody questions the funding.
Meanwhile every branch of science keeps reinventing the same underlying structure and renaming it, field by field, oblivious to the fact that someone settled the general case decades or centuries earlier. A tidy example: the probability integral transform — push data through its own cumulative distribution function and it becomes uniform; pull a uniform back through an inverse CDF and it becomes anything you like — is one simple idea from classical statistics. It has been independently rediscovered and renamed as the chi-squared and Kolmogorov–Smirnov tests, inverse-transform sampling and Monte Carlo simulation, copulas, the time-rescaling theorem for point processes, histogram equalization in image processing, rank histograms and Talagrand diagrams in weather forecasting, normalizing flows in deep learning, and conformal prediction — most without citing the others. Full history: skaters.microprediction.org/heritage.html.
Abstraction is what avoids paying that cost twice. It maps the world the way a zip code maps a location: a short, general-purpose address that lets you skip re-deriving the whole route every time you need to refer to the same place.
None of this is an objection to renaming as such. An economist calling a Lagrange multiplier a shadow price has added real interpretive content. The failure mode is the rename that happens because nobody realized there was already a name.