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# Verifiability, access, and allocation in maths
- URL: https://www.slightlyacidic.com/2026/09/19/verifiability-access-and-allocation-in-maths/
- Published: 2026-09-19T15:12:00.000Z
- Updated: 2026-09-28T15:17:44.000Z
- Author: VM
- Tags: artificial intelligence, Anthropic, Astronomy, ATLAS collaboration, BSL-4 laboratories, Claude AI, inequity, Large Hadron Collider, mathematics, social function, verifiability

When I was talking about [this post](https://rootprivileges.net/2026/08/26/the-mathematician-and-the-oracle/?ref=slightlyacidic.com) with a friend, he asked a thought-provoking question. In the post, I’d argued that I believe it should be appropriate for mathematics to consider a solution to a problem to be illegitimate if mathematicians had arrived at it with help from a machine, device or instrument that wasn’t equitably accessible to all mathematicians. My friend asked if this was like how not all physicists can access the Large Hadron Collider (LHC) and how not all biologists could access biosafety level-4 (BSL-4) labs.

By and large today, scientists accept that not every one of them needs to be able to access every instrument to the same degree. Scientific communities also accept work that, as a matter of routine, scientists have produced using scarce, expensive, geographically concentrated or otherwise access-controlled infrastructure. Against this background, let me resolve my position into three components. The first two are access to the instrument that facilitates a claim and what resources scientists *in toto* must be able to access to evaluate that claim. And it seems to me that while the first component can accommodate even radical inequity without invalidating the science of the claim, on the second component there must be no compromise.

For instance, a physicist in Chennai won’t be able to reproduce in her lab the data recorded by the ATLAS experiment at the LHC — but that doesn’t at the same time mean she gets to say “ATLAS has privately concluded that the Higgs boson particle exists”. Why? Because the ATLAS collaboration has documented the detectors’ various components and calibration readings, the team’s statistical methods, selection criteria, and software, and the ultimate uncertainties in the ATLAS data. As a result, another instrument like ATLAS may be able to test the ATLAS collaboration’s claims. (CERN also hosts several research groups that interrogate the data internally.) Thus, the underlying science remains reproducible even as the LHC and its experiments are far from being equitably accessible to all high-energy physics researchers everywhere.

The same argument goes for BSL-4 labs: that the constraints on which particular scientist can perform some analysis or procedure need not also constrain the ability of some claim in science to be reproducible.

In the same vein, in mathematics, being able to reproduce the process by which a claim was unearthed is less important than being able to reproduce the claim itself. I’d written in my post: “Selvi can be cleverer than Shankar and Shankar does not need Selvi’s brain in order to be able to check Selvi’s proof.” So if Selvi claims *P* \= true, it shouldn’t matter to Shankar, or to mathematics more broadly, if she had the help of a dozen graduates or if she stared at a wall for three months. What matters is that Selvi should provide a mathematical justification for her claim that *P* \= true, in the form of a step-wise proof that draws on the field’s tools and foundational assumptions (e.g. theorems, lemmas, specific assumptions, etc.) — and Shankar’s ability to verify it shouldn’t depend on his having privileged access to an oracular instrument.

Put another way: a mathematical claim must ultimately rest on an argument or artefact that other mathematicians **can** scrutinise without requiring privileged access to the resource(s) that produced it. With emphasis on the word ‘can’. In point of fact, mathematics usually has a much easier time separating discovery from justification than do the experimental sciences.

To mix things up a little, let’s add astronomical observatories to the mix of examples. With many of these observatories (worldwide) these days, astronomers from a different part of the world can apply for observing time; if the facility’s corresponding committee approves an application, the astronomers can use the facility to collect the data they need for their specific area of study. Observatories aren’t unique in using this model, which exemplifies how publicly funded scientific infrastructure can be availed to qualified researchers instead of restricting access.

A BSL-4 lab is, however, generally more restricted to scientists than an observatory. Every restriction always serves, or ought to serve, a social function, and here the additional restriction pertains to biological, and potentially national, security. Even so, a researcher can access the lab if she acquires the necessary qualifications, demonstrates work with other labs, etc. With an AI model like Claude, however, Anthropic may — and in fact already has — simply select a dozen mathematicians in private and give them some number of Claude-hours, leaving others with no way to avail such access themselves. The social function that the restriction has amounted to here is nothing more than increasing inequity.

Finally, to the third component of my original claim. Say Selvi and Shankar are competing to resolve a conjecture, and Anthropic invites Shankar to work with a powerful internal AI model. Shankar produces a proof with the model’s help, which he then verifies and publishes. Selvi can still check the proof. However, Shankar will also have ‘won’ the competition, and reaped the accompanying plaudits, credit, jobs, grants, etc., culminating, potentially, with the power to set the research agenda in his domain. So in addition to verifiability and access, I’d also include an ‘allocation’ criterion: if access to some machine, device or instrument must needs be limited, it must be achieved by institutions that can provide an account of why the limitation exists and how researchers may surmount it.

I think this is necessary to ensure verifiability and access also serve the ‘right’ social functions — however they are defined — rather than those that create or entrench the inequity that now haunts mathematics.