What understanding is for

Steven Strogatz is willing to imagine an artificial intelligence that leaves mathematicians with no claim to superior performance. In his conversation with Grant Sanderson, the creator of 3Blue1Brown, the Cornell mathematician considers a system that asks better questions, develops better theories and explains its results better than people do. What would human understanding be worth then?¹

A familiar answer is that understanding allows us to make progress. Strogatz points out the flaw in treating that history as a guarantee. What has depended on human understanding need not always depend on it. A more capable system might also discover the connections that make its results useful. Progress could continue without our having to understand.

Lawyers have a Latin phrase for their distance from mathematics: iudex non calculat, the judge does not calculate.² It offers little protection from the mathematicians’ question. Suppose AI could find better legal arguments, grasp people’s circumstances more accurately and make better judgements even about competing values. Suppose it could also explain the implications more clearly. This is a thought experiment, not a forecast. It removes the same assurance: that finding a good answer requires human understanding.

What makes a legal answer useful depends on the relationships law governs. One of law’s central purposes is to make cooperation possible.³ People pursuing different aims can coordinate their plans when they know what they may rely on. Understanding what I have promised, and what others owe me, helps me anticipate difficulties and decide how to respond. Legal commitments become part of how we think: we use them to interpret other people’s conduct and to decide what to do ourselves.

AI might organise our cooperation better, too. It could attend to everyone’s purposes and coordinate our actions while leaving us with little grasp of the legal arrangements. If our entire defence of understanding is that it improves cooperation, better performance can still replace it.

Whether that would be enough depends on the standing people should have within their cooperation. People should be able to examine the reasons for their obligations, form a view and offer reasons of their own. There is value in doing so even when it produces no better outcome: they can take a position on the terms under which they live together. AI may replace the process; people should retain their claim to a voice. That is a choice about how we should live together.

This claim limits what superior performance can authorise. Being better at judging a person’s interests does not, by itself, give anyone permission to bind them. An accurate prediction of what they would agree to is still not their agreement. Anyone claiming authority over them must be able to justify that authority, even when the decision itself is beyond reproach.

Even where a court has authority to bind a person, it still owes reasons for the particular decision. The judgment can bind someone who considers it wrong. That makes the opportunity to examine its reasons and raise serious objections especially important. The legal philosopher Lon Fuller identified participation through evidence and reasoned argument as a defining feature of adjudication.⁴ The Swiss Federal Supreme Court requires reasons that allow a person to grasp a decision’s implications and challenge it effectively; the essential points suffice.⁵

Participation of this kind does not demand complete personal expertise. People can trust advisers, delegate tasks and seek help from AI. The help should enable them to form a view of their own to the extent that they wish to do so. No one should have to earn access to law or assistance by demonstrating understanding. Understanding is an opportunity the law should provide, not a test people must pass before their interests count.

For that opportunity to be real, the necessary help must be within reach. Explanations, advice and participation take time and money, and people have unequal amounts of both. The value of closer examination must therefore be weighed against its cost. That includes what the affected person can afford and what they stand to lose by delaying a prompt, affordable resolution. A right to participate is of little use to someone who cannot afford to exercise it.

Affordable help does not remove unequal power, either. Someone with no acceptable alternative may understand unfavourable terms perfectly well and still have little choice. Clear terms are not necessarily fair terms. Alongside the opportunity to examine reasons, law must provide rights and the means to enforce them. Human understanding can contribute to that protection; it cannot supply all of it.

For lawyers, this establishes a standard that reaches beyond the quality of their answers. Their work should help people understand their legal position and exercise their rights. Where AI provides better help, that is a reason to use it. The value of human understanding does not reserve particular tasks for lawyers. What matters is what the assistance enables the person concerned to do.

Whether people or AI provide that assistance, it can lead to participation only if the procedures allow it. Reasons should disclose the facts, rules and judgements on which a decision depends. A person examining them needs access to the relevant records. A serious objection must be able to reach an institution required to consider it, give a reasoned response and, where warranted, secure a correction. An institution that owes people reasons must also be prepared to receive them.

Notes

1. Grant Sanderson, “Steven Strogatz on the Humanity of Math”. The far-reaching AI premise is discussed at approximately 00:08:53–00:12:34; understanding and its possible dispensability for further progress at approximately 00:23:28–00:35:38. Paraphrased from the machine-assisted transcript of the supplied recording; timestamps are approximate. Strogatz teaches at Cornell University and was elected to the National Academy of Sciences in 2024. The extension to law assumes superior performance; imitating people and outperforming them are different achievements. It leaves open whether the system itself understands.

   Watch the conversation Steven Strogatz · Cornell National Academy of Sciences · 2024 election Grant Sanderson · 3Blue1Brown

   Back to text

2. The maxim is used here as a lawyers’ joke. For its different meanings and history, see Hanjo Hamann, “Iudex Non Calculat: Exploring the Number-Aversion Maxim as an Intellectual Trans-Atlantic Export”, German Law Journal 27(4) (2026), pp. 651–677, especially the abstract and sections B and E.

   Original article

   Back to text

3. On law’s institutional functions of coordination and planning, see Scott J. Shapiro, “What Is the Rule of Recognition (And Does It Exist)?”, Yale Law School Public Law & Legal Theory Research Paper No. 181, pp. 3–4 and 8–9, and Part IV, pp. 16–20. The shared plan in that discussion principally concerns legal officials. This essay does not depend on accepting Shapiro’s legal theory as a whole.

   Original paper

   Back to text

4. Lon L. Fuller, “The Forms and Limits of Adjudication”, Harvard Law Review 92(2) (1978), pp. 353–409, especially pp. 363–367; on shared purposes and reciprocity, pp. 357–363. Fuller taught at Harvard Law School.

   Publisher’s record Scan of the original article

   Back to text

5. BGE 148 III 30, consideration 3.1 (22 October 2021), concerning Article 29(2) of the Swiss Constitution and Article 53 of the Civil Procedure Code. The reasons were held sufficient in that case. The judgment does not concern AI.

   Swiss Federal Supreme Court judgment

   Back to text