# How is education in Mathematics relevant to Law?

Many students who take courses in mathematics go on to pursue "non-mathematical" careers. I'm wondering, in particular, about those who go on to study Law, and how mathematics is (or can be made) relevant to them in the classroom. I have not specified a particular age of the students, but if you wish to restrict to (middle school, secondary school, college/university) in your answer, then that would be fine.

Question: What are concrete ways in which one's mathematics education can contribute to a career in law? (If your answer is, "It doesn't," then an explanation of this would be fine, too!) Connections between mathematics education at any level and its impact on careers in law would be most welcome.

For the motivation, see this meta question; moreover, this user recommended I post here.

Another interesting place to look is Law and Mathematics Professor Peter Rosenthal's MAA article; for example, consider the following excerpt:

Law sometimes makes a pretense of being logical, but it is only a pretense.

• Math majors regularly outrank prelaw students and a host of other majors on the LSAT. – James S. Cook Jun 27 '14 at 18:24
• Perhaps not for all law students, but there certainly is a segment who use math (or physics, or chemistry). Computer science and law are also an interesting cross-area (search for case law matching ...) – vonbrand Jun 29 '14 at 17:45
• I recommend deleting the fake quote from Kant, and that whole paragraph. The very article cited says "several Kant scholars said that they were not aware of such a quote". The closest actual Kant quote seems to be: "in addition to transcendental philosophy, there are two pure rational sciences, namely, pure mathematics and pure ethics." (marxists.org/reference/subject/ethics/kant/reason/ch03.htm). That's pretty different, and I'd prefer that this site avoid stretching history so far. – user173 May 16 '15 at 22:47

A 16 year old once told me that he has no need for mathematics since he wanted to become a lawyer. I told him that he wouldn't make a good lawyer if he jumps to such conclusions without first collecting all available evidence. So what evidence is there?

I have a book in front of me: Mathematics, Physics and Finance for the Legal Profession by Ashley Saunders Lipson, 2011. Chapters include Logic and Set Theory, Probability, Statistics, Graphs and Diagrams, Classical Physics, Modern Physics and Accounting and Finance. I have only read a little bit, yet already I have been pleasently surprised: The use of trig in land deeds; the logic in legal interpretations similar to the interpretations of Euclidean and non-Euclidean geometry; and an interesting question, can you patent a mathematical formula?

When I teach probability, I always discuss the Sally Clark case. It highlights what can happen when no-one in the case, whether it be defense or prosecution, judge or jury, has the ability to appreciate something as basic as independence of events. It makes you think!

• +1 for mentioning the Sally Clark case: she drank herself to death after being falsely convicted of murdering her son based in part on a misuse of probability by Prof. Roy Meadow. – Matthew Towers Jun 28 '14 at 15:56

If you mean Pure math, then a firm grasp of logic and logical arguments to form proofs may be incredibly helpful in building a good case. It would also help in finding logical flaws in opposing briefs. From an applied math view, being able to check the stats and whatnot that a contract is based on seems reasonable (like in insurance). Finally, for both types of math majors, you are likely to have friends in the CS, physics, and other science departments. Those people will always need patent lawyers to make them some money. Having a firm grasp of how their invention functions should make life a lot easier when trying to determine if they even have a case when you have noon-literal infringement.

The above is just some brainstorming. Hopefully it is helpful.

• Students of mine who have gone into law report that while other students (even pre-law students) struggle with learning logical argument, their math background made this (substantial) part of their legal training easy. – Jon Bannon Jan 1 '16 at 13:55

There is a whole book devoted to game theory and law: Game Theory and the Law by D. G. Baird, R. Gertner, and R. Picker, Harvard U. Press, 1994.

Although much of Game Theory was developed by mathematicians such as John Von Neumann, Lloyd Shapley, John Nash, and Alvin Roth, people who currently do research in game theory are more likely to teach in economics, operations research, or political science departments rather than mathematics departments, even though they have degrees in mathematics.

There are many math-related aspects of pure and applied law. Just look at the other answers. But the simplest example is:

Necessity and Sufficiency Take any example of a legal text mentioning conditions and ask a lawyer, if this means a necessary condition or a sufficient condition. You'll understand by his reaction.

Just as mathematical definitions and axiom systems and so on do not (and maybe cannot) genuinely capture "mathematical reality", (as a non-jurist) it seems that law does not and cannot capture "justice" (or "morality", etc).

In the case of mathematics, to my perception there is eventually more flexibility, once one is beyond the typical undergrad and beginning graduate curriculum. That is, the business is not nearly as rule-bound as undergrad curricula often are presented.

(Mercifully) I have no experience in law or the courtroom... but it would be my impression that judges and lawyers are far more bound by the random approximations to justice that are the laws on the books. Yes, of course, they are intended to approximate real justice and fair play, but this seems impossible to completely accomplish.

The upshot is that the somewhat rule-based undergrad math curriculum is perhaps a good abstracted version of the "game" part of law. Not many other undergrad curricula amount to adherence to possibly unfathomable, unbending rules, but, more often appeal (reasonably) to common sense. Not a bad thing! But, in the popular U.S. culture, appeals to "common sense" are often merely veiled appeals to previous prejudices or popular beliefs, rather than any sort of genuine seat-of-the-pants. (Perhaps certain higher-level video games may be a significant exception...) Thus, in the past, few undergrads have experience in manipulation of "rules", making deductions from the rules (without addressing the truth or falsity of the rules themselves), and so on.

Capsulization: where else to in-effect learn about modus ponens? :)

(The beyond-the-rules research parts of mathematics don't seem to have much real relation...)

• @BenjaminDickman, thanks for your observation... I was hasty! :) – paul garrett Jan 1 '16 at 15:24

I went to court once about a car accident. The other driver was there too, and each insurance company had sent a lawyer. My insurance company's lawyer had a short informal chat with me in the hall, and then when we were having the formal conversation with the judge, she helped me bring out the most salient points through her questions. I was very impressed.

She sorted through my jumble of comments in the hall, picked out the important things, and arranged them in an effective order. You do all of that when you're outlining a proof.

Also, in both fields, it's not enough to have things clear in your mind, you also have to get good at communicating your ideas to others in a persuasive way.

There is a book about statistics and the law: Morris H de Groot, Stephen E Fienberg & Joseph E Kadane: "Statistics and the Law", Wiley Classics Library.

http://www.amazon.com/Statistics-Law-Morris-H-DeGroot/dp/0471055387/ref=sr_1_1?s=books&ie=UTF8&qid=1431432099&sr=1-1&keywords=statistics+and+law (amazon also has a few other similar titles)

The Coase theorem, in some sense, underlies nearly all of the law, and an explicit understanding of this sort of thing is becoming increasingly important for legal scholars. Judge Richard Posner is a leading thinker on the economic foundations of the legal system and has written a large number of books on the subject. I took a class using his book Economic Analysis of Law in college, but I can't remember now how much economic jargon it relied on.

Writing arguments is most of the work in some math courses. In high school what is often taught is just algorithms for solving the homework problems, and that's worthless garbage except when there is some pre-identified occasion to use those algorithms outside the classroom. In some cases there is such an occasion, e.g. in a statistics course. But the kind of math course that emphasizes writing proofs can help lawyers learn to argue logically.

• Can whoever down-voted this explain why? – Michael Hardy May 14 '15 at 22:38
• I upvoted your answer, but thought to write to clarify that I did not downvote. – Pamela Lee Dec 31 '15 at 23:10
• I suppose someone might be put off by the "worthless garbage" phrase? After all, some peoples' lifes' work consists of training kids to execute those algorithms... not that I'm such a fan of that picture of "mathematics", either. – paul garrett Jan 6 '16 at 19:10