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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.

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    $\begingroup$ Math majors regularly outrank prelaw students and a host of other majors on the LSAT. $\endgroup$
    – James S. Cook
    Jun 27, 2014 at 18:24
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    $\begingroup$ 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 ...) $\endgroup$
    – vonbrand
    Jun 29, 2014 at 17:45
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    $\begingroup$ 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. $\endgroup$
    – user173
    May 16, 2015 at 22:47
  • $\begingroup$ The word "orthogonal" was once used by someone arguing a case before the US Supreme Court: behttps://www.librarything.com/topic/193156. Or listen at oyez.org/cases/2009/07-11191 starting at 22:29 for around 30 seconds. $\endgroup$
    – KCd
    Oct 15, 2023 at 5:40
  • $\begingroup$ @JamesS.Cook Almost all majors outperform pre-law on the LSAT. We're just seeing selection bias - I imagine the majority of pre-law students intend to go to law school and take the LSAT, but only the non-pre-law students who actually have an aptitude for law will take the LSAT. If you didn't study pre-law but are taking the LSAT, you are likely to do better than someone who did study pre-law, but I don't think it's anything specific to mathematics. $\endgroup$
    – Nuclear Hoagie
    Oct 24, 2023 at 13:56

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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!

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    $\begingroup$ +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. $\endgroup$
    – Matthew Towers
    Jun 28, 2014 at 15:56
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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.

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    $\begingroup$ 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. $\endgroup$
    – Jon Bannon
    Jan 1, 2016 at 13:55
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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.

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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.

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This is in addition to what's already been contributed, not instead of.

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.

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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...)

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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.

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Your client has been fired from his job for failing the Company comprehensive drug screening program of all one thousand employees.

The drug test is 99% accurate.

How might you proceed counselor?

OK, let's add some more specifics.

Assume that there are 10 employees that are actually using illegal drugs. What is the probability of guilt for your client?

It's 50/50, no better than a coin toss.

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I am a law student and realised i could use my knowledge of mathematics to study law. Since my brain is use to seeing formulas, I derived a technic in memorizing long chapters and quotes into equations

BP > CC > P/RPB. Is my definition of morality.

Body of principles derived from a particular code of conduct through a particular religion, philosophy or belief.

My brain easily sees the letters and during my law essay writings I can expand from these formulas. I have also summarized long essays with dates to very short formulas.

Thanks

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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)

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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.

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    $\begingroup$ 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. $\endgroup$
    – paul garrett
    Jan 6, 2016 at 19:10
  • $\begingroup$ +1 for worthless garbage, not that I believe all plug and chug is worthless garbage, instead that I side heavily for a discussion where we say what we think rather than what we think other people want to hear. $\endgroup$
    – James S. Cook
    Dec 23, 2020 at 1:56
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This is more physics than mathematics, but it can do:

In Belgium it is not allowed to pass a vehicle from the right side. Now imagine that you are driving your car on the most right lane, and one the second lane, a car is slowing down and suddenly turns to the right, hitting your car.

He might argue that you are passing from the right side, so you are wrong.
You might argue that you were doing an ERB (eenparig rechtlijnige beweging, in English you can call this a perfectly straight movement without speed modification). As you are not altering, nor your direction, nor your speed, you are not even performing a manoeuvre, so the word "passing" can't even be used and you are the one being right!

I'm not sure if this argument might hold in court, but if ever I get into such an accident, I'll already know my argument :-)

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Here is a nice article (written for undergraduates)

Gray, Mary W. "Statistics and the Law". Mathematics Magazine 56(1983), no.2, 67–81.

Mary Gray was both a mathematician and a lawyer. In this paper, she discusses court cases where mathematics (in particular, statistics) was incorrectly applied.

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Math can be used in court as part of admissible evidence although the records of it haven't been favorable towards mathematics since math had been used to prove innocent people guilty

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  • $\begingroup$ When you make an assertion, you should back up that assertion with referenced facts. This is doubly true in the law (where every sentence may have multiple citations to case law). Admissible as evidence where (different jurisdictions have different rules of evidence)? In what way has the record been unfavorable (whatever that means)? Which innocent people were "proved innocent" (an idea which does not exist in the law, usually)? Citations, please. $\endgroup$
    – Xander Henderson ♦
    Oct 9, 2023 at 2:31
  • $\begingroup$ @xander look up prosecutor fallacy. In People v. Collins, probability was misused to reach a guilty verdict. This led to the existence of the Collins test. In particular, the court expressed its concern that complex mathematics would distract the jury from weighing the credibility of witnesses and the reasonableness of their doubts. The court also expressed concern that if mathematics became common tools for prosecutors there would not be enough defense attorneys skilled at mathematics to put on a skilled defense. $\endgroup$
    – Lenny
    Oct 9, 2023 at 15:10

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