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Some background might be useful. In the 1800s, geometry was seen as the best math to train one's mind. Abraham Lincoln, for example, "kept a copy of Euclid in

Some background might be useful. In the 1800s, geometry was seen as the best math to train one's mind. Abraham Lincoln, for example, "kept a copy of Euclid in his saddlebag, and studied it late at night by lamplight; he related that he said to himself, "You never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father's house, and stayed there till I could give any proposition in the six books of Euclid at sight"." (quoting https://en.wikipedia.org/wiki/Euclid%27s_Elements https://en.wikipedia.org/wiki/Euclid%27s_Elements ). This held until around WWII. One way to see how curriculum has changed over the last 75 years is in Sheldon Glashow's autobiography. He graduated from the Bronx High School of Science in 1950. Quoting https://www.nobelprize.org/prizes/physics/1979/glashow/biographical/ https://www.nobelprize.org/prizes/physics/1979/glashow/biogr... , "High-school mathematics then terminated with solid geometry." In the post-war era, the government needed a lot of people trained in the physical sciences and engineering fields where applied skills in calculus was more important than abstract ideas of how to think. In the last 25 or so years there's been an effort to de-emphasize calculus as the end-goal progression for high school math, and to teach more statistics. AP Statistics wasn't offered until 1997, for example: https://en.wikipedia.org/wiki/AP_Statistics https://en.wikipedia.org/wiki/AP_Statistics This essay is part of that modern movement. That said, I think the author has almost dismissed the classic idea of a mathematical education - to learn logical thinking. The only mention of "proof" is in reference to Gelman's "restructuring mathematical education around understanding uncertainty rather than abstract proofs." I know nothing of Gelman's writing, but as the Lincoln example shows, abstract proofs are useful in constructing and analyzing legal arguments (and programming, IMO), in way I think should not be so readily set aside.

jfengel 2y ago
Law seems an odd application of proofs. I've never seen anything in law to which mathematical rigor could apply. Learning to reason is always good as a brain exercise. But legal "proof" has always struck me as laughably vague.
- milesrout 2y ago
  As someone with degrees in both law and mathematics I was struck by the similarities in the subjects when I learn law. Everyone was surprised when I told them that... except for my cousin, a mathematician. It didn't surprise him at all. Law (analytically - practically it is about problem solving, strategy, tactics, understanding your client's problems, clear presentation of ideas, etc. like any other business) is all about logic, reasoning, thinking clearly, separating precedent and antecedent, the logical flow of ideas, etc. In practice, legal reasoning is more inductive than deductive (not entirely), which means if has a different flavour in practice. It is still just as much about logic. But don't get distracted by things like the standard of proof etc. That has much more to do with the fact that you are making decisions based on unreliable and imperfect information, as opposed to reasoning about entirely abstract ideas like a mathematician.

jfengel 2y ago

Law seems an odd application of proofs. I've never seen anything in law to which mathematical rigor could apply. Learning to reason is always good as a brain exercise. But legal "proof" has always struck me as laughably vague.

milesrout 2y ago
As someone with degrees in both law and mathematics I was struck by the similarities in the subjects when I learn law. Everyone was surprised when I told them that... except for my cousin, a mathematician. It didn't surprise him at all. Law (analytically - practically it is about problem solving, strategy, tactics, understanding your client's problems, clear presentation of ideas, etc. like any other business) is all about logic, reasoning, thinking clearly, separating precedent and antecedent, the logical flow of ideas, etc. In practice, legal reasoning is more inductive than deductive (not entirely), which means if has a different flavour in practice. It is still just as much about logic. But don't get distracted by things like the standard of proof etc. That has much more to do with the fact that you are making decisions based on unreliable and imperfect information, as opposed to reasoning about entirely abstract ideas like a mathematician.