Defining Mathematics (Logic Reigns Alone)
A nine-card essay defining mathematics (after Eugenia Cheng) as the one field where logic reigns alone, unlike science, law and history, ending with a sigh at the task of defining logic.
Use this cartoon
Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2016-04-20-defining-mathematics/ (CC BY-NC 4.0)Transcript
[1] "If you've ever tried to define 'mathematics,' you've noticed it's surprisingly hard to pin down exactly what the subject is." A: "hmm… it's 'that required class with all the fractions'"
[2] "Well, I like Eugenia Cheng's take (which I paraphrase slightly): 'Mathematics is the study — using the rules of logic — of anything that obeys those rules.'"
[3] "Logic, of course, is key in every discipline. But usually, it has to perform as part of an ensemble, sharing the spotlight with other sources of insight and information."
[4] "In science, logic must compromise with experimental evidence." A: "These calculations imply the theory is true!" B: "Well, these experiments mean that it's false."
[5] "In law, it must compromise with custom and tradition." A: "But… this decision is so illogical!" Judge: "You say 'illogical,' I say 'bound by precedent.'"
[6] "In history, logic must compromise with the record of artifacts and documents." A: "But… by my reasoning, the war should've gone the other way!" B: "Yeah, that's not how the past works."
[7] "Mathematics is the realm that logic can navigate without crossing a border, without casting a shadow, without encountering another living soul. Without compromising."
[8] "In math, logic reigns alone." [a figure in a crown]
[9] "Now… to define logic…" A: "sigh…"