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It is a living field, of course, but I do think there are certain texts that we know we would include from Turing, Von Neumann, Goedel, Church, Shannon, Backus,
by thwayunion 4y ago
It is a living field, of course, but I do think there are certain texts that we know we would include from Turing, Von Neumann, Goedel, Church, Shannon, Backus, Hoare, Dijkstra, and I guess something about Perceptrons is now mandatory but IDK what text I'd choose. Beyond those texts things become hazier, but that's already at least a semester of undergraduate reading.
> Also the point of reading Euclid is not really to learn geometry but rather to investigate and examine the oldest, most primordial expression of the idea that math should be formalized using a few axioms.
Yeah, Euclid is important. It should be studied carefully in any Great Books program. But there's a lot of other important stuff to talk about and the extreme emphasis on Euclidean constructions is IMO a bit of a shibboleth.
- adamsmith143 4y agoI don't think the point of any great books program is to finish and say "You have now read everything of relevance, no need to read anymore." The curricula are broad and general so that if you have particular interests in a field you are now equipped to read all of the texts you mentioned on your own. If there was a specific "Great Mathematics Books" curriculum perhaps all the ones you mentioned would indeed be required.
- voldacar 4y agoI don't see a huge emphasis on Euclidean constructions, at least not in this particular curriculum. Euclid is just one book among several math books here. However I do think one issue with studying math from a great books perspective is that the level of prerequisite knowledge it takes to even read a lot of texts considered great would take many years of focused study to develop. I don't see Grothendieck in this list for instance. An intelligent child can read Euclid and follow along perfectly, because there isn't really any prerequisite knowledge needed.