Timeline for What advanced area of mathematics can be delved into with only basic calculus and linear algebra
Current License: CC BY-SA 2.5
5 events
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| Dec 21, 2010 at 9:22 | comment | added | Jason | @Zhen: Yes, we definitely would not want to translate Wiles's proof of Fermat's Last Theorem into a "formal proof". :) Also, my comment was intended to clarify to the OP the value of learning logic. I want to apologize for the fact that my wording suggested you weren't aware of the theorems in logic not proved with the two-column proof. | |
| Dec 21, 2010 at 7:42 | comment | added | Zhen Lin | @Jason I'm quite aware of that — I was simply making the amusing observation that the object "formal proof" studied in mathematical logic is, oxymoronically, precisely not the kind of "formal proof" we mean in the rest of mathematics (including in logic itself)! | |
| Dec 20, 2010 at 19:16 | comment | added | Jason | @Zhen, there are definitely two-column proofs in logic, but there is so much more. To name a few examples, you have the Compactness Theorem, Gödel's Completeness theorem, and Gödel's Incompleteness theorems. You also have all of the machinery involved in the proofs of the latter two results. Also, all of our proofs are theoretically supposed to be able to be transformed into a two-column proof to verify correctness, but I don't see that happening in practice anytime soon. | |
| Dec 20, 2010 at 14:07 | comment | added | Zhen Lin | I quite liked Thomas Forster's Logic, induction and sets — it has the right mix of philosophy and mathematics. It's also somewhat non-standard since he emphasises the notion of recursive types, which gives it a bit of a computer-science sort of flavour. I also advise some caution — a formal proof in the sense of logic, is quite different to a formal proof in the sense of mathematics! (Indeed, it's more akin to the so-called two-column proofs from high school, if I understand the descriptions correctly.) | |
| Dec 17, 2010 at 8:55 | history | answered | Jason | CC BY-SA 2.5 |