Timeline for What should we teach to liberal arts students who will take only one math course?
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| when toggle format | what | by | license | comment | |
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| Jun 22, 2010 at 20:14 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jun 21, 2010 at 3:58 | comment | added | Victor Protsak | Harry, you are under a mistaken impression that mathematical $\textit{reasoning}$ reduces to proofs and axiomatic method. There is no doubt that mathematical reasoning skills are widely applicable; on the other hand, while "arguing from definitions and axioms" is certainly useful in law, philosophy and logic, and theology, it plays only a minor role in the methodology of most sciences, such as biology, chemistry, or physics, which are $\textit{based}$ upon empirical evidence that you seem to disparage. Look for David Mumford's excellent thoughts on this. | |
| Jun 20, 2010 at 23:20 | vote | accept | Michael Hardy | ||
| Jun 20, 2010 at 23:21 | |||||
| Jun 20, 2010 at 13:41 | comment | added | Harry Gindi | Yes, I agree. I think that it's necessary to introduce students to proofs and the axiomatic method if this is the goal. The concept of a mathematical argument is much more elementary than any sort of argument that relies on empirical evidence. Learning to argue mathematically allows one to argue more efficiently and convincingly in other fields, because it teaches one to argue from the definitions and axioms. What are premises if not just axioms in disguise? | |
| Jun 20, 2010 at 12:56 | history | answered | tomturiel | CC BY-SA 2.5 |