Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Conway postulated that the Steiner-Lehmus theorem is unprovable using direct methods of proof. Can this be proven directly, that the Steiner-Lehmus theorem cannot be proven directly over Euclidean postulates?

share|improve this question
I considered "porting" my question from the FOM mailing list to MathOverflow, as you have done, but decided against it because I now feel that it is not a well-posed question. If you want to ask this question then I would suggest rephrasing it as follows: "Is there a satisfactory way to define formally what a `direct proof' is?" –  Timothy Chow Jul 6 '10 at 1:26
Note that the Conway article has a typo, the second form of the main equation should be $(c-a)\{ ac^2 + (a^2+3ab+b^2)c + b^2(a+b)\} = 0$. –  François G. Dorais Jul 6 '10 at 2:58
I doubt there is an answer better than Conway's answer: The proof must use some fact about the real numbers which is not true in an arbitrary field of characteristic zero. So coordinatize your proof and see what facts about the ground field are being used. For example, I believe that angle chasing, as in section 4.2 of Kiran Kedlaya's book math.mit.edu/~kedlaya/geometryunbound , works over any field. –  David Speyer Jul 6 '10 at 14:47

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.