Geodesic
What a rigorous proof should be like?
Matematičeskoe obrazovanie, Tome 68 (2013) no. 4, pp. 70-85

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This article deals with mathematical proofs. It's quite evident that humanity knew about proofs only after the art of writing had appeared. Today one can think about the following ‘`proportion": Texts had appeared — then proofs appeared. Computers appeared — ? In other words what will happen with the classical proofs which were and are the main part of math education tomorrow when computers will seriously change our point of view on computations and etc. We think that it isn’t necessary to use the formal proofs very often for example only at the beginning of some global investigation. After that everyone may restrict himself by such reasonings the result of which is to be clear a) is it possible to conduct the formal proof; b) is it possible to do this for a reader interested in. This is the main point of the m-comics's idea we suggest. It is illustrated by two examples: van der Waerden theorem on arithmetic progressions and Euler theorem on polyhedra. At the end we discuss the math-comics's analogous in other fields and a short review of math-comics's idea evolution in pedagogy is represented as well.
Keywords: formal proof, rigorous proof, m-comics, proof scheme. 
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     title = {What a rigorous proof should be like?},
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A. Ya. Belov; N. S. Kellin. What a rigorous proof should be like?. Matematičeskoe obrazovanie, Tome 68 (2013) no. 4, pp. 70-85. http://geodesic.mathdoc.fr/item/MO_2013_68_4_a4/