Nikolai Vavilov (St. Petersburg) 50 SHADES OF PROOF
Qui dit Mathématiques, dit démonstration. The only problem is that there is no obvious standard of proof, common for different areas of mathematics at different times.
For vast majority of mathematicians proofs are not mere texts, and are intimately
related to individual and collective understanding. From this viewpoint FORMAL
PROOFS are not higher forms of traditional proofs, they ARE NOT mathematical
PROOFS at all. Rather, they play a role of testimonies, or experimental evidence,
urging us to find a real proof that might give such an understanding.
I plan to discuss and illustrate by a medley of historical examples of various
levels, the difference between proofs, verifications, and their intermediate
forms, as far as their reliability, transparency, and durability.