I am currently a member of American Mathematical Society and when I have the chance I support the activity of this venerable and fundamental association by working as a reviewer for Mathematical Reviews. So, I have the opportunity to read Notices that is a beatiful journal published by AMS and send freely to all members. It can be found here. In the August issue I have read an Opinion by Melvyn B. Nathanson of CUNY that shocked me and mostly my fundations on mathematical truth. The article is here. I think that the core of this article resides on the idea that bosses of the community make truth, mostly when proof implies thousands pages of published material very difficult to be checked carefully. We all know that, for the Wiles’s proof of Fermat theorem, the community was lucky enough to catch such a bug in a long proof. This was conveniently corrected and all agreed that such a demonstration indeed was given. But when, for any reason, we have to rely on authorities to get the truth we are in serious troubles. This means that whatever they said should be taken as granted but in this case does seem that no protestation is indeed possible. As scientists we cannot accept “ipse dixit” position and if mathematics is in such a situation something must be done to correct it.
The next question to be answered is: What is the situation in physics? Physics, differently from mathematics, is an experimental science. This means that experiments should grant our ability to tell where the truth is. Today things do not seem to be that easy for a lot of reasons but I think other sources can give judgments better than mine.