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.

This entry was posted on Sunday, September 28th, 2008 at 7:36 pm and is filed under mathematics. You can follow any responses to this entry through the RSS 2.0 feed.
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Of course you can protest if you carefully checked the proof. I think this is actually better than experimental sciences, where you have to invest a lot of work to do the experiments, and then check the proof which involves mathematics. I don’t think there is something wrong with the way we do mathematics, the article shows just physical limitations of human ability.

That was my understanding. I did not aim to point out anything wrong about the way mathematics is currently done. But I can be worried if something that is claimed correct could not be or if some room is left to think so. About physics as you know, being a mathematician, our mathematical requirements are generally more loose and a physical theory does not require thousand pages for a proof. A first formulation of the Standard Model for leptons entered into four pages of Physical Review Letters. Finally, experiments proved this right and still today we have not such a sound mathematical basis for this model. An example is given by the Millenium Prize for Yang-Mills theory as you know.

Closer to home, if you want a real shock, read the paper on global warming and cosmic rays by the “Cloud Collaboration”. The proposal came out in 2001 and is quite inexpensive compared to the important results it would provide but has been ignored probably for political reasons. Shouting is more important than truth.

Of course you can protest if you carefully checked the proof. I think this is actually better than experimental sciences, where you have to invest a lot of work to do the experiments, and then check the proof which involves mathematics. I don’t think there is something wrong with the way we do mathematics, the article shows just physical limitations of human ability.

That was my understanding. I did not aim to point out anything wrong about the way mathematics is currently done. But I can be worried if something that is claimed correct could not be or if some room is left to think so. About physics as you know, being a mathematician, our mathematical requirements are generally more loose and a physical theory does not require thousand pages for a proof. A first formulation of the Standard Model for leptons entered into four pages of Physical Review Letters. Finally, experiments proved this right and still today we have not such a sound mathematical basis for this model. An example is given by the Millenium Prize for Yang-Mills theory as you know.

Marco

Closer to home, if you want a real shock, read the paper on global warming and cosmic rays by the “Cloud Collaboration”. The proposal came out in 2001 and is quite inexpensive compared to the important results it would provide but has been ignored probably for political reasons. Shouting is more important than truth.