Just a Theory?

 
https://barryhisblog.blogspot.com/p/just-theory.html

Pierre de Fermat statue in Beaumont-de-Lomagne

I live near Beaumont-de-Lomagne (https://fr.wikipedia.org/wiki/Beaumont-de-Lomagne), birthplace of Pierre de Fermat, magistrate, mathematician and contemporary of René Descartes of the "I think therefore I am" fame, after whom, Cartesian coordinates were named.

Fermat is known for his "last theorem" for which he never supplied a proof. See https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem. It took mathematicians 357 years to either prove or disprove his theorem. In the end, one Andrew Wiles presented a proof, but other mathematicians found errors in it. He withdrew it, and after a few more years' work, he fixed his proof. Fermat's last theorem is, after all, correct.

There is a book by Frederik Pohl and Arthur C. Clarke, speculating on what sort of proof could have been available to Fermat, but it doesn't offer one. Wiles had used mathematics that was developed well after Fermat's passing, that Fermat wouldn't have been cognisant of. https://en.wikipedia.org/wiki/The_Last_Theorem

Many people I communicate with seem to be a bit unsure about the distinction between the ideas of "theory" and "theorem".

From here on, when I use the word "theory", I mean a "scientific theory" - not just an opinion, a guess, speculation or conjecture. As Wikipedia has it, "a scientific theory is a tested and expanded hypothesis that explains many experiments. It fits ideas together in a framework. If anyone finds a case where all or part of a scientific theory is false, then that theory is either changed or thrown out." 

A theorem is a statement, normally a mathematical statement, which, if correctly formulated, is clearly true according to the axioms and rules of combination within its scope. It must be accompanied by a proof.

So theory and theorem are different things. 

I once had a series of message exchanges with one Werner Gitt, a creationist, who earned a crust by making arguments saying that genetic "information" had to have been sourced by an intelligence. He stated a whole series of "theorems", all of which were assertions unaccompanied by proofs. I told him repeatedly that you cannot call something a theorem if you had no proof of it. Gitt being German, I checked with my good FB friend, Hans-Richard Grümm, an Austrian physicist, that "theorem" means exactly the same thing in English and German. He confirmed that it does. Gitt promised to provide proofs, but never did. Last thing I heard was that he had gone on to a better place.

Related pages,

https://barryhisblog.blogspot.com/p/werner-gitt.html

https://barryhisblog.blogspot.com/p/generating-or-finding-information.html

https://barryhisblog.blogspot.com/p/genetic-information.html

https://barryhisblog.blogspot.com/p/on-proof.html

https://barryhisblog.blogspot.com/p/information-arises-naturally.html

https://barryhisblog.blogspot.com/p/falsifiability.html

https://barryhisblog.blogspot.com/p/dna-is-not-code.html

https://barryhisblog.blogspot.com/p/the-nature-of-scientific-knowledge.html

https://youtu.be/l6ev1lGq0B4?si=nlMugXSZK_EhzFy9