[FOM] Galois and P v. NP

Antonino Drago drago at unina.it
Tue Aug 17 16:59:46 EDT 2010

 About Galois's contribution to FoM Dana Scott <dana.scott at cs.cmu.edu>
 Sunday, August 15, 2010 8:49 PM
 suggested two references. I add the paper by Ivo Radloff: E´variste Galois: 
Principles and
 Applications, Historia Mathematica, 29 (2002) 114-137
 29 (2002), 114-137.

 However I think that this history is not a complete one.
 50 years before Galois, Lazare Carnot in his book of mechanics of 1783 
obtained the
 invariants of the momentum and the momentum-of-momentum by suitable
 "geometrical motions" (see my paper: A new appraisal of old formulations of
 mechanics,  Am. Journ. Physics, 72, no. 3 2004, 407-409). In the second 
edition (Principes fondamentales de l'equilibre et du mouvement, Paris, 
1803) he qualified his mathematical
 technique by showing that the geometrical motions are closed under
 composition (theorem III § 150, Corollary I § 151 and Corollary II § 152)
 and that there always exists the inverse motion (Theorem II §
 148). He claimed to to have found an entirely new science, which "is 
intermediate between mechanics and geometry".
A first analysis of the texts by Galois and Lazare Carnot shows several 
common features; first of all, in Galois' Memoire the characteristic notion 
 "adjunction" (written in capitals) actually was a characteristic notion of 
 Lazare Carnot's scientific works.

 Best regards
Antonino Drago

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