[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
of
"adjunction" (written in capitals) actually was a characteristic notion of
all
Lazare Carnot's scientific works.
Best regards
Antonino Drago
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