I'm wondering what is the purpose of Gauss in his letter to János Bolyai when he mentioned "howling Boeotians"? Is it related to some scientists or philosophers that opposed non-Euclidean geometry? I appreciate any information or suggestion.

up vote 4 down vote accepted

Gauss was probably afraid of attacks of some mathematicians and philosophers: the idea looked too radical for that time. The history shows that Gauss was right. When non-Euclidean geometry was published (by Lobachevski), it was had a poor reception in the beginning. Even among some mathematicians (for example Ostrogradskii). Later when Riemann published his ideas on what is called today Riemannian geometry he was also attacked by many people (including philosophers in his own university, like During).

The reason of these attacks is that at that time geometry was supposed to describe the so-called "real world", and that the geometry of the real world had to satisfy Euclidean axioms was considered "self-evident". An influential philosopher (Kant) even insisted that our brain is "hard-wired" for Euclidean geometry. Kant's ideas were dominating philosophy in the time of Gauss, at least in Germany. Even in the early 20th century some outstanding mathematicians (Steklov, for example) criticized Riemann's ideas as "unrelated to real world".

  • Actually, the problem was exactly the opposite. Euclidean geometry was seen as the only "true" geometry in some ideal sense, Kant put a new foundation under that in the form of synthetic a priori, and Gauss, Lobachevski, Riemann and others motivated the non-Euclidean geometry by the "real world" not affecting our senses with the precision of Euclid's axioms. So the spherical/hyperbolic deviations are possible and empirically testable rather than ruled out a priori. – Conifold Oct 9 at 0:24

Would have been easier if spelled right... sigh.

From an online dictionary

dull; obtuse; without cultural refinement.

In this case, a cultural slur on the residents of Boeotia, and presumably anyone else that Gauss disapproved of.

  • It means pretty much the same in German according to this dictionary which defines "Bö­o­ti­er" as "denkfauler, schwerfälliger Mensch", i.e. a lazy-minded, plodding person. – njuffa Oct 9 at 17:29

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