1831
In 1831 János Bolyai
was deployed to assist Gauss in his work. János was Farkas Boylai’s (Gauss’s
mathematician friend) son and hoped to help in Gauss’s long-life objective: to
prove the possible existence of a non-Euclidean geometry. Since the early 1800s
Gauss investigated and searched for proof that such a mathematical aspect could
be true. Sharing only his thoughts with his closest friends, Gauss never shared
his idea with the public scared that he would be scowled and as a consequence,
weaken his mighty figure in the field of geometry. He did however discus a
proof that he found that deduced the axiom of parallels from other Euclidean
axioms. Gauss even stated that he knew the existence of this non-Euclidean
geometry for 54 years, making this doubt be moulded when he was only 15 years
old! As a teenager this great mathematician already doubted the raw structure
of a secure Euclidean geometry, making his intelligence be even more
overlooked.
Gauss also had a major interest and appreciation
for differential geometry and published many papers on the subject.
Differential geometry focuses a lot on different dimensional planes and overall
linear algebra. Disquisitiones Generales Circa Superficies Curva (1828)
was his most praised work in this field. In fact, this paper rose from his
geodesic interests in whom he polished by working with the Danish grid.
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