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Authored by: Anonymous on Monday, October 15 2012 @ 04:35 PM EDT |
No, many things in Mathematics are accepted as axioms (or not accepted). Some of
the axioms are, or have been, quite controversial. The ancient "sum of
angles of a triangle=180 degrees" is perhaps the most famous controversial
axiom: eventually, mathematicians started exploring geometries where that axiom
was simply false--and found those geometries interesting and useful. Today,
mathematicians simply recognize two different fields of geometry, depending on
whether that axiom is true or false.
The "axiom of choice" is, perhaps, the axiom that causes more fervent
religious disputes today.
Then there are things that are generally believed to be true and provable, even
though no proof exists. Famously, in my generation the four-color-map hypothesis
and Fermat's last theorem were both finally proven (after hundreds of years of
attempts.) These generally wouldn't be called "axioms", although
frequently they'll be assumed in order to prove some other similarly-unproven
belief--because, the larger the group of equivalent axioms, the more likely that
SOME one of them can be proven (or disproven), thus proving (or disproving) the
whole lot.[ Reply to This | Parent | # ]
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