- Jan 17, 2014
Can you tell it to others?
The real question is, if God can make Euclid have said otherwise. Has Thomas considered time travel paradoxes?Also included on the list was, God cannot create a triangle whose angles do not add up to 180 degrees. Why not? Because Euclid said so. Euclid trumps God, in the view of Saint Thomas.
Except that an angle with a zero-length side is undefined. Unless you define a new geometry, which seems to be a popular panacea for all mathematical problems.What if you have a triangle where two of the sides are lying right on top of each other, with the third side having length zero. Is that a triangle? Euclid would had said no. And yet, if you think abut it, the three angles are 90 degrees, 90 degrees and 0 degrees, which does add up to 180.
Umm... I can't remember why I made this assumption a year ago.Have we (pre Wiles' result) "proved that no computational algorithm exists that will decide the issue?"
The problem of Fermat's theorem correctness has always been decidable (by default or due to actual existence of a solution). But in my hypothetical case:Is the answer to this decidability question different before and after 1996?
Self-criticism is a skill that one needs to practice constantly. Unfortunately, even scientists often fail to do so. And even modern science as an institution often punishes researchers for being patient and honest.Mathematicians and physicists are gluttons for punishment. They want their models to turn out to be wrong.
I bet none of the modern philosophers bothered to count teeth either.Aristotle, for instance, loudly asserted that women (being inferior) have fewer teeth than men. All he would have had to do was count them. But he didn't, because he "already knew the answer" -- why bother to count?
I mean there was significance to my login name Mathman!As fans of The Hitchhiker’s Guide to the Galaxy recall, in the far future scientists set their massive computers to work to answer the question, What is the meaning of life? After a few million years, the computer had finished its work and delivered the answer: 42.
(Unfortunately, everyone had forgotten what the question was.)
Recently a team of mathematicians, tapping into idle time on a network of 500,000 computers, has plumbed the depths of this mystery. 42 can be written as the sum of three cubes!!!
(-80538738812075974)[SUP]3[/SUP] + (80435758145817515)[SUP]3[/SUP] + (12602123297335631)[SUP]3[/SUP] = 42