Understanding the math of Fermat

A few words about a subject that often gets a bad rap: MATHEMATICS. I believe that most people who “don’t like math” or say “it’s Greek to me” do so primarily because of inexcusably poor math teachers. Anyone who can speak and understand a language (like English, Spanish, etc.) can learn math. You learned your native tongue as a child, and that’s the best time to learn math, because learning math is just like learning a language, but it’s much, much simpler than French or German. An equation is just a simplified sentence: the left-hand side is the subject, the equal sign is the verb, and the right-hand side is the direct object. Mathematics properly understood is the language of the universe. This is why Albert Einstein could say “Ich will Gottes Gedanken zu wissen, alles andere sind nur unwichtige Einzelheit!” (I want to know God’s thoughts, all the rest is just unimportant detail!) Math is NOT just a left-brain thing. Music and poetry are mathematical, and real math is creative, especially if you realize that it works the way your mind (and the infinite mind of God) works!

Fermat's Last Theorem is like a poem or sonata, and it describes a beautiful part of reality. Translated into English, it says: While two perfect square areas can be added to produce a third perfect square area, no two perfect cubes, or whole numbers raised to any other  power, can be added to produce a whole number result of the same power. Expressed in part in the language of mathematics, this is:

A, B, C = (1, 2, 3, ...):  A²+B²=C² → 3²+4²=5² , 5²+12²=13² ...  (called Pythagorean triples)

But A³+B³≠C^{3 ,} A⁴+B⁴≠C^{4  ...} Aⁿ+Bⁿ≠Cⁿ  (where ≠ means “cannot be equal to”)