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'''Infinite descent''' is a brilliant method of mathematical proof promoted by [[Pierre de Fermat]] in the 1600s.<ref>https://brilliant.org/wiki/general-diophantine-equations-fermats-method-of/</ref> This approach facilitates elegant proofs of challenging problems, and can be tremendously useful beyond mathematics too.
This approach is analogous to proof by induction except infinite descent goes in the backwards, or downwards, direction until a contradiction occurs, thereby proving the falsehood of the hypothesis. The approach can be summed up as this:
:Assume that a solution to an equation exists among positive integers. Then show that the existence of that solution implies the existence of another solution with smaller natural positive integers. Then show that yet another solution among positive integers must exist, and so on ad infinitum. But descent ad infinitum is impossible among positive integers, and hence a contradiction occurs. Therefore no solution can exist among positive integers.
== Infinite descent and the [[Bible]] ==
The insights from an approach of backward descent is hinted at in logic referenced by [[Jesus]]:<ref>John 8:58 (ESV).</ref>
{{cquote|Jesus said to them, “Truly, truly, I say to you, before Abraham was, I am.”}}
Jesus did not say, "I was," as one might expect, but rather "I am." In other words, infinite descent is available to Jesus, just as [[multiplication of the loaves]] is.<ref>The lack of a time barrier to [[Jesus]] could explain the puzzling results in a flawed attempt to date the [[Shroud of Turin]].</ref>
== References ==
<references/>
[[category:mathematics]]