'Proof' Review: Finding Truth in Numbers

wsj.com

36 points by Hooke 13 days ago


tromp - 10 days ago

https://archive.is/os3ew

NoahZuniga - 9 days ago

I don't like how they give and example of a geometric axiom and then give a number theory result. This makes it seem that the number theory result follows from the geometric axions.

asherlagrand - 9 days ago

[dead]

nyc111 - 9 days ago

"If the axioms are true, and the subsequent reasoning is sound, then the conclusion is irrefutable. What we now have is a proof: something we can know for sure."

... if the axioms are true. We still don't know for sure absolutely.

"The idea of self-evident truths goes all the way back to Euclid’s “Elements” (ca. 300 B.C.), which depends on a handful of axioms—things that must be granted true at the outset, such as that one can draw a straight line between any two points on a plane."

Strictly speaking, Euclid does not state axioms. He starts with 23 Definitions, 5 Postulates and 5 Common Notions. Drawing a straight line from any point to any point is stated as Postulate 1.

I realize this is a newspaper article.