Beautiful Poetry [LWN.net]

Beautiful Poetry

Posted Feb 14, 2026 19:08 UTC (Sat) by Wol (subscriber, #4433)
In reply to: Beautiful Poetry by Heretic_Blacksheep
Parent article: Poisoning scraperbots with iocaine

Assumptions come in two forms in philosophy/mathematics. You have axioms (we believe this because it's unproveable), and theories (we believe this because it appears to be correct).

The aim of mathematics is to turn theories into theorems (this can be logically proven provided our theories are correct).

In Science theories are the best we can get, because the only proof we have is "this doesn't work in real life".

These tow different approaches are how I personally differentiate Science from Maths.

And one of the best examples imho as to how things can be got wrong, and change over time, is geometry. Euclid laid down his axioms, including the statement "parallel lines never meet", which gave us the 3D geometry we're all familiar with. But at some point - about the time of Newton or even earlier - some people tried to formalise the axioms of geometry, and that one just "didn't fit". So people started thinking "what if it isn't an axiom at all", and we ended up with relativity and all that stuff :-)

It remains the defining axiom of 3D geometry, but it is a parochial axiom, not a universal one.

Cheers,
Wol

Beautiful Poetry

Posted Feb 15, 2026 2:17 UTC (Sun) by mathstuf (subscriber, #69389) [Link]

> Euclid laid down his axioms, including the statement "parallel lines never meet", which gave us the 3D geometry we're all familiar with. But at some point - about the time of Newton or even earlier - some people tried to formalise the axioms of geometry, and that one just "didn't fit".

Even Euclid (and contemporaries) didn't like it. That's why the parallel postulate isn't used for the entire first book until the end (constructing a square IIRC).