MathFoundations22: Difficulties with Euclid

There are logical ambiguities with Euclid's Elements, despite its being the most important mathematical work of all time. Here we discuss some of these, as well as Hilbert's attempt at an alternative formulation. We prepare the ground for a new and more modern approach to the foundations of geometry.

Category:

Science & Technology

Tags:

• Mathematics
• foundations
• geometry
• Euclid
• Elements
• weakness
• Hilbert
• Bertrand
• Russell
• formalism
• Wildberger

[relike868p]

I find myself fortunate when I can find a book on "Advanced Geometry" in my local library that presents the subject with Hilbert's framework, although it does not explicitly state its credits to him.

[idster7]

@MisguidedPKer You are putting more restrictions onto the problem than there is in its natural, abstract form when you say that one cannot go through the Earth. And even when you say that, you are not saying that a straight line is NOT the quickest way to get from point to point, you are saying that a curved line is the quickest only because the straight line is unachievable because one cannot go through the Earth.

[MisguidedPKer]

On the Contrary,we cannot go through the earth making this theory disproved if your according this to a map. Think of it Point A to Point B would we walk through the earth to get to a store?

No...

[idster7]

@MisguidedPKer i do not get your point. if the earth is curved, and a line travels across the curved earth, then a straight line theoretically going through the earth would get there quicker. so you haven't disproved euclid's definition.

[MisguidedPKer]

The easiest euclid definition to disprove is that the shortest time to a place is a straight line, its wrong because it has to have a slight curve due to the shape of the earth

[katiatzo]

waiting your next video...thanks...