What progress has been done on Hilbert's 6th problem?

[Anama Skout]

So Hilbert's[/PLAIN] 6^th problem says:

6. Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.
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What progress has been done on Hilbert's 6^th problem so far and what are the main difficulties? (in layman language)

 

[BvU]

You mean other than already related in layman terms on the link you start out with ? I don't know who the author is, but the wiki lemma is a good starting point for surfing around. I don't think there is any point in re-doing that.
Or do you mean from 2000 until now ? Then you are really at the forefront of science philosophy, together with some very big shots... better fly a little lower and do some reading, surfing and learning some basic physics.

 

[Anama Skout]

Or do you mean from 2000 until now ? Then you are really at the forefront of science philosophy, together with some very big shots... better fly a little lower and do some reading, surfing and learning some basic physics.

Yes, but I don't envisage to understand those things deeply, just a brief overview if there are recent interesting results and what the main difficulties are, such discussions always motivate me.

 

[ZapperZ]

Yes, but I don't envisage to understand those things deeply, just a brief overview if there are recent interesting results and what the main difficulties are, such discussions always motivate me.

But the problem here is that do you even understand the very thing that you quoted on your first post? You wanted an update or progress out of it, but I am not even sure if you even understand "it" as the starting point!

I see in another post in this same forum that you don't have a clear understanding of basic projectile motion, and also that English isn't your first language. So even if we could explain all this in "laymen's" term, I foresee either a misunderstanding, or misinterpretation of what will be presented, not just based on the language, but also based on cultural and social context.

This is neglecting the fact that I see this as purely a philosophical topic that is frowned upon on here.

Zz.

 

[BvU]

Yes, but I don't envisage to understand those things deeply, just a brief overview if there are recent interesting results and what the main difficulties are, such discussions always motivate me.

I can respect that. But then perhaps this insight by Alex can do the motivating as a substitute for the layman translation that we are somewhat reluctant to provide. (with good reasons, it will trigger a lot of nonsense, noise and what have you, as Zz said). You'll see John Bs' name reappearing there!

Perhaps there's a genuine expert listening in. Who knows. Someone who also has a talent for communication with laymen like us. In which case I'm glad I responded, because I'll get alerted via mail and may pick up some real news.

 

[mathman]

From Wikipedia:

At the present time, there are two foundational theories in physics: the Standard Model of particle physics and general relativity. Many parts of these theories have been put on an axiomatic basis. However, physics as a whole has not, and in fact the Standard Model is not even logically consistent with general relativity, indicating the need for a still unknown theory of quantum gravity. The solution of Hilbert's sixth problem thus remains open.

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I don't think much more can be said in layman's terms.