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

  • Thread starter Anama Skout
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In summary: The main difficulties are that we don't know how to axiomatize these physical theories in a way that is consistent with mathematics.
  • #1
Anama Skout
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So Hilbert's[/PLAIN] [Broken] 6th 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.
What progress has been done on Hilbert's 6th problem so far and what are the main difficulties? (in layman language)
 
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  • #2
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.
 
  • #3
BvU said:
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.
 
  • #4
Anama Skout said:
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.
 
  • #5
Anama Skout said:
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.
 
  • #6
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.

---------------------------
I don't think much more can be said in layman's terms.
 
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1. What is Hilbert's 6th problem?

Hilbert's 6th problem is one of the 23 unsolved problems in mathematics proposed by German mathematician David Hilbert in 1900. It focuses on the axiomatic foundation of physics and aims to find a set of consistent and complete axioms for mathematical physics.

2. Has any progress been made on solving Hilbert's 6th problem?

Yes, since its proposal, significant progress has been made in solving Hilbert's 6th problem. In the early 20th century, mathematicians such as Emmy Noether and Hermann Weyl made important contributions to the understanding of the mathematical foundations of physics. In recent years, the development of new mathematical theories, such as category theory, has also brought us closer to solving this problem.

3. What are some of the main challenges in solving Hilbert's 6th problem?

One of the main challenges in solving Hilbert's 6th problem is the lack of a unified mathematical theory that can fully describe the laws of physics. Additionally, the problem is complex and requires a deep understanding of both mathematics and physics.

4. How can solving Hilbert's 6th problem benefit science and society?

Solving Hilbert's 6th problem would have a significant impact on our understanding of the physical world and could lead to the development of new technologies. It would also provide a more solid foundation for future advancements in physics and mathematics.

5. Are there any ongoing efforts to solve Hilbert's 6th problem?

Yes, there are ongoing efforts by mathematicians and physicists to solve Hilbert's 6th problem. Some research institutions have dedicated teams working on this problem, and conferences and workshops are held to discuss potential solutions and progress made. However, it is still considered an open problem and continues to challenge scientists around the world.

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