Is Mathematics the Language of the Universe?

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SUMMARY

The discussion centers on the relationship between mathematics and fundamental physics, specifically whether mathematics serves merely as a descriptive language or if it exists independently as a universal truth. Participants emphasize that mathematics is a powerful tool for modeling natural phenomena, with a focus on its role in generating patterns. The conversation references Gödel's incompleteness theorem, highlighting the constructed nature of mathematical axioms and their implications for physics. Ultimately, the consensus suggests that while mathematical models may approximate reality, they are not absolute truths but rather effective frameworks for understanding physical laws.

PREREQUISITES
  • Understanding of Gödel's incompleteness theorem
  • Familiarity with Newtonian physics and relativity
  • Basic knowledge of mathematical modeling techniques
  • Concept of scientific approximation in physics
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  • Explore the implications of Gödel's incompleteness theorem on mathematical models in physics
  • Study the differences between Newtonian physics and Einstein's theory of relativity
  • Research mathematical modeling techniques used in physics
  • Investigate the concept of scientific approximation and its role in developing physical theories
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Philosophers of science, physicists, mathematicians, and anyone interested in the foundational questions of mathematics and its application in understanding the universe.

What is mathematics?


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I was just wondering what would be the general view concerning this topic. I think the poll is self explanatory, but what I am basically asking is Can fundamental physics be gleaned from promising mathematics? in other words, is Mathematics for you just a language which we use to describe the phenomena? or is it rather a language that has always existed wherein the truth can be achieved by its applications?

If you could also provide your opinion by supplementing a post on your view, would be great.

Note: the third option is for those who 'don't know and don't care' who may also think that asking such an existential question will lead us nowhere and hence it's pointless, which is obviously respectable as well.
 
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Mathematics is indeed a wonderful tool to describe the world around us. And it works as a language in which we can successfully render physics. However I like to think that mathematics is universal; the way in which we communicate does not alter what we are attempting to discover.
Just my opinion anyways...
 
Best description of maths I've seen is that it's the science of pattern. Exact models generate exact patterns. Then these can be measured for their fit against natural patterns.

The models can be "true" (crisply self-consistent in terms of their axioms) but their axioms are choices and so leave room for doubt. So maths is constructed, even if we feel it may have been constructed robustly and well.
 
apeiron said:
Best description of maths I've seen is that it's the science of pattern. Exact models generate exact patterns. Then these can be measured for their fit against natural patterns.

The models can be "true" (crisply self-consistent in terms of their axioms) but their axioms are choices and so leave room for doubt. So maths is constructed, even if we feel it may have been constructed robustly and well.

Yeah, indeed they leave room for doubt, Gödel himself wrote the incompleteness theorem. But I don't think that would matter much to Physics, when we think of how Physics is proven mathematically, we also see that it is just an approximation to the phenomenon. Like for instance, Newton's laws: could we say that they are disproved by relativity, since SR gives a more exact model to reality? Or is it also alright to say they work in that and that situations, while we don't have a complete theory to embrace all situations?
 

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