'On certainty' of mathematics

[Redsummers]

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.

 

[scottie_000]

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...

 

[apeiron]

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.

 

[Redsummers]

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?

 

[LudusRex]

I believe that mathematics is a crucial tool in understanding and describing the natural world. It is a language that allows us to communicate and make sense of complex phenomena, and it has been proven time and time again to be a powerful tool in predicting and explaining physical phenomena.

However, I do not believe that mathematics alone can provide us with a complete understanding of the universe. While it is a powerful tool, it is not infallible and can only describe what we observe and measure. It is important to remember that mathematics is a human construct and may not always accurately reflect the true nature of reality.

In terms of fundamental physics, I believe that mathematics can play a crucial role in developing theories and models, but it cannot be the sole basis for understanding the universe. Scientific theories must also be tested and validated through experimentation and observation.

In my opinion, the truth can be achieved through the application of mathematics, but it is not the only factor. It must be combined with empirical evidence and critical thinking to truly understand the natural world. As for the question of whether mathematics has always existed and whether it is a reflection of some ultimate truth, I believe that it is a philosophical and metaphysical question that cannot be definitively answered through scientific means.

Overall, I believe that mathematics is a powerful tool in scientific inquiry, but it should not be viewed as the only means of understanding the universe. It is just one piece of the puzzle and must be used in conjunction with other methods to achieve a comprehensive understanding of the natural world.