How related is Number Theory to Physics?

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SUMMARY

Number theory plays a significant role in various fields of physics, particularly in quantum mechanics and cryptography. The discussion highlights the potential need for new mathematical frameworks, such as those proposed in M-Theory, to further explore the universe's complexities. The proof of Fermat's Last Theorem has implications that extend beyond pure mathematics, influencing our understanding of physical theories. Additionally, the relationship between number theory and cryptography underscores its practical applications in securing information.

PREREQUISITES
  • Basic understanding of number theory concepts, including modular arithmetic.
  • Familiarity with quantum mechanics principles.
  • Knowledge of cryptography fundamentals and its mathematical underpinnings.
  • Awareness of advanced theoretical physics concepts, such as M-Theory.
NEXT STEPS
  • Research the applications of number theory in quantum mechanics.
  • Explore the implications of Fermat's Last Theorem in modern physics.
  • Study the mathematical foundations of cryptography, focusing on number-theoretic algorithms.
  • Investigate the development of new mathematical frameworks for theories like M-Theory.
USEFUL FOR

Students and professionals in mathematics, physics, and computer science, particularly those interested in the intersections of number theory, quantum mechanics, and cryptography.

Calabi_Yau
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As I've read and been told, you can never know too much mathematics when you study physics, and I think I read it somewhere here. I have also read that cutting-edge theories like M-Theory need most likely a new the invention of a new type of mathematics to be developed.

But my question is, how does number theory relate to physics? I would like to know its direct, or indirect applications, how did the Fermat's Last Theorem proof have possiby contributed to our understanding of the universe? I imagine there is much more to number theory than that, as my knowledge about the subject does not go much further than a bit of modular arithmetics.

This is by no means a rant against number theory, I'm only asking it because I am becoming very interested in it, and would like to know more about its pratical usefulness.
 
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Hmm. I, personally, don't know, but I can guess that a lot of the applications of NT are to be found in quantum mechanics.
 

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