Has Fermat's Last Theorem had any practical impact on our world?

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SUMMARY

Fermat's Last Theorem, proven by Andrew Wiles, has significantly influenced the field of elliptic curves, which are crucial in modern cryptography and coding theory. The theorem's implications extend to prime factorization of integers, a fundamental aspect of secure online transactions. While the theorem itself does not provide direct practical applications, its impact on elliptic curves enhances our understanding of encryption algorithms and their robustness against factorization challenges.

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Peter G.
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Hi,

I am working on a Theory of Knowledge Essay and I was thinking how the proof to Fermat's Last Theorem influenced our world. Did it have any practical impact on our world?

I am not sure if there is any concrete evidence of a practical application or something it allowed to breakthrough, but in any way, I'd like to hear your take on this.
 
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I'd say that Fermat's last theorem had a heavy influence on the study of elliptic curves. And elliptic curves can be used to find prime factorizations of integers. This kind of things are important in cryptography and coding theory.
 
That's great to know, thanks!
 
micromass said:
I'd say that Fermat's last theorem had a heavy influence on the study of elliptic curves. And elliptic curves can be used to find prime factorizations of integers. This kind of things are important in cryptography and coding theory.

Fermat was concerned that his online transactions weren't secure. Now he can rest easy :smile:

(edit) Or should he be nervous? Did Wiles's proof make progress on factorization easier? Or show that factorization is as difficult as the encryption algorithms need it to be?
 
Last edited:

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