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

  • Context: Undergrad 
  • Thread starter Thread starter Peter G.
  • Start date Start date
  • Tags Tags
    Theorem
Click For Summary

Discussion Overview

The discussion revolves around the practical impact of Fermat's Last Theorem on the world, particularly in relation to its influence on elliptic curves and their applications in cryptography and coding theory. Participants explore whether there are concrete applications or breakthroughs resulting from the theorem's proof.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that Fermat's Last Theorem has significantly influenced the study of elliptic curves, which are relevant for prime factorization and thus important in cryptography and coding theory.
  • Another participant humorously notes that Fermat might have been concerned about the security of online transactions, questioning whether Wiles's proof has made factorization easier or confirmed its difficulty in relation to encryption algorithms.

Areas of Agreement / Disagreement

Participants express differing views on the practical implications of Fermat's Last Theorem, with some suggesting a clear influence on elliptic curves and others questioning the extent of its impact on factorization and encryption.

Contextual Notes

The discussion includes uncertainty regarding the concrete applications of Fermat's Last Theorem and the implications of Wiles's proof on factorization and encryption algorithms.

Peter G.
Messages
439
Reaction score
0
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.
 
Mathematics news on Phys.org
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:

Similar threads

Insights Fermat's Last Theorem
  • · Replies 105 ·
4
Replies
105
Views
10K
High School Fermat's Last Theorem; unacceptable proof, why?
  • · Replies 12 ·
Replies
12
Views
3K
Graduate The Current State of Mathematical Rigour
  • · Replies 6 ·
Replies
6
Views
2K
Is mathematics invented or discovered?
  • · Replies 64 ·
3
Replies
64
Views
3K
Graduate Shinichi Mochizuki's ABC Conjecture and Replication Crisis in Maths
  • · Replies 33 ·
2
Replies
33
Views
9K
Undergrad Is there any interpretation of QM that doesn't clash with intuition?
  • · Replies 35 ·
2
Replies
35
Views
2K
Undergrad Could Tim Maudlin's Views on Bell and QM Be Flawed?
  • · Replies 37 ·
2
Replies
37
Views
6K
Graduate Is this the Future of Mathematics?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Elegant proof of Fermats Last theorem?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad What is the significance of rings in understanding Fermat's Last Theorem?
  • · Replies 9 ·
Replies
9
Views
6K