Why should we need to re-prove theorems that have been proved already?

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SUMMARY

The discussion addresses the necessity of re-proving established mathematical theorems despite their accepted truth. It is established that re-proving theorems is essential for verifying correctness, deepening understanding, and ensuring the integrity of mathematical knowledge. Re-proving also facilitates learning the methodology of proof construction, which is critical for advancing new theories. Analogies to programming and scientific experimentation emphasize that repetition and verification are fundamental to knowledge acquisition and validation.

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  • Foundations of formal logic and theorem formulation
  • Philosophy of mathematics regarding proof and truth
  • Basic understanding of mathematical rigor and verification processes

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  • Study formal proof verification tools such as Coq or Lean
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Mathematicians, mathematics educators, students learning proof techniques, and researchers interested in the philosophy and methodology of mathematical knowledge validation.

Mike_bb
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Hello!

If theorems always work and they are true statements then why should we need to re-prove theorems that have been proved already by many people?

Could anyone provide examples that confirm necessity of re-proving theorems?

Thanks!
 
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So that we understand the proofs, and can satisfy ourselves that they are indeed correct proofs. We don't take other people's word for it in mathematics.
 
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Also, so that we learn how to proceed in order to establish that something is correct. This is essential if the game is to acquire new knowledge and we want to be sure that it is correct and on the right track.
 
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Mike_bb said:
Hello!

If theorems always work and they are true statements then why should we need to re-prove theorems that have been proved already by many people?

Could anyone provide examples that confirm necessity of re-proving theorems?

Thanks!
Because the ones that haven't been proved are either unknown or too difficult.

You could say the same about learning to program. Or, carrying out experiments in a physics or chemistry lab that have been done countless times before.
 
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