As this incident demonstrates, errors can easily creep into mathematical proofs, even those written by experts. The only way to mitigate this is to use computer-readable proofs, which can be verified by algorithms to ensure correctness. Especially computer generated proofs should be distrusted unless their output is generated as a computer verifiable. Successful example is Flyspeck, that translated a proof with a large computer generated part into a computer readable one (http://www.proof-technologies.com/flyspeck/)
Computer-readable proofs provide a rigorous and reliable way to verify mathematical results, reducing the likelihood of mistakes and increasing confidence in the validity of mathematical arguments. However, the use of computer-readable proofs is still not widespread in the mathematical community, and it is not yet a standard part of mathematics education.
The tools are ready, it is just that doing the hard work going from a handwritten one to a computer-readable proof is not sufficiently appreciated. It should become more widely used in mathematics, and be incorporated into mathematics education curricula at all levels. Doing so will not only help prevent errors but also promote transparency and reproducibility in mathematical research.
Computer-readable proofs provide a rigorous and reliable way to verify mathematical results, reducing the likelihood of mistakes and increasing confidence in the validity of mathematical arguments. However, the use of computer-readable proofs is still not widespread in the mathematical community, and it is not yet a standard part of mathematics education.
The tools are ready, it is just that doing the hard work going from a handwritten one to a computer-readable proof is not sufficiently appreciated. It should become more widely used in mathematics, and be incorporated into mathematics education curricula at all levels. Doing so will not only help prevent errors but also promote transparency and reproducibility in mathematical research.