Can we trust a computer solution if we can’t verify it?

If you remember , Ray Kurzweil promised the arrival of a singularity as early as the 30s of this century. It seems that the first precursors are already appearing: our two former compatriots, Alexey Lisitsa and Boris Konev, working at the University of Liverpool, launched the task of Erdös discrepancy on the calculation. The task is considered unresolved, and the program launched by the researchers coped with the task. But! The problem is that the proof of the solution itself occupies 13 GB (once again, the text log file, which in essence is evidence, occupies 13 GB) and is difficult to verify. This suggests a simple question - can we trust the decision of the computer if we are not able to check its calculations?



In this case, many media outlets considered a certain Rubicon - the border beyond which a whole series of scientific computations are moving into the category of "unchecked". Yes, to test them, you can run another program that runs on other algorithms, but also works on something similar logic. And then the recursive question arises - is it possible to trust the verification of the solution if we also cannot verify it?

Actually, there is nothing to add. If you are interested in the details of the mathematical experiment and the names of the programs, then there is a good explanation in Russian, and here - the original study in English.