2 ms·

But a mathematical proof is like a card-pyramid, building steps upon steps to reach a very specific peak. Any bugs anywhere in the structure could be serious in

• shardling 14y ago
  Sure, but each step was probably reached with the aid of intuition -- in other words, the mathematician suspected that it had to be true before they found the particular formal proof employed. So long as the original intuition is actually correct, then any bug will probably be patchable. (Obviously there's no guarantee!)
• carstimon 14y ago
  This is kind of true, but not quite right. If there's a flaw serious enough to be too hard to patch, it's likely that some problem would have come up later. That is, some serious contradiction would be reached, or something really weird would happen that yells "either this is really unexpected, or you have a problem earlier." To stretch analogies: It seems like you're analogy is saying: My card pyramid is built, but now if I remove a card, it all falls down. The more apt analogy is: When you're building a structure, you might be off a little the first time you build it, but if the overarching design is sound it will still work out and you can fix it and try to be perfect again. If the overarching design is not sound, you won't be able to build it at all. What I'm trying to say is, problems in the more bottom layers are very unlikely.
  • codeulike 14y ago
    Hmm, yes I can see your point. The internal consistency of maths would be quite a good debugging tool.