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Friend of mine is older Russian mathematician - algebraist, in his late 70's. He has small picture of John G. Thompson on his work table. Thompson made an eno

Friend of mine is older Russian mathematician - algebraist, in his late 70's. He has small picture of John G. Thompson on his work table. Thompson made an enormous contribution to the proof. From what I remember reading, part of the proof was formally verified. It is intersecting to think, that we have proofs that are impossible to grasp in a lifetime. Though, it would be possible to use the results ! Imagine, sometime in a future, humanity would loose the original proof due to some catastrophic event, but it would be know that theorem still holds true.

raincom 6y ago
If humanity were to loose the original proof of some theorem X in 3000 AD, the only fact is known to them is that X is true, how on earth one should believe it? Just because that theorem X was proved in the West? Just reverse the case, and replace the West with Africa or China. Everyone in the West would laugh at claims that "Some Chinese/African proved a theorem in 300 BC, but that proof doesn't exist anymore". That's why Bill Thurston says this: “There is another effect caused by the big differences between how we think about mathematics and how we write it. A group of mathematicians interacting with each other can keep a collection of mathematical ideas alive for a period of years, even though the recorded version of their mathematical work differs from their actual thinking, having much greater emphasis on language, symbols, logic and formalism. But as new batches of mathematicians learn about the subject they tend to interpret what they read and hear more literally, so that the more easily recorded and communicated formalism and machinery tend to gradually take over from other modes of thinking. There are two counters to this trend, so that mathematics does not become entirely mired down in formalism. First, younger generations of mathematicians are continually discovering and rediscovering insights on their own, thus reinjecting diverse modes of human thought into mathematics. “

raincom 6y ago

If humanity were to loose the original proof of some theorem X in 3000 AD, the only fact is known to them is that X is true, how on earth one should believe it? Just because that theorem X was proved in the West? Just reverse the case, and replace the West with Africa or China. Everyone in the West would laugh at claims that "Some Chinese/African proved a theorem in 300 BC, but that proof doesn't exist anymore". That's why Bill Thurston says this: “There is another effect caused by the big differences between how we think about mathematics and how we write it. A group of mathematicians interacting with each other can keep a collection of mathematical ideas alive for a period of years, even though the recorded version of their mathematical work differs from their actual thinking, having much greater emphasis on language, symbols, logic and formalism. But as new batches of mathematicians learn about the subject they tend to interpret what they read and hear more literally, so that the more easily recorded and communicated formalism and machinery tend to gradually take over from other modes of thinking. There are two counters to this trend, so that mathematics does not become entirely mired down in formalism. First, younger generations of mathematicians are continually discovering and rediscovering insights on their own, thus reinjecting diverse modes of human thought into mathematics. “