Theoretical mathematics is usually so complex that even researchers promoting and developing this area of knowledge cannot fully understand it all.
Edition Motherboard published the opinion that many mathematicians simply believe that the foundations of any new discovery are reasonable. If one eminent researcher cites a mathematical proof in his work, others may assume that it is true without checking it out for themselves. This is what bothers the mathematician Imperial College London Kevin Buzzard, that if this is the case, then it could devalue many modern areas of mathematical knowledge.
Theoretical Jenga
Buzzard is concerned that many mathematical proofs are wrong – but errors are hidden under a pile of mathematical calculations, while many prominent figures simply assume that they have learned the innermost essence of mathematics.
“At one point I was worried that all the math published was wrong because mathematicians don’t check the details,” he told Motherboard, “but I’ve seen them wrong before.”
But mathematicians continue to build new theories and deduce new proofs, using the supposedly proven postulates. It is capable of accumulating theoretical errors and generating incorrect mathematical laws. This creates the danger that if any of the evidence at the beginning of the theoretical chain is suddenly refuted, it will bring down all the evidence and conclusions based on it.
To help mathematicians arrive at sound conclusions without having them plunge into thousands of pages of incomprehensible operations, Buzzard suggested in his opening remarks at a math conference that the direction for further research should be directed towards artificial intelligence tools that can do the hard work for them. .
“I think there is a non-zero chance that some of our great castles are built on sand,” read his presentation posted on Motherboard. “And I think it’s at least.”