Noga Aron, a mathematician at Princeton University, said their results demonstrate the importance of not taking anything for granted. “We need to question things that intuitively seem very likely to be true.”
Although Gladkov, Pak, and Zimin found many examples of small graphs that meet this conjecture, they ultimately found that they were more complicated and less intuitive than the more complex and less intuitive graphs that can be constructed given enough vertices and edges. It didn’t reflect the graph.
As Hollom says, “Do we actually understand all this as much as we think we do?”
Mathematicians still believe in the physics description of connected locations in solids that inspired the bunk conjecture. But they’ll have to find another way to prove it.
In the meantime, Park says it’s clear that mathematicians need to engage in more active discussions about the nature of mathematical proofs. He and his colleagues finally no longer have to rely on controversial computational techniques. They were able to disprove this speculation with complete certainty. But as attacks using computers and AI become more common in mathematics research, some mathematicians are debating whether the field’s norms will ultimately need to change. “This is a philosophical question,” Aron says. “How do we view proofs that are true only with high probability?”
“I think the future of mathematics is to accept probabilistic proofs like this,” says Doron, a mathematician at Rutgers University who is known for crediting his computer as a co-author on many papers.・Mr. Seilberger said. “In 50 years or less, people will have new attitudes.”
Some wonder if such a future threatens anything important. “Perhaps probabilistic proofs can compromise our understanding and intuition of what’s actually going on,” Aron says.
Park suggested creating a separate journal so that if these types of results become more common, their value to mathematicians is not lost. But his main goal is to start a conversation. “There is no right answer,” he said. “We want the community to think through whether the next result of this kind is important.” As technology continues to permeate and transform mathematics, this question will become increasingly pressing.
original story Reprinted with permission from Quanta Magazine, editorially independent publication simmons foundation Its mission is to enhance the public’s understanding of science by covering research developments and trends in mathematics, physical sciences, and life sciences.
