Μathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing impulses that disrupt those patterns.
That tension came up repeatedly in our coverage this past year. We covered breakthroughs in graph theory, combinatorics, number theory and geometry — areas where patterns arise in unexpected ways, sometimes because of connections between seemingly distinct mathematical structures, and sometimes because of hidden intrinsic mechanisms uncovered by mathematicians in new proofs.
In a riveting interview with our senior writer Jordana Cepelewicz, Andrew Granville discussed how calculation and experimentation can, in sometimes forgotten ways, help mathematicians search for hidden patterns. He also spoke about changes in what it takes to convince other mathematicians that a result is true, and why he believes that examining the social nature of mathematics is essential to understanding what a proof is.
This was one of several conversations we published this past year about the nature of mathematical truth. Eugenia Cheng spoke with Joy of Why podcast host Steven Strogatz about category theory, a sort of “mathematics of mathematics” that can scare off other mathematicians with its level of abstraction. And Justin Moore spoke with Strogatz about the limits of the axioms — basic, obvious truths — of set theory and why there will always be important, unanswerable mathematical questions.
Δεν υπάρχουν σχόλια:
Δημοσίευση σχολίου