This is actually one of the complaints made bout the modern world. It’s simply not possible to keep abreast of the advanced edges of more than one (perhaps two) fields any more, in the way that an 18th or 19th cent. bloke could be a polymath.
Klaus Roth, who has died aged 90, was the first British winner of the Fields Medal, the mathematical equivalent of the Nobel Prize, whose discoveries in number theory led to him being considered one of the greatest mathematicians of the second half of the 20th century.
Roth was, above all, a consummate problem-solver. His best-known work was in the field of Diophantine approximation, a branch of pure mathematics that deals with the approximation of real numbers by rational numbers. He was only 30 when he made a significant contribution to the Thue-Siegel theorem by proving that any irrational algebraic number has an approximation exponent equal to two. In 1958 he was awarded the Fields Medal on the strength of this breakthrough.
Undoubtedly great work to gain a Fields Medal. But I would wager that you’d need at least one degree in mathematics (or at least be able to pass the finals for one, whether you’ve done so or not) to even understand what it was that he had done, let alone replicate it or do it for the first time.
I am quite famously maths blind (statistics I can usually manage but not maths) so this might just be projection but I don’t think so. It’s all there in words and everything and I’ve not a clue what it all means. And while I’ve obviously got deficiencies in my education I’m not entirely stupid. I’m really pretty sure that this will be true or prize winning work in any field: those outside that field, without the underlying education, can no longer really follow what the arguments are.
I actually have some fun (for a given value of fun) with this each year with the Econ Nobel. Is it possible to put the point, in however bastardised a form, so that it can be understood by he layman. Krugman, Tirole, Deaton, yes, it can be and has been done. Those blokes who did heteroskedacity (Spelling?) not really, it was just possible to say they’d done something clever with numbers. Not what, just something.
Perhaps it’s not something to complain about, but something to celebrate? That we’re delving so deep into the secrets of the universe that no one human mind can encompass it all?