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by paulpauper 915 days ago
Would you be able to spot a Ramanujan from the dross?

yes, because math has a logical flow and rules, and most errors would be noticed

1 comments

Would you, though? Ramanujan famously left out his proofs quite often, relying on his intuition which was especially phenomenal. Many accomplished mathematicians did not see his genius for what it is and it took the support of Hardy to really further Ramanujan's career and accomplishments.
Maybe not me personally, but more accomplished, smarter mathematicians would. His results were checked as being correct and he did publish papers in which he showed some of the steps and this was before Hardy. T
Ramanujan was so ahead of his peers that they didn’t even know how to assess him or his work.

    After seeing Ramanujan's theorems on continued fractions on the last page of the manuscripts, Hardy said the theorems "defeated me completely; I had never seen anything in the least like them before",[76] and that they "must be true, because, if they were not true, no one would have the imagination to invent them".[76] Hardy asked a colleague, J. E. Littlewood, to take a look at the papers. Littlewood was amazed by Ramanujan's genius. After discussing the papers with Littlewood, Hardy concluded that the letters were "certainly the most remarkable I have received" and that Ramanujan was "a mathematician of the highest quality, a man of altogether exceptional originality and power".[74]: 494–495  One colleague, E. H. Neville, later remarked that "not one [theorem] could have been set in the most advanced mathematical examination in the world".
The current norms of pedagogy permit incremental improvements, but they fail to handle talent that is far and away better than the current top of the field. In fact they find ways to prohibit people from shaming them in such a way, which is understandable. But unfortunately, a Ramanujan today would probably be relegated to “remedial education” or institutionalized.

As for his results being checked, they were - after nearly a century in some cases:

    As late as 2012, researchers continued to discover that mere comments in his writings about "simple properties" and "similar outputs" for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death.
What I learned from reading about Ramanujan is that true geniuses are not just incrementally ahead of their field - they are so far ahead, it is literally unfathomable to laypeople and experts alike. The best approach is to step aside and try to nurture the talent without interfering in their methods and ways.