#modesofthought — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #modesofthought, aggregated by home.social.
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@khinsen @nicoformanek @gedankenstuecke He goes on to say,
To give an example, the snippet of knowledge that the adition of 1 and 4 produces the same multiplicity as the addition of 2 and 3, seems to me self-evident. It is a humble bit of knowledge; but, unless I deceive myself, it stands before me with a clarity of insight. I hesitate to claim any such self-evidence when larger numbers are involved. I have recourse to the indignity of proof. Other people have wider powers.
For example, consider Ramanujan, the great Indian mathematician whose early death was a loss to science analogous to that of Galois. It was said of him that each of the first hundred integers was his personal friend. In other words, his insights of self-evidence, and his delight in such insights, were of the same character as most of us feel for the integers up to the number 5.
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@khinsen @nicoformanek @gedankenstuecke Here's a delightful & apropos passage from Alfred North Whitehead's 'Modes of Thought':
There is very little large-scale understanding, even among mathematicians. There are snippets of understanding, and there are snippets of connections between these snippets. These details of connection are also understood. But these fragments of intelligence succeed each other. They do not stand together as one large self-evident coordination. At the best, there is a vague memory of details which have recently been attended to.
This succession of details of self-evidence is termed *proof*. But the large self-evidence of mathematical science is denied to humans.