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Title : "What did I learn?... That mathematics is both real and not real. Like novelists and musicians, mathematicians produce thought objects..."
link : "What did I learn?... That mathematics is both real and not real. Like novelists and musicians, mathematicians produce thought objects..."
"What did I learn?... That mathematics is both real and not real. Like novelists and musicians, mathematicians produce thought objects..."
"... that have no presence in the physical world. (Anna Karenina is no more actual than a thought about Anna Karenina.) Like other artists, mathematicians also have the run of a world that others hardly or only rarely visit. For mathematicians, though, this territory has more rules than it does for others. Also, what is different for mathematicians is that all of them agree about the contents of that world, so far as they are acquainted with them, and all mathematicians see the same objects within it, even though the objects are notional. No one’s version, so long as it is accurate, is more correct than someone else’s. Parts of this world are densely inhabited, and parts are hardly settled. Parts have been visited by only a few people, and parts are unknown, like the dark places on a medieval map. The known parts are ephemeral, but also concrete for being true, and more reliable and everlasting than any object in the physical world.... An imaginary world’s being infallible is very strange. This spectral quality is bewildering, even to mathematicians. The mathematician John Conway once said, 'It’s quite astonishing, and I still don’t understand it, despite having been a mathematician all my life. How can things be there without actually being there?'"From "Teaching Myself Calculus at Sixty-Five/I was never a good math student, but I was determined to penetrate the mysteries of mathematics" by Alec Wilkinson, who got a book out of this project — “A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age.”
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"... that have no presence in the physical world. (Anna Karenina is no more actual than a thought about Anna Karenina.) Like other artists, mathematicians also have the run of a world that others hardly or only rarely visit. For mathematicians, though, this territory has more rules than it does for others. Also, what is different for mathematicians is that all of them agree about the contents of that world, so far as they are acquainted with them, and all mathematicians see the same objects within it, even though the objects are notional. No one’s version, so long as it is accurate, is more correct than someone else’s. Parts of this world are densely inhabited, and parts are hardly settled. Parts have been visited by only a few people, and parts are unknown, like the dark places on a medieval map. The known parts are ephemeral, but also concrete for being true, and more reliable and everlasting than any object in the physical world.... An imaginary world’s being infallible is very strange. This spectral quality is bewildering, even to mathematicians. The mathematician John Conway once said, 'It’s quite astonishing, and I still don’t understand it, despite having been a mathematician all my life. How can things be there without actually being there?'"
From "Teaching Myself Calculus at Sixty-Five/I was never a good math student, but I was determined to penetrate the mysteries of mathematics" by Alec Wilkinson, who got a book out of this project — “A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age.”
From "Teaching Myself Calculus at Sixty-Five/I was never a good math student, but I was determined to penetrate the mysteries of mathematics" by Alec Wilkinson, who got a book out of this project — “A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age.”
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