Letters to a Young Mathematician (2011)
“I’ll send you some interesting problems to work on if you want to flex your research muscles already; just stay clear of angle trisection. Why? Because you’ll be wasting your time.
Methods that go beyond the traditional unmarked ruler and compass are well known; methods that do not cannot possibly be correct. We know that because mathematics enjoys a privilege that is denied to most other walks of life. In mathematics, we can prove that something is impossible.
In most walks of life, “impossible” may mean anything from “I can’t be bothered” to “No one knows how to do it” to “Those in charge will never agree.” The science fiction writer Arthur C. Clarke famously wrote that “When an elderly and distinguished scientist declares something to be possible, he is very likely right. When he declares it to be impossible, he is almost certainly wrong.” (Clarke was writing in 1963, when most scientists, especially elderly and distinguished ones, were almost certainly “he.”) But applied to mathem...aticians and mathematical theorems, Clarke’s statement is plain wrong.MoreLess
Methods that go beyond the traditional unmarked ruler and compass are well known; methods that do not cannot possibly be correct. We know that because mathematics enjoys a privilege that is denied to most other walks of life. In mathematics, we can prove that something is impossible.
In most walks of life, “impossible” may mean anything from “I can’t be bothered” to “No one knows how to do it” to “Those in charge will never agree.” The science fiction writer Arthur C. Clarke famously wrote that “When an elderly and distinguished scientist declares something to be possible, he is very likely right. When he declares it to be impossible, he is almost certainly wrong.” (Clarke was writing in 1963, when most scientists, especially elderly and distinguished ones, were almost certainly “he.”) But applied to mathem...aticians and mathematical theorems, Clarke’s statement is plain wrong.MoreLess
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