Mathematics and logic
retrospect and prospects
by Mark Kac · first published 1968
2mentions
2recommended by
2HN commenters
2011–2019first – last mentioned
100% recommend
1. Infinity of primes 2. Arbitrarily long sequences of successive integers, all not primes 3. Number of primes between 1 and n 4. Euler’s formula yields primes for x=0,1,2,3,…39 5. Irrational numbers: Algebraic, Transcendental (transcends operations of ordinary arithmetic) 6. Irrationality of square root of 2 7. Covering intervals 8. Euler’s constant C: 9. Approximating irrationals by rational numbers 10. Cantor’s existence proof of transcendental numbers 11. Non-constructibility of cube root of 2 12. Impossibility of finding center of circle with straightedge alone 13
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Mathematics and Logic by Mark Kac and Stan Ulam (1992 Dover paperback, ISBN 978-0486670850) [1] Mathematics, Form and Function by Saunders Mac Lane (1986 Springer-Verlag hardcover, ISBN 0-387-96217-4) [2] [1]: https://www.cut-the-knot.org/books/kac/index.shtml…
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?” ↗Mark Kac and Stanislaw Ulam explained these concepts pretty intuitively in their beautiful book Mathematics and Logic. But, who was the first person who thought that mathematics could be explained without diagrams? Or equations? Edit: In particular they showed on pages 58-60, without using jargon, how the idea of permutations…
on “Can't solve a quintic? Galois Theory in 1500 words” ↗