Mathematics

Considered all together, the posts of this blog are usually not about mathematics. I am however a mathematician, and some posts do pertain to mathematics; then I try to assign to them the category Mathematics. The category has subcategories:

  • Exposition

  • Mathematical Topics

  • Mathematicians

  • Philosophy of Mathematics.

I list the categorized posts below.

Exposition

The aim of some posts is just to present a piece of mathematics: a theorem, a structure, a concept. I have assigned to these posts the subcategory Exposition.

  1. The von Neumann natural numbers: a fractal-like image (4/10/2013)
  2. Self-similarity (4/12/2013)
  3. Self-similarity again (1/21/2014)
  4. The Parabola (10/8/2014)
  5. The Hyperbola (10/10/2014)
  6. The geometry of numbers in Euclid (1/2/2017)
  7. The Tree of Life (2/12/2018)
  8. Boolean Arithmetic (5/5/2018)
  9. On Gödel’s Incompleteness Theorem (12/15/2018)
  10. Logic of Elliptic Curves (1/6/2019)
  11. Elliptical Affinity (4/17/2019)
  12. Ordinals (11/16/2019)
  13. An Exercise in Analytic Geometry (8/5/2020)
  14. Discrete Logarithms (8/14/2020)
  15. LaTeX to HTML (9/9/2020)
  16. Knottedness (9/24/2020)
  17. Why It Works (9/26/2020)

Mathematical Topics

Calculus

  1. Limits (5/4/2013)
  2. Learning mathematics (5/14/2013)
  3. Salvation (2/24/2020)
  4. More of What It Is (9/21/2020)

Conic Sections

  1. NL III: “Body As Mind” (1/25/2014)
  2. The Parabola (10/8/2014)
  3. The Hyperbola (10/10/2014)
  4. Elliptical Affinity (4/17/2019)
  5. An Exercise in Analytic Geometry (8/5/2020)

Mathematicians

A number of mathematicians are named in posts, and then they are probably tagged; a tag used a number of times may become a category.

Archimedes

  1. Limits (5/4/2013)
  2. Learning mathematics (5/14/2013)
  3. Bosphorus Sky (12/19/2014)
  4. Victor Vasarely (3/26/2017)
  5. Hypomnesis (7/30/2017)
  6. On Gödel’s Incompleteness Theorem (12/15/2018)
  7. Salvation (2/24/2020)
  8. More of What It Is (9/21/2020)

Euclid

  1. Learning mathematics (5/14/2013)
  2. Psychology (8/28/2013)
  3. The Tradition of Western Philosophy (9/10/2013)
  4. NL I: “Body and Mind” (1/13/2014)
  5. NL III: “Body As Mind” (1/25/2014)
  6. The Peace of Liberal Education (1/13/2015)
  7. Equality Is Not Identity (1/26/2015)
  8. Thales of Miletus (12/24/2016)
  9. The geometry of numbers in Euclid (1/2/2017)
  10. Victor Vasarely (3/26/2017)
  11. On Gödel’s Incompleteness Theorem (12/15/2018)
  12. On the Idea of History (10/20/2019)
  13. Salvation (2/24/2020)
  14. Doing and Suffering (3/2/2020)
  15. Discrete Logarithms (8/14/2020)
  16. More of What It Is (9/21/2020)
  17. Multiplicity of Mathematics (10/8/2020)
  18. Mathematics and Logic (10/13/2020)

G. H. Hardy

  1. Learning mathematics (5/14/2013)
  2. Confessions (1/4/2017)
  3. Hypomnesis (7/30/2017)
  4. NL XIX: Two Senses of the Word “Society” (9/1/2017)
  5. Women and Men (10/11/2017)
  6. Şirince January 2018 (2/4/2018)
  7. Boolean Arithmetic (5/5/2018)

Philosophy of Mathematics

In the extensive post called “Effectiveness” (taking its title and main theme from Wigner’s “Unreasonable Effectiveness of Mathematics in Physics’’), I quoted Maugham’s description (in the story called “Appearance and Reality”) of a French mannequin (i.e. model) as being

a philosopher only in the sense in which we are all philosophers, that she exercised thought in dealing with the problems of existence.

Any of my posts that involve mathematics will do so for philosophical reasons, at least in Maugham’s sense.

Those posts that are devoted specifically to thought about mathematics are assigned the category Philosophy of Mathematics. The posts may have little to do with the academic discipline having the same name. My thought may be distinguished by its distinction between

  • what mathematics does (the actual) and

  • what it is trying to do (the ideal).

With what mathematics does, I include what the teaching of mathematics does—or tries to do, or ought to try to do. Perhaps my main ideas can all still be found in “The Point of Teaching Mathematics,” from the first year of this blog.

More recently, “What Mathematics Is” begins a series of four posts looking at just that.

Obviously “On Gödel’s Incompleteness Theorem,” but also “Mathematics and Logic,” take up Gödel’s results.

  1. The Point of Teaching Mathematics (12/26/2012)
  2. Limits (5/4/2013)
  3. Learning mathematics (5/14/2013)
  4. Academic Freedom (3/25/2016)
  5. The geometry of numbers in Euclid (1/2/2017)
  6. On Gödel’s Incompleteness Theorem (12/15/2018)
  7. Anthropology of Mathematics (10/13/2019)
  8. Salvation (2/24/2020)
  9. What Mathematics Is (9/15/2020)
  10. More of What It Is (9/21/2020)
  11. Multiplicity of Mathematics (10/8/2020)
  12. Mathematics and Logic (10/13/2020)
  13. Pacifism (10/29/2020)

Mathematics

Everything in the category.

  1. The Point of Teaching Mathematics (12/26/2012)
  2. The von Neumann natural numbers: a fractal-like image (4/10/2013)
  3. Self-similarity (4/12/2013)
  4. Limits (5/4/2013)
  5. Learning mathematics (5/14/2013)
  6. The Tradition of Western Philosophy (9/10/2013)
  7. NL II: “The Relation Between Body and Mind” (1/20/2014)
  8. Self-similarity again (1/21/2014)
  9. NL III: “Body As Mind” (1/25/2014)
  10. NL V: “The Ambiguity of Feeling” (2/17/2014)
  11. Şirince 2014 (7/19/2014)
  12. Facts (NL IX, ‘Retrospect,’ first 6 paragraphs) (8/1/2014)
  13. The Parabola (10/8/2014)
  14. The Hyperbola (10/10/2014)
  15. Uniformity (11/21/2014)
  16. Bosphorus Sky (12/19/2014)
  17. The Peace of Liberal Education (1/13/2015)
  18. The Academic Battery Cage (1/22/2015)
  19. Equality Is Not Identity (1/26/2015)
  20. The Facebook Algorithm (3/17/2015)
  21. Nesin Matematik Köyü, Ocak (January) 2016 (1/26/2016)
  22. Academic Freedom (3/25/2016)
  23. Thinking & Feeling (7/20/2016)
  24. Happiness (11/3/2016)
  25. Thales of Miletus (12/24/2016)
  26. The geometry of numbers in Euclid (1/2/2017)
  27. Confessions (1/4/2017)
  28. Şirince January 2017 (1/17/2017)
  29. Victor Vasarely (3/26/2017)
  30. Hypomnesis (7/30/2017)
  31. Women and Men (10/11/2017)
  32. Şirince January 2018 (2/4/2018)
  33. The Tree of Life (2/12/2018)
  34. Boolean Arithmetic (5/5/2018)
  35. Effectiveness (5/17/2018)
  36. What It Takes (5/26/2018)
  37. On Gödel’s Incompleteness Theorem (12/15/2018)
  38. Logic of Elliptic Curves (1/6/2019)
  39. Piety (3/14/2019)
  40. Elliptical Affinity (4/17/2019)
  41. NL I: “Body and Mind” Again (8/17/2019)
  42. Math, Maugham, and Man (9/1/2019)
  43. On Chapman’s Homer’s Iliad, Book XVIII (9/20/2019)
  44. Anthropology of Mathematics (10/13/2019)
  45. On the Idea of History (10/20/2019)
  46. Ordinals (11/16/2019)
  47. Salvation (2/24/2020)
  48. Poetry and Mathematics (7/5/2020)
  49. An Exercise in Analytic Geometry (8/5/2020)
  50. Discrete Logarithms (8/14/2020)
  51. LaTeX to HTML (9/9/2020)
  52. What Mathematics Is (9/15/2020)
  53. More of What It Is (9/21/2020)
  54. Knottedness (9/24/2020)
  55. Why It Works (9/26/2020)
  56. Multiplicity of Mathematics (10/8/2020)
  57. Mathematics and Logic (10/13/2020)
  58. Pacifism (10/29/2020)
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