5 ideas
| 291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
| Full Idea: Don't assume that wisdom is the automatic consequence of old age. | |
| From: Plato (Laches [c.381 BCE], 188b) | |
| A reaction: I have taught teenagers who seemed to me wiser than nearly all the adults I have ever met. |
| 12427 | All of mathematics is properties of the whole numbers [Kronecker] |
| Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers. | |
| From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5 | |
| A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim. |
| 10091 | God made the integers, all the rest is the work of man [Kronecker] |
| Full Idea: God made the integers, all the rest is the work of man. | |
| From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro | |
| A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |
| Full Idea: To be unafraid (like a small child who doesn't understand the danger) and to be brave are two quite different things. | |
| From: Plato (Laches [c.381 BCE], 197b) |