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“The necessary incompleteness of even our formal systems of thought demonstrates that there is no non-shifting foundation on which any system rests. [...] Our knowing minds are not embedded in truth. Rather the entire notion of truth is embedded in our minds[.]”
― Incompleteness: The Proof and Paradox of Kurt Gödel
― Incompleteness: The Proof and Paradox of Kurt Gödel
“The rules of evidence can deliver very persuasive results, sometimes contrary to the strictly argued certainties of mathematics. […] Hypothesis: No human can possibly be more than nine feet tall. Confirming instance: A human being who is 8'11¾" tall. The discovery of that person confirms the hypothesis … but at the same time casts a long shadow of doubt across it!”
― Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
― Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
“When I was young, I had to choose between the life of being and the life of doing. And I leapt at the latter like a trout to a fly. But each deed you do, each act, binds you to itself and to its consequences, and makes you act again and yet again. Then very seldom do you come upon a space, a time like this, between act and act, when you may stop and simply be. Or wonder who, after all, you are.”
― The Farthest Shore
― The Farthest Shore
“Do nothing because it is righteous or praiseworthy or noble to do so; do nothing because it seems good to do so; do only that which you must do and which you cannot do in any other way.”
― The Farthest Shore
― The Farthest Shore
“Published mathematical papers often have irritating assertions of the type: “It now follows that…,” or: “It is now obvious that…,” when it doesn't follow, and isn't obvious at all, unless you put in the six hours the author did to supply the missing steps and checking them. There is a story about the English mathematician G.H. Hardy, whom we shall meet later. In the middle of delivering a lecture, Hardy arrived at a point in his argument where he said, “It is now obvious that….” Here he stopped, fell silent, and stood motionless with furrowed brow for a few seconds. Then he walked out of the lecture hall. Twenty minutes later he returned, smiling, and began, “Yes, it is obvious that….” If he”
― Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
― Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
Peter’s 2024 Year in Books
Take a look at Peter’s Year in Books, including some fun facts about their reading.
58 books
|
3 friends
573 books
|
25 friends
559 books
|
7 friends
80 books
|
5 friends
45 books
|
1 friend
Favorite Genres
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