Famous Math Problems by Norman J Wildberger

source: njwildberger  2017年2月28日
We look at famous math problems, both unsolved and solved. These will span both pure and applied mathematics; some will be ancient problems, others relatively new, but hopefully they will all be interesting.

1 42:03 1: Factoring large numbers into primes
2 33:12 2: The Collatz conjecture (3n+1 problem)
3 43:49 3: Apollonius' circle construction problems
4 34:03 4: The Graceful Tree Conjecture
5 32:05 5: Omar Khayyam and the Binomial Theorem
6 43:29 6: Archimedes' squaring of a parabola
7 33:34 7: Newcomb's paradox
8 42:16 8: Euler's triangulation of a polygon
9 40:01 9: Distances to the sun and moon
10 43:32 10a: The integral of x^n
11 39:37 10b: The integral of x^n (cont.)
12 26:05 11: Steiner's regions of space problem
13 41:50 12: Euclid's construction problems I
14 58:24 13a: The rotation problem and Hamilton's discovery of quaternions I
15 59:47 13b: The rotation problem and Hamilton's discovery of quaternions (II)
16 56:14 13c: The rotation problem and Hamilton's discovery of quaternions III
17 1:01:33 13d: The rotation problem and Hamilton's discovery of quaternions IV
18 45:34 14: Japanese Temple Problems I
19 35:48 15: Euler's relation between vertices, edges and faces of the Platonic solids
20 37:30 16: The area of a triangle and Archimedes' formula
21 30:48 17: Are all true mathematical statements provable?
22 44:04 19a: The most fundamental and important problem in mathematics
23 37:40 19b: The rational number line and irrationalities
24 43:30 19c: Stevin numbers, infinitesimals and complex numbers
25 1:10:07 19d: Dedekind cuts and computational difficulties with real numbers