纪录片: Counting from Infinity
3000 years ago Euclid proved infinity of Prime numbers, but conjectured also infinity of twin primes :
(3,5), (5,7), (11,13)….
Some with gap of ‘4’ ( Cousin primes)
(7,11), (19,23) , (29,31)…
Gap of ‘6’ (Sexy Primes):
The Twin Prime gaps (2,4,6 …) are bounded by max. 70,000, (min.2.)
Terence Tao mobilised the Internet community ‘Polymath Project’, using Zhang’s Sieve Method, reduce 70,000 to (hopefully) 16.
Introduction to the Wolfram Language” –
Group is the “mathematical language” of Symmetry — the beauty which pleases human’s eyes and animal’s eyes: We are attracted by a symmetrical face (五官端正), bees are attracted by a symmetrical flower…
Group was discovered by a 19-year-old French genius Evariste Galois (sound: \ga-lua, 1811-1832), who was attempting to explain why any quintic equations (polynomial with degree 5 or more) could not have a solution formula (like quadratic, cubic, equations) using +, -, ×, /, nth root radicals. This 300-year problem since 16th century defeated even then the world’s greatest Mathematician Gauss. Before a fatal duel which killed him, Galois wrote down his discovery of ‘Group Theory’ which was understood only 14 years later by Professor Louisville of the Ecole Polytechnique — ironically the same university which failed Galois twice in admission exams (Concours, aka French imitation of Chinese 科举).
Group has 4 properties: “CAN I ?”
N: Neutral element (or Identity)
Rubik’s cube is group. It is a fun game.
Music is group. It is pleasing to ears if the music is nice, or “symmetric”.
Video (Bilingual in English subtitled in Chinese)
The traditional way of cutting cake a la ‘Camembert Cheese’ is wrong.