What makes a good Conjecture?

If you can’t prove, then makes an outrageous conjecture!

Examples:

  1. Fermat’s Last Theorem (Conjecture for 380 years until proven as “Theorem” in 1994)
  2. Poincare “Conjecture” = (Theorem proven by Grigoli Perelman )
  3. Goldbach’s Conjecture (best proof by 陈景润 “1+2”)
  4. Yang-Mills Conjecture (7 Millennia Clay-Prize Problems)
  5. Collatz Conjecture

https://www.quantamagazine.org/the-subtle-art-of-the-mathematical-conjecture-20190507/

Music = Math + History

To really appreciate music, you must understand this Math & history :
5 notes to 7 notes to 12 notes.
& fractions: 3/2, 3/4, 2/1 (octave)

Music = Math + History

1. Ancient China 600 BC 管仲 (5 notes 宫商角徵\zhǐ羽)

2. Pythagoras 450 BC (7 notes, Chords 和弦)

3. Modern Music: 十二平均律 (明朝 1600 AD 朱载堉- > Bach 1700 AD)

https://m.toutiaoimg.com/group/6683391962764018183/?app=news_article_lite&timestamp=1581773659&req_id=20200215213418010194100050312DF0B9&group_id=6683391962764018183

Pythagoras did not believe in Irrational numbers (sqroot 2) , so only 7 integer notes.

17CE Chinese 明朝 Prince invented 12 notes music, using a giant 81-row Abacus to compute the12th root of 2 (picture below) :

https://chinoiseries2014.wordpress.com/2019/02/07/%e5%8d%81%e4%ba%8c%e5%b9%b3%e5%9d%87%e7%8e%87/