This is a possible concise summary:
The text is a transcript of a video that tells the stories of six people who achieved remarkable feats in mathematics, sometimes by accident or without formal education. They are:
- George Danzig, who solved two unsolved problems in statistics, thinking they were homework.
- Eugene Choon, who found an alternative method to verify Carmichael numbers, while working as a delivery man.
- Shakuntala Devi, who was known as the human computer for her ability to perform complex calculations mentally.
- Grigori Perelman, who proved the Poincare conjecture, one of the millennium prize problems, but declined the award and recognition.
- Ufot Ekong, who scored the highest marks in 50 years at Tokai University and solved a 30-year-old math problem.
- John Forbes Nash Jr, who changed the field of game theory and won the Nobel prize, despite suffering from paranoid schizophrenia.
Here are the key facts extracted from the text:
1. Jersey Neyman, a Polish mathematician, was teaching a first-year graduate-level statistics class at the University of California in Berkeley in 1939.
2. A student, George Dantzig, arrived 20 minutes late to class and missed the opening section of Neyman's lecture.
3. George Dantzig copied down two problems from the blackboard, assuming they were homework, and took them home to solve.
4. The two problems were famously unsolved problems in statistics, and Dantzig solved them in a few days.
5. Dantzig submitted his solutions to Neyman, who was shocked to discover that the student had solved the problems.
6. Neyman wrote an introduction for Dantzig's paper and wanted to check with him before sending it off for professional publication.
7. Dantzig's work was published in 1940, and he went on to have an incredible career, winning numerous awards and influencing a new generation of mathematicians.
8. Dantzig's work on simplex programming was essential to the development of linear programming.
9. Eugene Choon, a Chinese migrant, was a humble worker with no college education who had a passion for numbers.
10. Choon studied animal breeding at a vocational school but had almost no knowledge of geometry or calculus.
11. Choon poured over calculations in his free time and came up with multiple theories, sending them to different university professors over eight years.
12. Choon's alternative method to verify Carmichael numbers was recognized by a professor at Xi'an Jiaotong University in China.
13. Shakuntala Devi was born in 1929 into a family of Indian circus performers and was a mathematical prodigy.
14. Devi's father took her on road shows to demonstrate her extraordinary mathematical abilities, making her the breadwinner of her family at the age of six.
15. Devi toured Europe in 1950, completing complex sums in a matter of seconds, and was known as the "human computer."
16. Devi established a list of Guinness World Records for her mathematical abilities.
17. Grigori Perelman was born in 1966 in the Soviet Union and had an aptitude for math from a young age.
18. Perelman represented the Soviet Union in the 1982 International Mathematical Olympiad and achieved a perfect score.
19. Perelman proved the Poincaré conjecture, a problem that had been unsolved for over 100 years.
20. Perelman declined the Fields Medal and the $1 million prize, citing his dislike of the organized mathematical community.
21. Ufot Ekong was a Nigerian student who worked part-time jobs to put himself through higher education.
22. Ekong studied Japanese for a year and a half and became fluent in the language before enrolling in an electrical and engineering degree at Tokai University in Tokyo.
23. Ekong solved a math problem that had hounded the electrical engineering field for over 30 years.
24. Sharaya Ray was a 16-year-old Indian-born student who solved a math question that had been posed by Sir Isaac Newton.
25. John Forbes Nash Jr. was a mathematician who made significant contributions to game theory and was awarded the Nobel Prize in 1994.
26. Nash struggled with paranoid schizophrenia and spent time in and out of psychiatric hospitals.
27. Nash's story was immortalized in a biography called "A Beautiful Mind," which was adapted for the big screen.