Citation
Credit Haobai Wang and identify this thirtyone-chapter public reading edition. English remains a working translation.
Formal web edition
Haobai Wang. 偶然的数学：概率论的历史、思想与数学结构. 2026. Formal web version 7, first 9 chapters. Official reading URL.
@misc{wang2026chance_en,
author = {Wang, Haobai},
title = {{The Mathematics of Chance: The History, Ideas and Mathematical Structures of Probability}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation}
}Citing this public reading edition
Author-authorized thirtyone-chapter public reading edition; source fingerprints are on the versions page.
@misc{wang2026chance_en,
author = {Wang, Haobai},
title = {{The Mathematics of Chance: The History, Ideas and Mathematical Structures of Probability}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation}
}Citing a chapter draft
Chapter 1: A Game of Chance Left Unfinished
@misc{wang2026chance_ch1_en,
author = {Wang, Haobai},
title = {{Chapter 1: A Game of Chance Left Unfinished (Continued)}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/01-gambling.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 8755a4871493f31d780be02a160a3b3bd1bb2a630d3d0ceeab050549c888868e}
}Chapter 2: From Chance to Knowledge—How Do We Discover Unknown Probabilities?
@misc{wang2026chance_ch2_en,
author = {Wang, Haobai},
title = {{Chapter 2: From Chance to Knowledge—How Do We Discover Unknown Probabilities?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/02-inference.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 877bf501293c0c9ac633c55b9b104a9e0e483bd705a21b3f5421b01620fde578}
}Chapter 3: The Birth of the Bell Curve—Why Do Countless Random Phenomena Approach the Same Distribution?
@misc{wang2026chance_ch3_en,
author = {Wang, Haobai},
title = {{Chapter 3: The Birth of the Bell Curve—Why Do Countless Random Phenomena Approach the Same Distribution?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/03-normal.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 41700173640fcf48154d87355ff12b32a0936f973e21b594dc3d1d1283bf90d7}
}Chapter 4: When Randomness Enters Time—From Random Walks to Brownian Motion
@misc{wang2026chance_ch4_en,
author = {Wang, Haobai},
title = {{Chapter 4: When Randomness Enters Time—From Random Walks to Brownian Motion}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/04-brownian.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 fdbc3299fbd8bb58dbc7a9021e4c3f1963519b85114704404bb55cf9053c089e}
}Chapter 5: The Price of an Infinite World—Why Does Probability Need Measure Theory?
@misc{wang2026chance_ch5_en,
author = {Wang, Haobai},
title = {{Chapter 5: The Price of an Infinite World—Why Does Probability Need Measure Theory?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/05-measure.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 2d43c0f0e705f9ca7058b448128d42873cc04b72c44b6ac851c10156df5133e4}
}Chapter 6: The Rebirth of the Average—From Weighted Sums to the Lebesgue Integral
@misc{wang2026chance_ch6_en,
author = {Wang, Haobai},
title = {{Chapter 6: The Rebirth of the Average—From Weighted Sums to the Lebesgue Integral}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/06-integral.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 7220fb2c8b0555cfdc9825fa9b3ec10a47ea5f6365e27c7f2b36ff13a10be16b}
}Chapter 7: What Does Convergence Mean? Four Limits in a Random World
@misc{wang2026chance_ch7_en,
author = {Wang, Haobai},
title = {{Chapter 7: What Does Convergence Mean? Four Limits in a Random World}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/07-convergence.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 a253bca6b555aafd23b0d0e86a532bd192cc6183ae7896087bd3613bf3f71940}
}Chapter 8: How Can We Construct an Infinite Random Experiment?
@misc{wang2026chance_ch8_en,
author = {Wang, Haobai},
title = {{Chapter 8: How Can We Construct an Infinite Random Experiment?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/08-infinite-experiments.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 440098ae9971a3d6a69d3618a4dfe6ae01957df696bd42a1e4c5dd1fc4433008}
}Chapter 9: After Seeing Part of the World—Conditional Expectation and Information
@misc{wang2026chance_ch9_en,
author = {Wang, Haobai},
title = {{Chapter 9: After Seeing Part of the World—Conditional Expectation and Information}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/09-conditional-expectation.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 71874c0148bd69e7bd02dcdd2b60f38480550b81d3db8737f7c303d221826521}
}Chapter 10: How Can One Probability Be Decomposed in Terms of Another?—Densities, Conditional Laws and Probability Kernels
@misc{wang2026chance_ch10_en,
author = {Wang, Haobai},
title = {{Chapter 10: How Can One Probability Be Decomposed in Terms of Another?—Densities, Conditional Laws and Probability Kernels}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/10-densities-and-kernels.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 36a082c967287501a13301672d4f41968e10d09e96e57d82f41a413813331ec6}
}Chapter 11: How Can a Distribution Be Recorded by a Function?—Characteristic Functions, Independent Sums and Gaussian Limits
@misc{wang2026chance_ch11_en,
author = {Wang, Haobai},
title = {{Chapter 11: How Can a Distribution Be Recorded by a Function?—Characteristic Functions, Independent Sums and Gaussian Limits}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/11-characteristic-functions.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 e3c1626860facf109009a7f312d6cabdfb51283faee7d9546d1c12b6d3183544}
}Chapter 12: When Can Infinitely Many Additions Still Have an Answer?
@misc{wang2026chance_ch12_en,
author = {Wang, Haobai},
title = {{Chapter 12: When Can Infinitely Many Additions Still Have an Answer?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/12-infinite-sums.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 61b08d8b3240f75028db31ea0a009de92f193086f39f233f6b56ef3ef77dffdb}
}Chapter 13: Why Do Rare Events Produce New Stable Laws?
@misc{wang2026chance_ch13_en,
author = {Wang, Haobai},
title = {{Chapter 13: Why Do Rare Events Produce New Stable Laws?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/13-rare-events.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 f97c9ad75dd5f902201c7ddb434ba6d1f703fdae5c7c583cab8d9d0ad4f7b58a}
}Chapter 14: Not Every Limit Is Gaussian—Triangular Arrays, Stable Laws and Infinite Divisibility
@misc{wang2026chance_ch14_en,
author = {Wang, Haobai},
title = {{Chapter 14: Not Every Limit Is Gaussian—Triangular Arrays, Stable Laws and Infinite Divisibility}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/14-arrays-and-stability.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 b130a011c1d9800aa2c3dd783823c43dc015877ad86fd0126a71f1da5c86fd66}
}Chapter 15: What Becomes of a Game That Remains Fair Forever?
@misc{wang2026chance_ch15_en,
author = {Wang, Haobai},
title = {{Chapter 15: What Becomes of a Game That Remains Fair Forever?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/15-martingales.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 22a36ff54f1b63686b74ab22fd5412911b6093b38d18c803cb125f5e34f4cce7}
}Chapter 16: What If the Player Chooses When to Stop?
@misc{wang2026chance_ch16_en,
author = {Wang, Haobai},
title = {{Chapter 16: What If the Player Chooses When to Stop?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/16-stopping-times.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 5e6d7ce7396fc89e05e5fe0ad6e351d76225c47eca0c270ea71ff648aac070ac}
}Chapter 17: Does the Present Suffice to Determine the Future?
@misc{wang2026chance_ch17_en,
author = {Wang, Haobai},
title = {{Chapter 17: Does the Present Suffice to Determine the Future?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/17-markov-chains.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 c565fa4330e537b2ed018ad85d0e5f619ed5cd000345da158b16fbd094f4c49d}
}Chapter 18: Why Do Some Random Walks Return While Others Escape?
@misc{wang2026chance_ch18_en,
author = {Wang, Haobai},
title = {{Chapter 18: Why Do Some Random Walks Return While Others Escape?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/18-return-and-escape.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 e58ea7350c7f47c1322705667827185dba61b1d8d1cd0d8a526b0c0c7b58418c}
}Chapter 19: Waiting for a New Beginning
@misc{wang2026chance_ch19_en,
author = {Wang, Haobai},
title = {{Chapter 19: Waiting for a New Beginning}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/19-renewal.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 dd88e7d982412082f66306da5caf70277c4c31a5d22a31d79fac1264594e2851}
}Chapter 20: How Does One Ancestor Become a Random Family?
@misc{wang2026chance_ch20_en,
author = {Wang, Haobai},
title = {{Chapter 20: How Does One Ancestor Become a Random Family?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/20-branching.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 7684ef60a3e9b241e0a597dfc78eb206b588ed21a6b6065d9f9f57f57d636c0e}
}Chapter 21: Waiting without Memory
@misc{wang2026chance_ch21_en,
author = {Wang, Haobai},
title = {{Chapter 21: Waiting without Memory}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/21-poisson-process.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 9303af69f7e94acff7e36aee25e98076dbd38b80d437531e718b4261aab82f02}
}Chapter 22: How Can a Random Process Jump?—Continuous-Time Markov Chains
@misc{wang2026chance_ch22_en,
author = {Wang, Haobai},
title = {{Chapter 22: How Can a Random Process Jump?—Continuous-Time Markov Chains}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/22-continuous-time-chains.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 2d124c0fb0a1d471a9f3ce4260955089253121c4bc3c3ce120b3ffe4a8f1ab0a}
}Chapter 23: How Can Gaussian Snapshots Become Continuous Paths?—Continuous Modifications, Gaussian Processes and Wiener Measure
@misc{wang2026chance_ch23_en,
author = {Wang, Haobai},
title = {{Chapter 23: How Can Gaussian Snapshots Become Continuous Paths?—Continuous Modifications, Gaussian Processes and Wiener Measure}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/23-gaussian-paths.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 181018945fbd70dab44bbf4b8903138124937261fcd39e95339993076ecb6983}
}Chapter 24: How Does an Entire Random Path Converge?—Portmanteau, Prokhorov and Path-Space Topologies
@misc{wang2026chance_ch24_en,
author = {Wang, Haobai},
title = {{Chapter 24: How Does an Entire Random Path Converge?—Portmanteau, Prokhorov and Path-Space Topologies}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/24-path-convergence.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 7546e973450bffe39bb88dd0789e956d9554394ba4696bb92d2d8612cd2b7417}
}Chapter 25: When Does a Random Walk Become Brownian Motion?—Donsker’s Invariance Principle
@misc{wang2026chance_ch25_en,
author = {Wang, Haobai},
title = {{Chapter 25: When Does a Random Walk Become Brownian Motion?—Donsker’s Invariance Principle}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/25-donsker.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 5fe3825a3fa1c5a610d3de11c019c0bfd6be4a0d122586ebb69ca5338e423072}
}Chapter 26: Why Is a Continuous Path So Rough?
@misc{wang2026chance_ch26_en,
author = {Wang, Haobai},
title = {{Chapter 26: Why Is a Continuous Path So Rough?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/26-brownian-properties.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 036fbfdfc7b7bdf4ea655495b5b6ab4b240ca92221682cee624dc7be8577ec66}
}Chapter 27: What If Random Motion Jumps as Well as Diffuses? — Lévy Processes and Lévy–Khintchine Theory
@misc{wang2026chance_ch27_en,
author = {Wang, Haobai},
title = {{Chapter 27: What If Random Motion Jumps as Well as Diffuses? — Lévy Processes and Lévy–Khintchine Theory}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/27-levy-processes.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 506cd8afcfcfabd87ae225a6621692fdcb60b32c6739c83c9db68b41d060a17b}
}Chapter 28: Why Does Random Motion Produce Deterministic Equations? — Semigroups, Generators and Resolvents
@misc{wang2026chance_ch28_en,
author = {Wang, Haobai},
title = {{Chapter 28: Why Does Random Motion Produce Deterministic Equations? — Semigroups, Generators and Resolvents}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/28-semigroups.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 41fab1b8126ee661609581edd058fe92465a6df4bd097ee882d837708f5e9a61}
}Chapter 29: When Small Probabilities Become Exponentially Small — Large Deviations
@misc{wang2026chance_ch29_en,
author = {Wang, Haobai},
title = {{Chapter 29: When Small Probabilities Become Exponentially Small — Large Deviations}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/29-large-deviations.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 29eda2aefe30a79afb6e1895d6cb2313f35e2e3500b072e5307c934c2a2b935b}
}Chapter 30: What Does It Mean to Know Before It Happens?
@misc{wang2026chance_ch30_en,
author = {Wang, Haobai},
title = {{Chapter 30: What Does It Mean to Know Before It Happens?}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/30-predictability.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 db6cf755485573fa1cee29e7686f5d7afc240a5a000f89f5fa56843fbaa37480}
}Chapter 31: How Can We Integrate Along a Nondifferentiable Random Path? — Itô Integral and Quadratic Variation
@misc{wang2026chance_ch31_en,
author = {Wang, Haobai},
title = {{Chapter 31: How Can We Integrate Along a Nondifferentiable Random Path? — Itô Integral and Quadratic Variation}},
year = {2026},
url = {https://chance-mathematics-six-chapters.goldenmath7.chatgpt.site/en/chapters/31-ito-integral.html},
note = {thirtyone-chapters-11e3e21; academic final review not implied; English is a working translation; SHA-256 bafd196ddb8d4bdda604833e940480b94056e55893f49e2e4d80e60027b2b6b4}
}A citation supplies scholarly attribution; it is not permission to republish, adapt or commercially reissue protected material.