Physics In History on X: “The mathematical symbols “∫” for integration and “d” in derivatives were introduced by Leibniz — and the world still uses them today.
https://t.co/zBqERm9HK5″ / X https://share.google/ta79WilFZNkFs7O4v
Euclidean Division
Galois 1829 ENS Concours, he had failed 2x two years ago in X Concours.
https://youtu.be/pK5okqQ2VHM?si=PEsJHg6Smtiwgx0K
Galois paper 2 question Concours ENS.
After failing X consecutive 2 years, his Prof Richard advised him to attempt ENS, a teacher college Ecole Normal Sup, not as esteemed as X (Ecole Polytechnique).
Galois entered ENS finally (top student in written papers). However 1 year later he was expelled by ENS for joining the Revolution to overthrow the corrupted French King (who took over Napoleon after his Waterloo defeat).
This ordinary “Euler-Lagrange Equation” is the origin of Theoretical Physics , pioneered by Emmy Noether, who discovered ‘Symmetry’ (L) in the ‘Conservation of Energy’.
An Art graduate in English and French languages, Noether continued studying Maths for 6 yrs under David Hilbert. She was also ” Der ” (masculin = Le) ” Father ” of Abstract Algebra.
https://vt.tiktok.com/ZSA2q7xsx/
New Pope has a math degree.
Romanian President has a PhD Math from Ecole Normale Supérieure (Paris), also had won IMO Gold twice.
if include those naturalized in USA, France ,who are they ?
Including naturalized citizens, the totals for the U.S. and France increase significantly. Below is the breakdown:
Native-born: 9
Naturalized:
Total U.S. Fields Medalists: 14 (9 native + 5 naturalized)
Native-born: 8
Naturalized:
Total French Fields Medalists: 13 (8 native + 5 naturalized)
国家/ 本地 / 移民 / 总共
USA 9 5 14
France 8 5 13
Notes:
Citations:
[1] About half of Fields medalists were also ex IMO contestants : r/math https://www.reddit.com/r/math/comments/vzz93o/about_half_of_fields_medalists_were_also_ex_imo/
[2] [PDF] “13 = The Number of French Fields Medal Winners” “Artur Ávila, a … https://toronto.consulfrance.org/IMG/pdf/13_medailles_fields-en.pdf
[3] Fields Medal – Wikipedia https://en.wikipedia.org/wiki/Fields_Medal
[4] The Complete List of Fields Medal Winners – areppim https://stats.areppim.com/listes/list_fieldsxmedal.htm
[5] U.S. Dominance in Mathematics Awards: Fields Medal Distribution … https://www.reddit.com/r/Infographics/comments/1e824x6/us_dominance_in_mathematics_awards_fields_medal/
[6] Immigrants’ pivotal role in TeamUSA’s Olympic success – The Hill https://thehill.com/opinion/immigration/566991-immigrants-pivotal-role-in-teamusas-olympic-success/
[7] Artur Ávila: The man who calculates – Revista Fapesp https://revistapesquisa.fapesp.br/en/artur-avila-the-man-who-calculates/
[8] [PDF] Foreign-Born and Second-Generation Born Immigrant Athletes … https://d101vc9winf8ln.cloudfront.net/documents/50039/original/Foreign-Born_and_Second-Generation_Born_Immigrant_Athletes_Round_Out_Team_USA_2024_Olympics_GMU_IIR.pdf?1721670739
[9] John Forbes Nash Jr. – Wikipedia https://en.wikipedia.org/wiki/John_Forbes_Nash_Jr.
[10] Chinese mathematician solves century-old problem, becomes … http://www.ecns.cn/cns-wire/2025-03-12/detail-ihepqcpn0566350.shtml
[11] Champion Bobsledder Kaillie Humphries Granted U.S. Citizenship … https://norrismclaughlin.com/ib/citizenship/champion-bobsledder-kaillie-humphries-granted-u-s-citizenship-olympics/
[12] Carnegie Corporation of New York Honors 34 Distinguished … https://www.carnegie.org/news/articles/carnegie-corporation-new-york-honors-34-distinguished-immigrants-whose-contributions-our-democracy-inspire-us-all/
[13] Fields Medal – Wikipedia https://en.wikipedia.org/wiki/Fields_Medal
[14] About half of Fields medalists were also ex IMO contestants : r/math https://www.reddit.com/r/math/comments/vzz93o/about_half_of_fields_medalists_were_also_ex_imo/
[15] Jean-Pierre Serre – Wikipedia https://en.wikipedia.org/wiki/Jean-Pierre_Serre
[16] Fields Medal winners : Revista Pesquisa Fapesp https://revistapesquisa.fapesp.br/en/fields-medal-winners/
[17] Nationality and Citizenship in Sports: a Look Into the Laws of France … https://insidesynchro.org/2019/06/19/nationality-and-citizenship-in-sports-a-look-into-the-laws-of-france-fina-and-the-ioc/
[18] Hugo Duminil-Copin is awarded the Fields Medal http://www.universite-paris-saclay.fr/en/news/hugo-duminil-copin-awarded-fields-medal
西方“高等数学” 源自 古代中国（汉， 三国，南北朝，唐，宋， 明）
https://vt.tiktok.com/ZShaWB8Yy/
留法数学家 (*) 吴文俊 晚年 研究 中国古代数学，发明 AI ”机械证明几何”…
接近100岁时， 他 大胆 “发狂言” 说：
“西方数学 不是源自 希腊，而是中国古代数学！！”
这句话 西方人和中国人都不信。
例子： 早西方500 -1000 年的数学
2 CE 东汉 .刘徽 Limit -> 17CE Newton, 19CE Cauchy
4CE 南北朝.祖冲之-> π = 3.1415926
3CE 三国.吴国赵爽-> 16CE Vieta Theorem
3CE 汉.九章算术 行列式 -> 18 CE Determinant by Leibniz
13CE宋. 杨辉 -> 17CE Pascal triangle
(*) Bourbaki 学派 唯一华人， 陈省身的学生， WW2 前放弃Fields Medal 回中国 抗战 。他的法国 Strasbourg U 博士学生 Grothendieck (Fields Medal) 后来是21世纪 发明Algebraic Geometry (Shieves, Motif, Topos, Category) 大师。
数学的开宗立派的宗师 “万神之神”：
第一个是Euclid: Geometry
…
9 CE Iranian al-Khwārizmī: Algebra
16CE Descartes(Fermat): 解析几何
17CE : Newton/Leibniz: Calculus
18 CE: Euler
19CE: Cauchy ε-δ Analysis, Cantor Set Theory, Gauss /Riemann
20 CE: 陈省身： 微分几何
x + 2 = 5），而是线性方程组，比如：3x + 2y = 10 2x + 3y = 13
例子（《九章算术》里的题目）：
今有上禾三秉，中禾二秉，下禾一秉，实三十九斗；
上禾二秉，中禾三秉，下禾一秉，实三十四斗；
上禾一秉，中禾二秉，下禾三秉，实二十六斗。
问上、中、下禾实一秉各几何？
翻译成现代方程：3x + 2y + z = 39 2x + 3y + z = 34 x + 2y + 3z = 26
解法步骤：
[3 2 1 | 39] [2 3 1 | 34] [1 2 3 | 26]
[6 4 2 | 78] [6 9 3 |102]0 5 1 | 24 → 5y + z = 24z=2, y=4, x=9。《九章算术》的解方程法就是“摆算筹 + 消元”，逻辑和现在数学课教的差不多，只是工具更原始。古人真·硬核！
商高定理 比毕达哥拉斯定理更早。
– 商高定理是古代中国数学家商高在公元前11世纪提出的，而毕达哥拉斯定理是在公元前6世纪由希腊数学家毕达哥拉斯提出的。
– 商高定理在《周髀算经》中记载，比毕达哥拉斯定理早了500多年。
商高定理 11 BCE, Pythagorean 6 BCE
Chinese discovered 500 years earlier.
https://vt.tiktok.com/ZSMhVNbUb/
清朝（数学家 李善兰 ）如何 做 Calculus ?
李善兰 继续 100年前 明朝 Ricci Mateo/ 徐光启 翻译 Euclidean Geometry （9 of 13 volumes) 剩下 的 最后 4 volumes.
Fermat and Descartes both invented the Analytical Geometry (解析几何) by different approaches – Fermat’s method (using a rough notion of “Limit”) is better, also laid the foundation of “Calculus” for Newton who admitted he stood on the shoulder of a giant (Fermat).
Lycée Pierre de Fermat (Classe Préparatoire) was my “alma mater” (1977-1979) where Fermat worked as a Toulouse (AirBus City) Chief Judge in 17CE.
Probability:
17CE : inventors Pascal & Fermat,
thru 19CE mostly by French mathematicians using (Finite) Set Theory.
Forgotten : Renaissance era the Italian Cardano (reveal to the world the “i” complex number secret in solving cubic equation) who gave the operations “+” or “x” for probability of 2 dependent or independent events, respectively.
After 20 CE ,
“Modern Probability” by Russian.
https://v.ixigua.com/MxguTWP/
六个阶段：代表人物
1. 启蒙 第一代： 1900 – 1949 （留美博士： 姜立夫 / 江泽涵 (翻译 同调Homology/同伦 Homotopy) / 杨武之（杨振宁的父亲，陈省身的老师）， 留法博士：熊庆来 (华罗庚的恩师), 留日： 陈健功 / 苏步青 ）
1a: 外国教授来华教书： Bertrand Russell (UK, Logic), Hadamard (France),维纳(USA, MIT), etc.
1b. 数学系建立： 北京大学， 南开， 浙江/复旦，东南大学（现 南京大学）。
2. 第二代： 1949 – 1978 （中间10年断层： 文化大革命）- 留法博士：陈省身 (“Gauss II”)，留英：华罗庚 (3 years under Cambridge Prof Hardy)
2a: 1950s 中学数学教育改革， 大量翻译外国中学教材： 范氏大代数 (College Algebra), 葛氏三角(Grandville Trigonometry), 欧式几何。
3. 第三代： 1978 邓小平恢复大学科研教育 – 本土：陈景润 （厦门大学本科毕业，华罗庚 的 研究生），留法博士： 吴文俊
3a. 1985 中国参加IMO Olympiad 比赛。1989-1990 首 2 次 中国得 IMO 团体冠军。
4. 第四代： 留美博士：丘城桐（陈省身的学生）， 张益唐（北大 硕士 / Purdue PhD)
5. 第五代： 留美博士： 田刚（丘城桐的哈佛学生）
6. 第六代［ 本土］： 北大：韦东奕， 清华：“求真学院”（丘城桐回国建立 80数学 天才 培训班：本科+硕/博 = 8 年）
【数学家却经常数学考试不及格】
Charles Hermite是 Galois 的同校&同师傅的Lycée Louis Le Grand学弟（小15届），数学老师Richard留着Galois 的旧作业交给Hermite 学习。
他发明 共轭矩阵 Conjugate Matrix， 第一人1873 证明 e is Transcendental, 他的德国学生Lindemann 1882 用他的方法证明 (pi) π transcendental. Lindermann 回德国，培养德国Gottingen派的学生Félix Klein, Gauss, Riemann, Hilbert, Noether…取代巴黎派，德国成为“世界数学中心”（till WW2中心 移到美国哈佛）
Hermite 跛脚， 被 军校 Ecole Polytechnique “X” 踢出大学一年级。（他是最后一名考进“X“, after 5 attempts）!
后来他出名了， X 请他 当Concours （ 科举）数学主考官。大讽刺！ 他出的X 数学 特别难，现在依旧。考生要进 特别的Top Préparatoires （M’ 班 ）老师训练题目，déjà -vu past year 考题 才会解。（同IMO Olympiad 数学难题的道理， Galois就是自以为“天下第一天才”，没练习旧考题，不及格 2次）
Since 1850, Pure Math leading with Abstract Algebra “Group Theory”, etc …however, after 2000, Applied Math catching up with Pure Math in IT (Category Theory, Fuzzy Logic, AI, Algebraic Toplology…).
https://v.ixigua.com/MDAP476/
Determinant (行列式) is the unique Math “object” invented before its parent Object “Matrix” (矩阵)。Why？
BCOS Determinant was imported from China (15 CE 明朝.程大位) via Japan (关孝和) to Europe (Leibniz), while Matrix was only invented in 19CE by J.J. Sylvester (John Hawkins University).
The word “Determinant” was coined by Gauss (at 21 years old) in his first masterpiece 《Disquisitiones Arithmeticae》 (where “Modular Arithmetic” was born).
A-level Math is up till 17CE (Newton Calculus), Undergrad Math is 19 CE (Galois – Abstract Algebra), but 20CE Math is 4 times of ALL Maths combined since Babylon / Greek till today.
https://v.ixigua.com/2NExMLc/
数学科学百年回顾（一）
1900 是近代 数学Modern Math 的分水岭， 由（1830）法国神童 Evariste Galois 的Group Theory 打下的基础， 一发不可收拾。
A-level 之前学的 是 从 古典希腊 到 牛顿（1730） Calculus 的数学。
从1730-1830, 数学教育有一个100年“龙沟”, 许多高中数学/ IMO 精英 进 清华/北大/Classe Préparatoire, 跨不过这个“沟”, 失去兴趣。
【一对精灵：阿贝尔与伽罗瓦 – 今日头条】
https://m.toutiao.com/is/8maaW54/
【中国古代哲学中的现代数学思想2——《庄子》篇 – 今日头条】
https://m.toutiao.com/is/RtBXJNF/
【代数学发展简史 – 今日头条】
Algebra 代数 =》
Number Theory 数论 =》 Abstract Algebra 抽象代数
https://m.toutiao.com/is/RRTENFh/
https://v.ixigua.com/ewewDnA/
Estimate : 400 < a < 500, take a = 4
金庸武术的道理 和学数学一样：
1）华山正邪二派 ： 气宗 (正) vs 剑宗 (邪)
数学：数学理论 vs 刷题技巧
2）虚竹 ：忘掉以前的少林功夫才能学 消遥派
数学： 忘掉A-level 前的思维 (concrete) ，才能学好大学抽象(Abstract ) 数学.
3) 少林寺僧好高鹜远：还没学精本派“一阳指”，就想去换 印度鸠摩罗的功夫。
数学： 先打好 大学基础数学 (Epsilon-Delta, Abstract Algebraic Structures) ，才去学其他的高深东西 (Category, Differential Geometry, Algebraic Topology,… )
https://v.ixigua.com/e5Y62ye/
金庸的武林江湖 宗师 vs 数学江湖
东邪(孤僻冷漠) ：黄药师 vs 德国. Gauss
西毒 (妒忌，狠毒) ：欧阳锋 vs 法国. Cauchy (迫害 年轻天才 Abel, Galois )
南僧（避世隐士）: 大理国王 一灯大师 vs 法国.Fermat
北丐 （流浪天涯）：洪七公 vs 匈牙利. Paul Erdos
吴文俊，陈省身在 WW2昆明西南联大的弟子， 留法Strasbourg University, 兼任 博士生的tutor， 教导 法国未来的 大师Grothendieck (两人都是新数Bourbaki 学派 最后一批会员) 。
吴文俊在1975 文革后才研究 中国古代数学，从中得灵感，发明 电脑 机器化 AI 证明axiom-based 几何定理。得 1st batch Run- Run Shaw (东方Nobel Prize) $1 m Prize.
数学家清心寡慾不爱斗争，一心专注 “数学之美” ，其他生活繁琐的事(文革 批斗) 都看得开。所以多长寿 (Newton, 陈省身， Hadamard, 杨振宁, 也都90＋) ，吴文俊也高寿活到98岁。
https://v.ixigua.com/efrQhx8/
https://v.ixigua.com/eMvs7pn/
他没有介绍王孝通的特例解， 只是16CE Cartan 的 i 通解。
意大利人 Cartan 是个医生/赌徒/数学爱好者，定义
Probability * (or＋) between P(A) and P(B) whether A, B are (in-) dependent event.
https://v.ixigua.com/ej7X49B/
数学领域的全才 PolyMath：
1. Analysis,
2. Algebra,
3. Number Theory,
4. Geometry,
5. Topology
Math Online Tom Circle 