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Rózsa Péter,递归函数理论的创始人

已有 760 次阅读 2022-5-18 17:24 |个人分类:解读哥德尔不完全性定理|系统分类:科研笔记

罗兹·佩特(Rózsa Péter1905-1977)(原名Politzer)在一个饱受战争和内乱蹂躏的国家长大,在那里,仅仅是日复一日的生活就绝非易事。她对数学理论做出了重大贡献,为此在她的一生中得到了一些认可,但是她的名字,应该和计算理论的创始人(哥德尔、图灵、丘奇、克莱因)的名字写在一起,今天却几乎被遗忘。在这一点上,她无疑与同一时期的其他东欧科学家有着同样的命运。

没有其他领域能像数学这样提供发现的快乐,这也许是人类最大的快乐 罗兹·佩特在她对普通听众的演讲中说,这些演讲的题目常常是数学是美丽的,在别人的口中,这可能是一种天真的流露;对她来说,却是来之不易的智慧。

佩特于1922年进入罗兰大学,打算学习化学,但很快发现她的真正兴趣是数学。她与世界著名的数学家一起学习,包括Lipót FejérJósef Kürschák,正是在这里,她遇到了一个长期合作者卡尔马尔(László Kalmár),他第一次让她注意到递归函数的课题。

1927年毕业后,佩特靠做家教和在高中教书为生,开始了研究生学习。卡尔马尔告诉她哥德尔在不完备性问题上的工作,于是她设计了自己的不同的证明,重点是哥德尔使用的递归函数。她在1932年苏黎世举行的国际数学家大会上发表了一篇关于递归函数的论文,首次提出将此类函数作为数学的一个独立子领域来研究。随后,她发表了更多的论文,并于1935年以最优异的成绩获得博士学位。1937年,她成为《符号逻辑杂志》的特约编辑。


1939年通过的法西斯法律禁止她教书,并曾短暂地被关在布达佩斯的犹太人区,但佩特在战争年代继续工作。1943年,她撰写并印刷了一本名为《玩转无限》的书,为非专业读者讨论了数论和逻辑的观点。许多副本被炸毁,这本书直到战争结束才被分发。她在法西斯主义下失去了她的兄弟和许多朋友及数学家同行,《玩转无限》后来的版本有一篇前言纪念他们。


1945年,战争结束后,她在布达佩斯师范学院获得第一个正式职位。1951年,她出版了一本专著《递归函数》,该书经历了许多版本,并为她赢得了国家的Kossuth奖。当师范学院在1955年关闭时,她成为了Eötvös Loránd大学的教授,直到她在1975年退休。1976年,她出版了《计算机理论中的递归函数》。

她被几代学生称为Rózsa阿姨,并致力于为女孩和年轻女性增加数学方面的机会。1977年,她在自己的生日前夕去世。在她的悼词中,她的学生Ferenc Genzwein回忆她教导,在无尽探索真理中, “只有事实适合于打开思想和精神的包装”("that facts are only good for bursting open the wrappings of the mind and spirit" in the "endless search for truth.")


原文:

Founder of Recursive Function Theory

Rózsa Péter (originally Politzer) grew up in a country torn by war and civil strife in which simply living from day to day was never easy. She made major contributions to mathematical theory for which she received some recognition in her lifetime, but her name, which should be written together with the names of the founders of computational theory (Gödel, Turing, Church, Kleene), is all but forgotten today. In this, she no doubt shares the fate of other Eastern European scientists of the same period.

"No other field can offer, to such an extent as mathematics, the joy of discovery, which is perhaps the greatest human joy," said Rózsa Péter in her lectures to general audiences, which were often titled "Mathematics is Beautiful." In the mouth of another, this might be a naive effusion; for her, it was hard-won wisdom.

Péter enrolled at Eötvös Loránd University in 1922 with the intention of studying chemistry but soon discovered that her real interest was mathematics. She studied with world-famous mathematicians, including Lipót Fejér and Jósef Kürschák, and it was here that she met a longtime collaborator, László Kalmár, who first called her attention to the subject of recursive functions.

After she graduated in 1927, Péter lived by taking tutoring jobs and high-school teaching. She also began graduate studies. Kalmár told her about Gödel's work on the subject of incompleteness, whereupon she devised her own, different proofs, focusing on the recursive functions used by Gödel. She gave a paper on the recursive functions at the International Congress of Mathematicians in Zurich in 1932, where she first proposed that such functions be studied as a separate subfield of mathematics. More papers followed, and she received her Ph.D. summa cum laude in 1935. In 1937, she became a contributing editor of the Journal of Symbolic Logic.


Forbidden to teach by the Fascist laws passed in 1939, and briefly confined to the ghetto in Budapest, Péter continued working during the war years. In 1943, she wrote and printed a book, Playing with Infinity, a discussion of ideas in number theory and logic for the lay reader. Many copies were destroyed by bombing and the book was not distributed until the war ended. She lost her brother and many friends and fellow mathematicians to Fascism, and a foreword to later editions of Playing with Infinity memorializes them.


In 1945, the war over, she obtained her first regular position at the Budapest Teachers' College. In 1951 she published a monograph, Recursive Functions, which went through many editions and which earned her the state's Kossuth Award. When the teachers' college was closed in 1955, she became a professor at Eötvös Loránd University, until her retirement in 1975. In 1976, she published Recursive Functions in Computer Theory.

She was called Aunt Rózsa by generations of students and worked to increase opportunities in mathematics for girls and young women. She died on the eve of her birthday in 1977. In her eulogy, her student Ferenc Genzwein recalled that she taught "that facts are only good for bursting open the wrappings of the mind and spirit" in the "endless search for truth."


参考文献:

[1] Founder of Recursive Function Theory, https://www.sdsc.edu/ScienceWomen/peter.html

[2] RQZSA(ROSA)PETER B. ANDRASFAI

https://pp.bme.hu/ee/article/view/4651/3756


参考文献:

1https://en.wikipedia.org/wiki/R%C3%B3zsa_P%C3%A9ter

2file:///Users/yli/Downloads/1204835279.pdf

INTERVIEW WITH RóZSA PéTER by ISTVáN TAMáSSY Translated by LEON HARKLEROAD




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