莱斯兹劳·卡尔玛——匈牙利“波利雅学派”的中坚和计算机科学的先驱
莱斯兹劳·卡尔玛(Laszlo Kalmar)是匈牙利著名的数学家和计算机科学家。他1905年3月27日出生在索莫其县(Somogy Coun tY)的一个小山村里，他的父亲是匈牙利著名风景区巴拉顿湖(Lake。Balaton)边上一个地主庄园的管家，但在卡尔玛上小学时就去世了。上完小学以后，他母亲带他到首都布达佩斯上中学，但不久也离开了人世，因此卡尔玛上大学时已是孤儿。在布达佩斯大学，费尔教授(Lipot Feher)和科尔萨克教授(Joseph Kurschak)对他的影响最大，使他对数学产生了浓厚的兴趣，并培养了抽象思维的能力。
Laszlo Kalmar当时，匈牙利的数学研究中心不在布达佩斯，而在布达佩斯东南方约160km处匈、罗、南三国交界处的塞格德(Szeged)。塞格德大学的波利雅数学研究所(Bolyai Methematics lnstitute)是世界闻名的数学中心，曾经产生过一批数学大师，如提出抽象希尔伯特空间概念的李兹(Frzyes Riesz)，发现包含成对正交函数的特殊系统的哈尔(AlfrdHaar，他发现的这种系统现在被叫做“哈尔系统’’)，等等。这个研究所之所以有名，另一个原因是他们出版了一本高质量的数学期刊Acta Scientiarum Mathematicarum，冯·诺伊曼、控制论之父维纳(NobertWiener)、比尔霍夫(George D．Birkhoff)等著名大师的一些重要论文就是在这个刊物上发表的。
波利雅数学研究所创办于1872年，原来不在塞格德大学，而在位于被喀尔巴阡山脉围绕的特兰西瓦尼亚高地的中心城市克卢日的一所名为“弗朗茨·约瑟夫”的皇家匈牙利大学(Fran Josef Royal Hungarian University)内。第一次世界大战后，特兰西瓦尼亚地区划归罗马尼亚，弗朗茨·约瑟夫大学被迫迁移至匈牙利领土上，在布达佩斯工作了两年以后，正式迁至塞格德，并改名为塞格德大学。卡尔玛的数学老师费尔教授原先就是波利雅数学研究所的，后来留在了布达佩斯大学。
1927年，卡尔玛来到波利雅数学研究所。当时该数学所有3个领军人物，被称为"big three”，除了上面提到的李兹、哈尔外，另一人是数学物理学部主任奥托维(Rudolf Ortvay)。卡尔玛开始时任奥托维的助手。李兹、哈尔原先就有两个年轻有为的助手(李兹的助手Tibor Rad后来移居美国，任俄亥俄州立大学数学教授)，卡尔玛的到来，使波利雅形成了以"big three”加"big three assistants"为核心的研究队伍，成为波利雅数学研究所的黄金时代。
在波利雅，卡尔玛的主要兴趣在集合论和数理逻辑方面。同时，他对冯·诺伊曼的研究工作也十分感兴趣。在经历了第二次世界大战的艰难时期以后(期间，李兹、卡尔玛等科学家都饱受甄别之苦，大学也在罗、匈之间往返迁移)，卡尔玛一方面致力于波利雅研究所的重建工作，另一方面将自己的注意力转向计算机科学。1956年，他开始开发“逻辑机”(logical machine)。逻辑机实际上是一台专用计算机，用以解包含若干逻辑变量的命题公式。给定变量的值的范围，机器就能给出公式的真值。合取、析取、否定等逻辑运算是用开关元件组成的电路完成的。输入通过插塞、拨动开关实现，输出则以信号灯指示。用继电器组成的存储器可用来存放多个公式，因此机器可同时对多个公式估值。机器于1958年建成，限于设备条件，公式最多可有8个变量，6个逻辑运算。在当时条件下，达到这个水平已经相当不容易了。
计算机高级语言出现以后，卡尔玛致力于研究能直接执行用高级语言编写的程序的机器。1959年，卡尔玛提出了“面向公式的机器”(formula-directed machine)的概念，并完成了机器的详细设计。但限于缺乏资金支持，卡尔玛的设计未能实现。但他的许多设计思想被乌克兰的计算机科学家格罗希柯夫(V．M．Glushkov，他也是一位计算机先驱)用于其MIR计算机系列中。1973年，卡尔玛又进一步改进了其“面向公式的机器”的设计，使之能处理多变量函数，在数据结构方面也有不少创新。然而，1975年卡尔玛宣布退休，第二年8月2日不幸去世，他的设计只能停留在纸面上。综观其一生，卡尔玛忠实地贯彻着波利雅数学研究所的信条，即这个所在塞格德扎下根基后的首任所长李兹所宣称的：“一个教授的责任就像天线发射无线电波一样，传播真正科学的思想；至于是否有人接收，这不是最重要的。”(“A Professor’s duty is tO radiate pure science as an antenna does：itradiates whether somebody receives it Or not，that is not up tO it．”)
卡尔玛生前只有一个荣誉头衔，那就是匈牙利科学院院士。1990年，波利雅数学研究所为纪念卡尔玛，将研究所一分为二，一个是“卡尔玛研究所”(Kalmar lnstitute)，一个是“控制论实验室”(Labora—tory。fCybernetics)。二者在国际学术界仍享有盛名。他获得过的奖励包括卡索斯奖(Kossuth Prize，1950，卡索斯是19世纪匈牙利的爱国者和政治家)、匈牙利国家奖(Hungarian State Prize，1975)。
个人简历编辑本段回目录
László Kalmár (March 271905 - August 21976) was a Hungarian mathematician and Professor at the University of Szeged. Kalmár is considered the founder of mathematical logic and theoretical Computer Science in Hungary.
His early life mixed promise and tragedy. His father died when he was young, and his mother died when he was 17, the year he entered the University of Budapest, making him essentially an orphan.
Kalmár's brilliance manifested itself while in Budapest schools. At the University of Budapest, his teachers included Kürschák and Fejér. His fellow students included the future logician Rózsa Péter. Kalmár graduated in 1927. He discovered mathematical logic, his chosen field, while visiting Göttingen in 1929.
Upon completing his doctorate at Budapest, he took up a position at the University of Szeged. That university was mostly made up of staff from the former University of Kolozsvár, a major Hungarian university before WWI that found itself after the War in Romania. Kolozsvár was renamed Cluj. The Hungarian university moved to Szeged in 1920, where there had previously been no university. The appointment of Haar and Riesz turned Szeged into a major research center for mathematics. Kalmár began his career as a research assistant to Haar and Riesz. Kalmár was appointed a full professor at Szeged in 1947. He was the inaugural holder of Szeged's chair for the Foundations of Mathematics and Computer Science. He also founded Szeged's Cybernetic Laboratory and the Research Group for Mathematical Logic and Automata Theory.
In mathematical logic, Kalmár proved that certain classes of formulas of the first order predicate calculus were decidable. In 1936, he proved that the predicate calculus could be formulated using a single binary predicate, if the recursive definition of a term was sufficiently rich. (This result is commonly attributed to a 1954 paper of Quine's.) He discovered an alternative form of primitive recursive arithmetic, known as elementary recursive functions, based on primitive functions that differ from the usual kind. He did his utmost to promote computers and computer science in Hungary. He wrote on theoretical computer science, including programming languages, automatic error correction, non-numerical applications of computers, and the connection between computer science and mathematical logic.
Kalmar was elected to the Hungarian Academy of Sciences in 1949, and was awarded the Kossuth Prize in 1950 and the Hungarian State Prize in 1975.
In 1933 Kalmár married Erzsébet Arvay; they had four children.
Kalmar defined what are known as elementary functions -- number-theoretic functions (i.e. those based on the natural numbers) -- built up from the notions of composition and variables, the constants 0 and 1, repeated addition + of the constants, proper subtraction ∸, bounded summation and bounded product (Kleene 1952:526). Elimination of the bounded product from this list yields the subelementary or lower elementary functions. By use of the abstract computational model called a register machine Schwichtenberg provides a demonstration that "all elementary functions are computable and totally defined".(p. 58)
