塞迈雷迪·安德烈Endre Szemerédi

塞迈雷迪·安德烈出生于第二次世界大战期间，八岁时母亲去世。他有两个兄弟，但三个男孩都被送到不同的孤儿寄宿学校。他在[14]中解释了数学在小学时如何对他有用：-

……我上小学时，又矮又弱，强壮的孩子会打我。所以我必须找个人保护我。我还算幸运，因为班上最强壮的孩子对数学一窍不通。他从来解不出作业题，更别说通过考试了。所以我替他解作业题，考试时坐在他旁边。当然，我们作弊了，他通过了考试。但他是个诚实的人，此后总是保护我免受其他大孩子的欺负，所以我很安全。因此，我早期对数学的兴趣更多是出于需要和自身利益，而不是其他任何东西。小学时我做了很多数学，但只停留在那个水平，解小学的习题。

他在中学没有专攻数学，因为他父亲希望他成为一名医生。这是因为当时医学职业被认为地位最高、收入最好。因此他在学校学习生物学，毕业后进入医学院。

安德烈只在医学院待了六个月，但在第一学期结束前就退学了。他说[14]：-

我意识到，由于多种原因，这并不适合我。

主要原因是[16]：-

我不确定自己能否承担如此责任的工作。你还得大量学习，而这我并不擅长。

由于不知道自己适合什么，他在精密机械公司经营的一家机械制造厂当了一名工厂工人。他干了将近两年，直到一次偶然事件使他成为数学家。

在高中时，他最好的朋友是Gábor Ellmann，他是班上迄今为止最好的数学家。Ellmann于1958年开始在布达佩斯的厄特沃什·罗兰大学学习数学和物理学。一天，安德烈正走过布达佩斯市中心，这时他看到了Ellmann，便上前与他聊天。Ellmann本来要去见他的女朋友，但由于他迟到了十五分钟，她没有等他。安德烈和Ellmann聊了起来，自然，Ellmann问安德烈他在做什么。当他听说他的工厂工作时，Ellmann告诉安德烈，他应该去厄特沃什·罗兰大学学习数学。这不仅是他Ellmann的看法，他说，他还知道他们的高中数学老师Sándor Bende一直认为安德烈应该学习数学。安德烈一直尊重朋友的建议，所以他照做了，于1960年进入厄特沃什·罗兰大学。

在大学的第一年，即1960-61学年，安德烈学习了数学和物理课程，最终目标是成为一名高中教师。他觉得所参加的课程一点也不令人兴奋，但还是继续读到了第二年。就在那时，安德烈的情况发生了巨大变化，带来这一变化的人是图兰·帕尔[16]：-

图兰·帕尔讲授了一门精彩的、为期一整年的数论综合课程。

他在[14]中描述了图兰·帕尔的 课程如何改变了他的志向：-

他的课讲得完美无缺。不知怎的，他能与各种不同类型的学生交流，从较差的学生到优秀的学生。我对这些课印象极深，以至于我决定要成为一名数学家。

在本科阶段，安德烈与两位杰出的年轻数学家András Sárközi和János Komlós合作。András Sárközi（1941年生于布达佩斯）于1959年至1963年是厄特沃什·罗兰大学的学生。随后他成为厄特沃什·罗兰代数与数论系的研究员。János Komlós（1942年生于布达佩斯）也是厄特沃什·罗兰大学的学生。他在雷尼·奥尔弗雷德的指导下于1967年获得博士学位。安德烈于1965年在厄特沃什·罗兰大学获得硕士学位。那时，他已有三篇论文被接受发表，随后加入了匈牙利科学院数学研究所。这三篇论文是（与János Komlós和András Sárközi合作）On sums of powers of complex numbers（1964年），（与András Sárközi合作）Über ein Problem von Erdős und Moser（1965年），以及（与András Sárközi合作）On the sequence of squares（1965年）。

在数学研究所，安德烈开始与常客埃尔德什合作。此时埃尔德什没有固定职位，而是在世界各地的大学之间奔波。然而，他经常访问布达佩斯，因为他的母亲继续住在匈牙利。安德烈说[14]：-

埃尔德什有许多问题、猜想。其中一些不太难，但另一些极其困难。幸运的是或不幸的是，他的许多问题的解答只需要初等方法。当然，仅使用初等方法的证明往往并不简单，因为人们可能必须以极其复杂和精巧的方式将基本要素组合起来。知道自己知识非常有限，我很高兴埃尔德什愿意与我合作。与他以及一位同行数学家András Sárközi一起，我们撰写了大量关于数论的论文。

事实上，安德烈与埃尔德什的第一篇论文也包括Andras Sárközi作为合著者。这就是论文On divisibility properties of sequences of integers（1966年）。安德烈继续与埃尔德什撰写了许多（约30篇）合著论文，但实际上，这一数字被他在这些早期日子里的另一位合著者Andras Sárközi远远超过，后者保持着与埃尔德什合著论文最多的记录（约50篇）。由于他迄今为止所做的令人印象深刻的工作，安德烈于1967年被亚诺什·波尔约数学会授予Grünwald奖，并在次年再次获得该奖。这个以Géza Grünwald（1910-1943）命名的奖项授予杰出的年轻研究人员。

在这个阶段，安德烈没有博士学位，鉴于匈牙利当时与俄罗斯有着紧密联系，且亚历山大·格尔丰德是世界领先的数论学家，安德烈申请在莫斯科进行研究，由亚历山大·格尔丰德作为他的学位论文导师。然而，一个不幸的拼写错误（一个“a”而不是“o”）意味着当他1967年到达莫斯科时，他发现自己被分配为伊斯拉埃尔·盖尔范德的学生[14]：-

我立刻意识到这并不适合我，伊斯拉埃尔·盖尔范德也意识到了这一点，并建议我不要再做数学了，他对我说：“试着去找另一个职业吧；世界上有很多职业你可能都会成功。”当时我二十七岁，而他那些明星学生都在二十岁左右，二十七岁就被认为老了！

伊斯拉埃尔·盖尔范德那种类型的数学完全不适合安德烈，但他不想放弃，不想作为一个失败者回到匈牙利。不过，他确实有一点运气，因为在他作为博士生在俄罗斯的第一年快结束时，匈牙利德布勒森有一个会议，亚历山大·格尔丰德参加了。安德烈作为一名会说俄语的匈牙利学生，被指派去照顾他并带他参观。亚历山大·格尔丰德一听说发生的错误，就说他回到莫斯科后会安排安德烈成为他的学生。遗憾的是，这未能实现，因为亚历山大·格尔丰德在回到莫斯科两个月后就去世了。安德烈继续做伊斯拉埃尔·盖尔范德的学生，但被允许写关于组合学的学位论文。他还必须参加其他考试，并由谢尔盖·伯恩斯坦就亚历山大·卡里洛夫关于表示论的出版物中的两个习题对他进行考试。谢尔盖·伯恩斯坦[14]：-

……在解答中发现了错误，但他说重要的是我投入的努力，而不是结果，他让我通过了考试。

提交学位论文后，安德烈于1970年获得莫斯科国立大学的副博士学位（相当于博士学位）。回到匈牙利科学院数学研究所后，安德烈于1973年获得了他们的雷尼·奥尔弗雷德奖，这是一个年度奖项，旨在表彰过去五年中在数学研究方面的杰出表现。到1973年，安德烈已经发表了30多篇论文，两年后，即1975年，他发表了一个极其重要的结果，现在被称为安德烈定理。这个结果曾在1936年由埃尔德什和图兰·帕尔在论文On some sequences of integers中猜想。安德烈定理指出，在任何具有正密度的整数集中，都存在任意长的等差数列。以下是安德烈定理的精确陈述：

对于每个正整数$k$和每个$1 ≥ d > 0$，存在一个整数$N$，使得$\{1, 2, ..., N\}$中包含的每个大小至少为$dN$的子集$A$都包含一个长度为$k$的等差数列。

蒂莫西·高尔斯写道[8]：-

这个定理是二十世纪数学的亮点之一，但它也处于大量近期研究的核心。他还给了我们安德烈正则引理，这个结果源于安德烈定理的证明，但后来成为极值组合学中的一个主要工具。

这些卓越成就的细节也在4中给出：-

安德烈的证明是组合推理的杰作，立即被公认为具有非凡的深度和重要性。证明中的一个关键步骤，现在被称为安德烈正则性引理，是对大图的结构分类。随着时间的推移，这个引理已成为图论和理论计算机科学的中心工具，导致了性质测试中重大问题的解决，并催生了图极限理论。还有更多的惊喜在等待着。除了对离散数学和加性数论的影响之外，安德烈的定理还启发了哈里·弗斯腾伯格将遍历理论发展到新的方向。哈里·弗斯腾伯格通过在遍历理论中建立多重回归定理，给出了安德烈定理的新证明，从而出人意料地将离散数学中的问题与动力系统理论联系起来。这一基本联系导致了许多进一步的发展，例如Green-陶哲轩定理断言存在任意长的素数等差数列。

安德烈因其杰出工作继续获奖。Society for Industrial and Applied Mathematics于1975年授予他乔治·波利亚成就奖，1979年，他获得了匈牙利科学院奖。1982年，他当选为匈牙利科学院通讯院士，并于1987年成为正式院士。1986年，安德烈移居美国，被任命为罗格斯大学新泽西州计算机科学教授。然而，他继续在布达佩斯的匈牙利科学院数学研究所雷尼·奥尔弗雷德担任教授。除了继续担任这两个职位外，安德烈还担任过几个访问教授职位：斯坦福大学，1974年；麦吉尔大学，1980年；南加州大学，1981-1983年；芝加哥大学，1985-1986年；加州理工学院费尔柴尔德杰出学者，1987-1988年；蒙特利尔数学研究中心的艾森斯塔特讲席，2003年；普林斯顿高等爱德华·斯图迪研究所，2007-2008年和2009-2010年；以及乔治·伯克利数学科学研究所的大卫·艾森布德教授，2008年。

在我们上面提到的奖项之后，安德烈被授予：American Mathematical Society的Leroy P 凯瑟琳·斯蒂尔研究开创性贡献奖，2008年：-

... 因其论文“关于不包含k项等差数列的整数集”；

他获得了由瑞典皇家科学院决定的Rolf Schock数学奖，2008年；科罗拉多大学DeLong讲座系列，2010年；尼尔斯·阿贝尔奖，2012年[4]：-

……因其对离散数学和理论计算机科学的根本性贡献，并表彰这些贡献对加性数论和遍历论产生的深远而持久的影响；

他于2012年11月14日在纽约市华尔道夫酒店举行的晚宴上，从美国匈牙利基金会获得了乔治·华盛顿奖。

授予安德烈的另一项荣誉在[12]中有所描述：-

2010年，在安德烈70岁生日之际，雷尼·奥尔弗雷德数学研究所和亚诺什·波尔约数学会在布达佩斯组织了一次会议以庆祝他的成就。在会议之前出版的《不规则的心》一书中，写道：“安德烈有一颗‘不规则的心’；他的大脑连接方式与大多数数学家不同。我们中的许多人都钦佩他独特的思维方式，他非凡的远见。”

同样在2010年，安德烈被布拉格的查理大学授予荣誉博士学位。

总结安德烈截至2012年的成就，蒂莫西·高尔斯写道[8]：-

有些数学家因一两个重要定理而闻名。另一些则因大量重要且高水准的成果而著称。偶尔，会有数学家因两者而闻名。如果不讨论安德烈定理和安德烈正则引理，对安德烈工作的任何叙述都是不完整的。然而，安德烈远不止这两个定理。正如我在开头提到的，他已发表了200多篇论文，而且在71岁时，他丝毫没有放缓的迹象。

安德烈在[16]中声称自己是一位不会使用计算机的计算机科学教授：-

我不懂计算机，尽管我在罗格斯大学计算机科学系工作。我可以证明我妻子回复了我所有的电子邮件。我阅读它们，但我不知道如何使用计算器——我是说计算机，我有时只是称它为计算器。[我不学习使用计算机是因为]我对此实在太笨了，我完全不明白。我理解互联网，那只是一个图，我可以建模。但计算机、编程语言、如何搜索信息，我不懂。我对相机也无能为力，我从未学会如何拍照。我也不会打开DVD播放器，如果我妻子不启动我想看的电影，或者我的一个孙子不过来帮我，我就束手无策。

在[16]中，安德烈描述了他的一些爱好：-

我过去喜欢散步，但自从髋部出现问题后，这就更困难了。我每周打一次网球，但有一位教练把球打得正好在我面前弹起；我甚至不需要移动。两个月前我开始打乒乓球。我和家人一起看电影，我们去剧院，我在电视上观看任何类型的体育比赛。如果你问我这方面的事，我可以告诉你任何事情：我关注体育已有数十年。足球、一级方程式、篮球，甚至看似无聊的运动如棒球或橄榄球。当然还有网球。我网球打得不好，但比赛开始时，我立刻就能看出纳达尔的策略是什么。你不需要成为数学家才能做到这一点，只需要是一个体育狂热者。

安德烈与Anna Kepes（生于1945年）结婚；他们有五个孩子。Anna Kepes 安德烈编辑了Art in the Life of Mathematicians（2015年）一书。许多顶尖数学家为这本书贡献了他们对艺术、绘画、音乐、舞蹈、摄影等的思考。Anna为她丈夫的70岁生日组织了一个展览“数学家世界中的艺术”，这本书就是从展览中诞生的。

最后让我们引用罗格斯大学计算机科学系主任 Michael Littman 的话[11]：-

数学家也是人。有些人傲慢讨厌。有些人则真正富有人情味。安德烈 是一个非常非常和善的人。他有着温暖含笑的眼睛，举止温和沉静。他非常宽宏大量，非常慷慨。他并不认为自己是世界上唯一在这个领域工作的人。

Endre Szemerédi was born during World War II and his mother died when he was eight years old. He had two brothers but the three boys were all sent to different boarding schools for orphans. He explains in [14] how mathematics proved useful to him in elementary school:-

... when I was in elementary school, I was very short and weak and the stronger guys would beat me up. So I had to find somebody to protect me. I was kind of lucky, since the strongest guy in the class did not understand anything about mathematics. He could never solve the homework exercises, let alone pass the exam. So I solved the homework exercises for him and I sat next to him at the exam. Of course, we cheated and he passed the exam. But he was an honest person and he always protected me afterwards from the other big guys so I was safe. Hence my early interest in mathematics was driven more by necessity and self-interest than by anything else. In elementary school I worked a lot with mathematics but only on that level, solving elementary school exercises.

He did not specialise in mathematics at secondary school because his father wanted him to become a medical doctor. This was because, at this time, the medical profession was thought to be that of the highest status and best paid. Therefore he studied biology at school and, after graduating, entered medical school.

Szemerédi only spent six months at the medical school but he dropped out before the end of the first semester. He said [14]:-

I realized that, for several reasons, it was not for me.

The main reasons were [16]:-

I was not sure I could do work bearing such responsibility. You also had to study a lot, which I wasn't good at.

Not knowing what was right for him, he took a job as a factory-hand in a machine-making factory run by the Precision Mechanics Corporation. He spent almost two years in this job before a chance event led to him becoming a mathematician.

At high school his best friend had been Gábor Ellmann who had been by far the best mathematician in his class. Ellmann had begun his studies of mathematics and physics at Eötvös Loránd University in Budapest in 1958. One day Szemerédi was walking through the centre of Budapest when he saw Ellmann and went to chat to him. Ellmann had been going to meet his girlfriend but, as he was fifteen minutes late, she had not waited for him. Szemerédi and Ellmann chatted and, naturally, Ellmann asked Szemerédi what he was doing. When he heard about his factory job, Ellmann told Szemerédi that he should go to Eötvös Loránd University and study mathematics. Not only was this Ellmann's opinion but, he said, he knew that their high school mathematics teacher Sándor Bende had always thought that Szemerédi should have studied mathematics. Szemerédi had always respected his friend's advice and so he did as suggested and entered Eötvös Loránd University in 1960.

In his first year at university, academic year 1960-61, Szemerédi took mathematics and physics courses with the eventual aim of becoming a high school teacher. He did not find the courses that he attended at all stimulating but continued into his second year. It was at that time that things changed dramatically for Szemerédi and the person who brought about that change was Paul Turán [16]:-

Turán gave a wonderful, all-year comprehensive course on number theory.

He describes how Turán's course changed his ambitions in [14]:-

His lectures were perfect. Somehow he could speak to all different kinds of students, from the less good ones to the good ones. I was so impressed with these lectures that I decided I would like to be a mathematician.

While an undergraduate, Szemerédi collaborated with two outstanding young mathematicians András Sárközi and János Komlós. András Sárközi (born in Budapest in 1941) was a student at Eötvös Loránd University from 1959 to 1963. He then became a Research Fellow in the Department of Algebra and Number Theory at Eötvös Loránd. János Komlós (born in Budapest in 1942) was also a student at Eötvös Loránd University. He obtained his doctorate in 1967 having been advised by Alfréd Rényi. Szemerédi graduated with a Master's Degree from Eötvös Loránd University in 1965. Then, having already had three papers accepted for publication, he joined the Mathematical Research Institute of the Hungarian Academy of Sciences. These three papers were (with János Komlós and András Sárközi) On sums of powers of complex numbers (1964), (with András Sárközi) Über ein Problem von Erdős und Moser (1965), and (with András Sárközi) On the sequence of squares (1965).

At the Mathematical Research Institute, Szemerédi began to collaborate with Paul Erdős who was a frequent visitor. By this time Erdős had no fixed position but went from one university to another around the world. However, he visited Budapest frequently since his mother continued to live in Hungary. Szemerédi said [14]:-

Paul Erdős had many problems, conjectures. Some of them were not so hard, but the others were extremely difficult. Fortunately or unfortunately the solution to many of his problems required only elementary methods. Of course quite often the proofs using only elementary methods are not simple because one may have to put together basic ingredients in extremely complicated and sophisticated ways. Knowing that I had a very limited knowledge, I was very happy that Paul Erdős was willing to work with me. With him and a fellow mathematician András Sárközi we wrote a large number of papers on number theory.

In fact Szemerédi's first paper with Erdős also included Andras Sárközi as a co-author. It was the paper On divisibility properties of sequences of integers (1966). Szemerédi went on to write many (around 30) joint papers with Erdős but, in fact, this number was well beaten by his other co-author from these early days, Andras Sárközi, who has the record of the most joint papers with Erdős (around 50). For the impressive work he had done up to this time Szemerédi was awarded the Grünwald Prize in 1967 by the János Bolyai Mathematical Society, and he received the prize again in the following year. This prize, named for Géza Grünwald (1910-1943) was awarded to outstanding young researchers.

At this stage Szemerédi did not have a doctorate and, given that Hungary now had strong links with Russia and Alexander Gelfond was a world leading number theorist, Szemerédi applied to do research in Moscow with Gelfond as his thesis advisor. However, an unfortunate spelling error (an "a" instead of an "o") meant that when he arrived in Moscow in 1967 he discovered that he had been assigned to be Israil Moiseevic Gelfand's student [14]:-

I realised immediately that this was not for me, and Gelfand also realized it and advised me not to do mathematics anymore, telling me: "Just try to find another profession; there are plenty in the world where you may be successful." I was twenty-seven years old at the time, and he had all these star students aged around twenty, and twenty-seven was considered old!

Gelfand's type of mathematics did not suit Szemerédi at all but he did not want to give up and return to Hungary as a failure. He did have a piece of luck, however, for around the end of his first year as a doctoral student in Russia, there was a conference in Debrecen in Hungary which Gelfond attended. Szemerédi, as a Hungarian student who could speak Russian, was assigned to look after him and show him round. Once Gelfond heard of the error that had occurred, he said that when he returned to Moscow he would arrange for Szemerédi to become his student. Sadly, this was not to be since Gelfond died two months after returning to Moscow. Szemerédi continued as Gelfand's student, but was allowed to write his thesis on combinatorics. He had to take other examinations too and was examined by Sergei Bernstein on two exercises from Alexander Kirillov's publications on representation theory. Sergei Bernstein [14]:-

... found the error in the solution, but he said that it was the effort that I had put into it that was important rather than the result, and he let me pass the exam.

After submitting his thesis, Szemerédi was awarded a candidate's degree (equivalent to a Ph.D.) from Moscow State University in 1970. Back in the Institute of Mathematics of the Hungarian Academy of Sciences, Szemerédi was awarded their Alfréd Rényi Prize in 1973 which was an annual award to recognise outstanding performance in mathematical research during the previous five years. By 1973 Szemerédi had published over 30 papers and, two years later, in 1975, he published a highly significant result which is now known as Szemerédi's Theorem. This result had been conjectured in 1936 in the paper On some sequences of integers by Erdős and Paul Turán. Szemerédi's Theorem states that in any set of integers with positive density, there are arbitrarily long arithmetic progressions. Here is a precise statement of Szemerédi's Theorem:

For every positive integer $k$ and every $1 ≥ d > 0$ there exists an integer $N$ such that every subset $A$ contained in $\{1, 2, ..., N\}$ of size at least $dN$ contains an arithmetic progression of length $k$.

Tim Gowers writes [8]:-

This theorem is one of the highlights of twentieth-century mathematics, but it also lies at the heart of a great deal of very recent research. He also gave us Szemerédi's regularity lemma, a result that originated in the proof of Szemerédi's theorem but went on to become a major tool in extremal combinatorics.

Details of these remarkable achievements are also given in [4]:-

Szemerédi's proof was a masterpiece of combinatorial reasoning, and was immediately recognized to be of exceptional depth and importance. A key step in the proof, now known as the Szemerédi Regularity Lemma, is a structural classification of large graphs. Over time, this lemma has become a central tool of both graph theory and theoretical computer science, leading to the solution of major problems in property testing, and giving rise to the theory of graph limits. Still other surprises lay in wait. Beyond its impact on discrete mathematics and additive number theory, Szemerédi's theorem inspired Hillel Furstenberg to develop ergodic theory in new directions. Furstenberg gave a new proof of Szemerédi's theorem by establishing the Multiple Recurrence Theorem in ergodic theory, thereby unexpectedly linking questions in discrete mathematics to the theory of dynamical systems. This fundamental connection led to many further developments, such as the Green-Tao theorem asserting that there are arbitrarily long arithmetic progressions of prime numbers.

Szemerédi continued to receive prizes for his outstanding work. The Society for Industrial and Applied Mathematics awarded him their Pólya Prize for Achievement in 1975 and, in 1979, he received the Prize of the Hungarian Academy of Sciences. In 1982 he was elected as a Corresponding Member of the Hungarian Academy of Sciences and became a full member in 1987. In 1986 Szemerédi moved to the United States when he was appointed State of New Jersey Professor of Computer Science at Rutgers University. However, he continued to hold his professorship at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences in Budapest. In addition to continuing to hold these two positions, Szemerédi held several visiting professorships: Stanford University, 1974; McGill University, 1980; University of Southern California, 1981-1983; University of Chicago, 1985-1986; Fairchild Distinguished Scholar, California Institute of Technology, 1987-1988; Aisenstadt Chair at Centre de Recherche Mathématique in Montreal, 2003; Institute for Advanced Study, Princeton, 2007-2008 and 2009-2010; and Eisenbud Professor, Mathematical Sciences Research Institute, Berkeley, 2008.

After the prizes we have mentioned above, Szemerédi was awarded: the Leroy P Steele Prize of the American Mathematical Society for Seminal Contribution to Research, 2008:-

... for his paper "On sets of integers containing no k elements in arithmetic progression";

He won the Rolf Schock Prize in Mathematics decided by the Royal Swedish Academy of Sciences, 2008; the DeLong Lecture Series, University of Colorado, 2010; the Abel Prize, 2012 [4]:-

... for his fundamental contributions to discrete mathematics and theoretical computer science, and in recognition of the profound and lasting impact of these contributions on additive number theory and ergodic theory;

He received the George Washington Prize, from the American Hungarian Foundation, at a dinner held at the Waldorf Astoria Hotel, New York City on 14 November 2012.

Another honour given to Szemerédi is described in [12]:-

In 2010, on the occasion of Szemerédi's 70th birthday, the Alfréd Rényi Institute of Mathematics and the János Bolyai Mathematical Society organized a conference in Budapest to celebrate his achievements. In the book, 'An Irregular Mind', published prior to the conference, it is stated that "Szemerédi has an 'irregular mind'; his brain is wired differently than for most mathematicians. Many of us admire his unique way of thinking, his extraordinary vision."

Also in 2010 Szemerédi was awarded an honorary doctorate by the Charles University of Prague.

Summing up Szemerédi's achievements up to 2012, Tim Gowers writes [8]:-

Some mathematicians are famous for one or two major theorems. Others are famous for a huge and important body of high-class results. Very occasionally, there is a mathematician who is famous for both. No account of Szemerédi's work would be complete without a discussion of Szemerédi's theorem and Szemerédi's regularity lemma. However, there is much more to Szemerédi than just these two theorems. He has published over 200 papers, as I mentioned at the beginning, and at the age of 71 he shows no signs of slowing down.

Szemerédi claims in [16] to be a professor of computer science who does not know how to use a computer:-

I don't know computers, despite the fact that I work at the Department of Computer Science at Rutgers University. I can prove that my wife answers all my emails. I read them, but I don't know how to use the calculator - I mean computer, I just sometimes call it a calculator. [I don't learn to use a computer because] I'm just simply too stupid for it, I don't understand the whole thing. I understand the internet, that's just a graph, I can model it. But the computer, programming languages, how to search for information, I don't know. I'm also incompetent with cameras, I never learned how to take pictures. And I can't turn the DVD player on, I am helpless if my wife doesn't start the movie I want to watch, or one of my grandchildren doesn't come over to help me out.

In [16] Szemerédi describes some of his hobbies:-

I used to love to take walks, but since I've been having hip problems, that is more difficult. I play tennis once a week, but with a trainer who hits the ball so that it bounces right in front of me; I don't even have to move. Two months ago I started playing ping pong. I watch movies with my family, we go to the theatre, I watch any kind of sport on TV. If you ask me about that, I can tell you anything: I have been following sports for decades. Soccer, Formula 1, basketball, even seemingly boring sports like baseball or football. Tennis too, of course. I can't play tennis well, but when the game starts, I see immediately what Nadal's strategy is. You don't have to be a mathematician to do that, only a sports fanatic.

Szemerédi is married to Anna Kepes (born 1945); they have five children. Anna Kepes Szemerédi edited the book Art in the Life of Mathematicians (2015). A number of leading mathematicians contributed their thoughts on art, painting, music, dance, photography etc. for this book. Anna organised an exhibition "Art in the World of Mathematicians" for her husband's 70th birthday and the book grew out of the exhibition.

Let us end by quoting Michael Littman, chairman of the Department of Computer Science at Rutgers University [11]:-

Mathematicians are people, too. Some are arrogant and obnoxious. Some are truly humane. Szemerédi is a sweet, sweet man. He has these warm smiling eyes, a nice calm way about him. He's very magnanimous, very generous. He doesn't think he's the only one who works in this field in the world.