雅科夫·西奈Yakov Sinai

西奈 Grigorevich 西奈的父母，Grigory Sinai和Nadezda Veniaminovna 韦尼阿明·卡甘，都是从事研究工作的微生物学家。西奈的母亲Nadezda在他三岁时去世，她是在自己的实验室研制疫苗时感染了病毒性脑炎。这个家庭有着深厚的数学渊源，因为西奈 Grigorevich的祖父（Nadezda 卡甘的父亲）是韦尼阿明·卡甘，莫斯科国立大学微分几何教研室主任，他在那里创立了一个重要的微分几何学派。同样值得记录的是，这个家庭是犹太人，韦尼阿明·卡甘曾长期与反犹主义作斗争。然而，这是一个几代人都在俄罗斯科学和文化生活中发挥过重要作用的家庭。韦尼阿明·卡甘对他的孙子有很大的影响。他于1952年从莫斯科国立大学的讲席上退休，那一年他的孙子西奈 Grigorevich进入了力学与数学系。我们还应该提到这个家庭的另一位成员，即Grigory Isaakovich Barenblatt（1927-2018）。他是Isaak Grigorievich Barenblatt和Nadezda Veniaminovna 卡甘的儿子，因此是雅科夫·西奈的同母异父兄弟。他在莫斯科国立大学力学与数学系师从Boris Moiseevich Levitan（1914-2004）和安德雷·柯尔莫哥洛夫，于1950年毕业。两年后，他与Iraida Nikolaevna Kochina结婚，后者是尼古拉·科钦和佩拉格亚·波鲁巴里诺瓦-科奇纳的两个女儿之一。

谈到他的学生时代，西奈说[17]：-

我在学生时代参加过许多数学奥林匹克竞赛，但从未取得过任何成功，也从未获得过任何奖项。我对那些从未在奥林匹克竞赛中获胜的年轻人说这些；将来可能会有补偿。那时，我的祖父年事已高，没有精力把我推向数学。我还有一个同母异父的兄弟，G I Barrenblatt，他在莫斯科国立大学工作，他坚信我应该从事数学职业。

1941年5月，德国军队入侵苏联，到那年10月已逼近莫斯科。此时西奈 Grigorevich六岁，已经开始上学，但莫斯科开始疏散。直到1943年，西奈一家才得以返回莫斯科。西奈说[17]：-

1943年，我家从莫斯科疏散回来后，我进入了学校。那时男孩和女孩分开学习；每年年底，我们大约有十门考试。疏散之前，生活是不同的。在莫斯科，公寓里禁止开窗，因为必须保持黑暗。1943年，窗户又被允许打开了。在莫斯科没有明显的战争迹象，但由于斯大林时代，生活很艰难。

到他十六岁时，他在莫斯科18上高中，有幸遇到了一位优秀的数学老师：-

我们高中有一位非常好的数学老师。他叫Vasily Alekseevich Efremov，是一位出色的老派教师。他总是把题目工整地写在一张纸上发给我们。由于他组织有方、鼓舞人心，数学在我们中间非常受欢迎。我们讨论并尝试解他出的题。那时我在班上并不是最好的。肯定还有其他学生比我强得多。

由于西奈是犹太人，他上大学并不容易。当时某些苏联大学有蓄意的歧视政策，阻止犹太人入学。由于西奈是犹太人，当他参加莫斯科国立大学的入学考试时，他被判不及格。只有他的祖父韦尼阿明·卡甘和莫斯科国立大学校长伊万·彼得罗夫斯基的干预，才使决定被推翻，西奈获准开始大学学习。

西奈 从 米哈伊尔·阿列克谢耶维奇·拉夫连季耶夫 那里修了一门分析课，从 Nikolai Guryevich Chetaev 那里修了一门经典力学课，从 尤金·登金 那里修了一门代数课。他在莫斯科国立大学的第一个导师是 Chetaev，后者是分析力学专家，尤其是运动稳定性方面的专家。西奈 很快对 Chetaev 所研究的动力系统产生了兴趣。然而，他换了导师，开始与 尤金·登金 一起工作。尤金·登金 建议 西奈 研究的问题，促成了他的第一篇论文 On the distribution of the first positive sum for a sequence of independent random variables（俄文）（1957）。1957 年，西奈 从莫斯科国立大学获得第一个学位，并开始跟随 安德雷·柯尔莫哥洛夫 攻读硕士学位（相当于博士学位）的研究。然而，他进入研究生院的过程并不顺利，因为他再次不得不参加入学考试。他被要求参加共产主义党史考试，由于他对这个题目毫无兴趣，他没有通过。帕维尔·亚历山德罗夫 是数学负责人，他和 安德雷·柯尔莫哥洛夫 一起去见党史系主任，请求允许 西奈 重考。他又参加了一次共产主义党史考试，以 B 等成绩通过。这被认为勉强足以让他开始研究生学习。

他于 1960 年获得硕士学位，并于同年被任命为莫斯科国立大学概率与统计方法实验室的研究员。他继续在 安德雷·柯尔莫哥洛夫 的指导下攻读博士学位（相当于德国的 教授资格论文（Habilitation））。当时其他教职员对他产生了重大影响，尤其是 伊斯拉埃尔·盖尔范德 和 Vladimir Abramovich Rokhlin，他们主持了动力系统度量理论讨论班。西奈 在攻读硕士学位前后发表的论文包括：On the concept of entropy for a dynamic system（俄文）（1959）；Flows with finite entropy（1959）（俄文）；The central limit theorem for geodesic flows on manifolds of constant negative curvature（1960）（俄文）；以及 Dynamical systems and stationary Markov processes（1960）（俄文）。

早在1959年这些论文的第一篇中，西奈就给出了使人们能够计算大量动力系统的熵的定理。“安德雷·柯尔莫哥洛夫-西奈熵”这一术语很快被确立[20]：-

西奈的工作涉及度量动力系统，即随时间变化的系统，如天气、行星运动和经济系统。这些系统在短期内（短期是相对于所讨论的问题而言）可以被精确度量；但从长期分析时，这些系统难以理解和预测。西奈第一个提出了确定给定动力系统复杂度的数的数学基础。他的数学系统被称为安德雷·柯尔莫哥洛夫-西奈熵。

西奈论文的高质量和重要性使他受邀在1962年斯德哥尔摩国际数学家大会上作报告。尤金·登金和伊斯拉埃尔·盖尔范德都受邀作全会报告，但未出席。安德雷·柯尔莫哥洛夫确实出席了大会，并宣读了尤金·登金的报告。西奈应组织委员会邀请作了半小时报告Probabilistic ideas in ergodic theory。他还宣读了德米特里·阿诺索夫的简短报告The roughness of geodesic currents in compact Riemannian manifolds of negative curvature。

1971年，按照谢尔盖·彼得罗维奇·诺维科夫的建议，西奈接受了苏联科学院理论物理研究所列夫·朗道高级研究员的职位。谢尔盖·彼得罗维奇·诺维科夫刚刚被任命为该研究所数学部的负责人。西奈继续在莫斯科国立大学任教，但直到1981年他才成为那里的教授。12的作者解释了原因：-

1968年，他（与许多其他数学家一起）签署了那封著名的为A S Esenin-Vol'pin辩护的公开信，这长期以来成为阻止他成为教授的障碍（他直到1981年才成为教授，距他提交博士学位论文已过去17年）。

Alexander Sergeyevich Esenin-Volpin既是一位诗人，也是一位数学家，他领导了苏联的人权运动。从1949年开始，Volpin因反苏诗歌而多年身陷囹圄，或作为社会危险分子被流放。西奈因支持Volpin而深受其害。例如，1970年他受邀在尼斯国际数学家大会上作报告。然而，苏联当局不允许他前往尼斯。许多其他人也被阻止参加尼斯大会，包括尤金·登金、伊斯拉埃尔·盖尔范德、尤里·弗拉基米罗维奇·林尼克、尤里·伊万诺维奇·马宁、伊戈尔·沙法列维奇和谢尔盖·彼得罗维奇·诺维科夫，后者本应在大会上获得约翰·查尔斯·菲尔兹奖章。然而，西奈得以接受邀请，在1990年京都国际数学家大会上作全体报告之一；他报告了Hyperbolic Billiards。继续他在国际数学家大会上的贡献，我们注意到2001年他被任命为国际数学联盟的约翰·查尔斯·菲尔兹奖章委员会主席，该委员会决定了次年北京大会上约翰·查尔斯·菲尔兹奖章的颁发。

1993 年，他被任命为普林斯顿大学数学系教授。他继续保留在 列夫·朗道 理论物理研究所的职位，但放弃了在莫斯科国立大学的职位。1997-1998 年期间，他是普林斯顿大学 Thomas Jones 教授，2005 年他是加利福尼亚州帕萨迪纳加州理工学院的 Moore 杰出学者。他继续在普林斯顿大学担任教授，直到 2023 年成为荣休教授。他继续（2023 年）在莫斯科的 列夫·朗道 理论物理研究所担任教授。

我们已经考察了西奈在其职业生涯早期做出的深刻贡献。也许对他截至1990年代初成就的最佳总结见于[5]：-

西奈在遍历理论、动力系统和统计力学领域做出了奠基性、深刻且极具影响力的工作。早在六十年代，他就对现在所谓的混沌的原理有了深刻理解，并且是最早认识到这一现象对动力学重要性的人之一。他还在统计力学方面做了基础性工作。除了对这些学科的许多重大贡献外，他还通过若干著名阐述性文本和众多研究生产生了非常广泛的影响。

西奈的工作围绕一个宏大目标：把描述多粒子系统行为的基本物理定律，作为支配单个粒子相互作用的简单规则的直接推论推导出来。在这方面他取得了一些显著成功。在遍历理论中，他对双曲系统、台球和硬球气体的工作，为目前用于证明此类系统是遍历的以及研究其行为的更精细统计性质的许多技术奠定了基础。他影响了遍历理论的总趋势，使其从研究相当人为构造的例子转回最初推动这门学科的问题，即对路德维希·玻尔兹曼遍历假设的证实。

将安德雷·柯尔莫哥洛夫熵理论应用于光滑动力系统的想法是西奈提出的。俄罗斯学派此前的工作完全是在概率系统的背景下研究由安德雷·柯尔莫哥洛夫引入的熵。他在这方向上的结果是新的且出人意料的。他研究了具有横截叶状结构的动力系统类，现在称为稳定和不稳定流形，并证明这一类中的所有系统都是遍历的、混合的且具有K性质。随后他引入了马尔可夫分划的概念，并为双曲系统构造了这样的分划。

西奈奠定了台球理论的基础，最近他还为此构造了马尔可夫划分，以及硬球气体运动理论的基础。他对统计力学做出了许多贡献，特别是相变理论。他关于这一主题的书广为人知。近年来，西奈使用重正化方法对KAM理论做出了重要贡献。他目前正在量子混沌中发展一些全新且非常有趣的想法。

考虑到西奈论文的深度和独创性，他如此多产实属非凡。在[29]中，列有386篇以西奈为作者或合著者的论文。然而，西奈认为撰写论文是研究中 least 有趣的部分。他觉得这很无聊，因为他已经实现了解决可能思考了数年、期间不得不将其他一切置之脑后的问题的目标。

西奈因其杰出贡献获得了许多重大奖项、奖金和荣誉。例如，他获得了以下奖章和奖项：国际纯粹与应用物理联合会统计物理委员会颁发的路德维希·玻尔兹曼金奖（1986年）；美国物理学会颁发的海涅曼奖（1989年）；USSR Academy of Sciences颁发的马尔可夫奖（1990年）；的里雅斯特阿卜杜斯·萨拉姆国际理论物理中心颁发的保罗·狄拉克奖章（1992年）；沃尔夫数学奖（1997年）；巴西科学功绩奖（2000年）；工业与应用数学学会颁发的莫泽奖（2001年）；弗雷德里克·埃塞尔·内默斯数学奖（2002年）；伦敦大学安德雷·柯尔莫哥洛夫讲座与奖章（2007年）；意大利都灵科学交流研究所颁发的约瑟夫·拉格朗日奖（2008年）；国际数学物理协会颁发的儒勒·昂利·庞加莱奖（2009年）；USSR Academy of Sciences信息传输研究所颁发的多布鲁申国际奖（2009年）、勒罗伊·P凯瑟琳·斯蒂尔奖（2013年）、尼尔斯·阿贝尔奖（2014年）以及马塞尔·格罗斯曼奖（2015年）。

以下是这些奖项引文的一些摘录。沃尔夫奖（1997年）[7]：-

西奈获奖是因为“他在统计力学和动力系统遍历理论及其物理学应用中的数学严格方法方面做出了基础性贡献。”西奈将动力系统和概率论的强大工具应用于数学物理问题，并经常为此开发新工具。他被普遍认为是统计物理数学领域的世界领袖。他遵循安德雷·柯尔莫哥洛夫学派的传统，首先为任意保测映射的不变熵制定了严格定义。他随后的工作涵盖了从台球运动的遍历性到准周期埃尔温·薛定谔算子的谱性质等领域。统计力学是现代数学中最活跃和最有成果的领域之一，而西奈是当今公认的领袖。

2002年弗雷德里克·埃塞尔·内默斯数学奖[20]：-

他的工作彻底改变了动力系统的研究，并影响了统计力学、概率论和统计物理。

儒勒·昂利·庞加莱奖（2009年）授予了西奈：-

……因其在动力熵、遍历理论、混沌动力系统、相变的微观理论以及统计力学中的时间演化方面的开创性工作。

勒罗伊·P·斯蒂尔终身成就奖于2013年1月10日星期四在圣地亚哥举行的美国数学会与美国数学协会联合会议上颁发给西奈。该奖授予西奈，以表彰[26]：-

……他在塑造动力系统理论中的关键作用，以及他对遍历理论、概率论、统计力学和数学物理的开创性贡献。

引文如下：-

西奈的研究展现出卓越的分析技巧、出众的几何直觉以及对 underlying 物理现象的深刻理解的独特结合。他的工作凸显了动力系统与统计力学之间深刻而意想不到的联系。……在过去十五年中，西奈将动力系统和数学物理的新工具与洞见引入统计流体力学，为克洛德-路易·纳维-乔治·加布里埃尔·斯托克斯系统获得了新结果。具体而言，与D Li一起，西奈设计了一种新的重整化方案，使得能够证明三维克洛德-路易·纳维-乔治·加布里埃尔·斯托克斯系统复解的有限时间奇点存在性。西奈的数学影响是压倒性的。在过去半个世纪里，他撰写了250多篇研究论文和多部著作。西奈的著名专著《遍历理论》（与Cornfeld和Fomin合著）已成为几代人的该学科入门书，并且至今仍是经典。

2014年，西奈因其[1]而获得了许多人认为是最负盛名的数学奖项，即尼尔斯·阿贝尔奖：-

……对动力系统、遍历理论和数学物理的基础性贡献。

该奖项的颁奖词以[28]的话结尾：-

西奈培养并影响了他研究领域中一代顶尖专家。他的许多研究已成为数学物理学家的标准工具箱。他的工作已经并将继续对数学和物理学，以及这两个领域日益富有成果的相互作用产生广泛而深远的影响。

Stein Arne Nistad对颁奖典礼作了有趣的描述[32]：-

西奈走进奥斯陆大学的礼堂，领取今年的尼尔斯·阿贝尔奖——这一奖项如同物理学或医学的诺贝尔奖一样罕见而享有盛誉，此次政要和伟人云集，可能是今年挪威首都活动中最杰出的一次聚会。墙上，挪威艺术家Edvard Munch的十一幅巨幅壁画以北极光和人生各阶段的意象照亮了宽阔的大厅。观众包括来自国内外的学者、国家和国际媒体，以及对数学领域有着高于平均水平兴趣的各界人士。音乐家们入场，年轻的王储Haakon代表其父亲，几乎毕恭毕敬地将美丽而沉重的尼尔斯·阿贝尔奖交给微微驼背的学术巨人。

作为尼尔斯·阿贝尔奖颁奖活动的一部分，Arne B Sletsjøe 撰写了四篇基础文章，阐释了西奈引入的思想，你可以在THIS LINK查看。

2015年，西奈获得了马塞尔·格罗斯曼奖 [10]：-

……因将混沌系统的数学应用于物理学和宇宙学。

引文强调了他与相对论天体物理学界相关的贡献 [10]：-

对广义相对论界尤其值得注意的是，他在1983年与叶夫根尼·利夫希茨、I M Khalatnikov、K M Khanin 和 L N Shchur 合作的开创性论文中，关于早期宇宙学随机本质的基本结果。列夫·朗道曾将初始宇宙奇点问题指定为理论物理学的三个基本问题之一，而他学派的成员 V Belinski、I Khalatnikov 和叶夫根尼·利夫希茨随后在1969年至1970年代的一系列论文中，找到了大爆炸或大挤压奇点附近的一般宇宙学解。这个“BKL解”产生了一个混沌动力系统，其特征是正的安德雷·柯尔莫哥洛夫-西奈熵。BKL解的高维类似物的混沌行为也已被 T Damour、M Henneaux 和 H Nicolai 破译。因此，安德雷·柯尔莫哥洛夫-西奈学派的结果阐明了BKL宇宙学解的随机本质。

列夫·朗道研究所的首席计算物理研究员 Lev Shchur 解释了西奈参与这篇1983年论文的经过 [33]：-

有一次，我们正在研究一个当时很时髦的宇宙学问题，在解决它的过程中，我们强烈怀疑答案可以精确得到，而不仅仅是数值近似。我们打电话给西奈，分享了我们的猜测。他思考了两分钟，说：“如果它能被解决，那么只能这样解决。”两小时后，解决方案就准备好了。除其他事项外，这表明他在团队中工作得多么出色。当一位年轻科学家在研讨会上走近他并谈论某事时，西奈可以轻松地回答：“你在做这个吗？我这里也有想法，我们一起做吧。”

许多数学学会和科学院选举西奈为会员或荣誉会员：American Academy of Arts and Sciences（1983年）；USSR Academy of Sciences（1991年）；London Mathematical Society（1992年）；Hungarian Academy of Sciences（1993年）；United States National Academy of Sciences（1999年）；Brazilian Academy of Sciences（2000年）；欧洲科学院（2008年）；Royal Society of London（2009年）；American Mathematical Society，会士（2013年）；以及挪威科学与文学院（2014年）。他获得了以下荣誉学位：华沙大学（1993年）；布达佩斯科技经济大学（2002年）；耶路撒冷希伯来大学（2005年）；以及华威大学（2010年）。

西奈还受邀做了许多著名讲座或系列讲座，包括：哈佛大学Loeb讲师（1978年）；柏林国际数学物理大会全会发言人（1981年）；马赛国际数学物理大会全会发言人（1986年）；以色列杰出讲师（1989年）；墨西哥所罗门·莱夫谢茨讲座（1990年）；京都国际数学家大会全会发言人（1990年）；耶路撒冷希伯来大学埃德蒙·朗道讲座（1993年）；第一届拉丁美洲数学大会全会发言人（2000年）；American Mathematical Society会议“数学的挑战”全会发言人（2000年）；德国柏林Andreevski讲座（2001年）；加州大学乔治·伯克利分校Bowen讲座（2001年）；加州理工学院Leonidas Alaoglu纪念讲座（2002年）；哥伦比亚大学约瑟夫·里特讲座（2004年）；意大利米兰列奥纳多·达·芬奇讲座（2006年）；意大利比萨伽利略讲席（2006年）；爱尔兰都柏林三一学院都柏林高等研究院和威廉·哈密顿数学研究所弗瑞兹·约翰 T Lewis系列讲座（2007年）；以及德克萨斯州休斯顿莱斯大学Milton Brockett Porter系列讲座（2007年）。

2005年他七十岁生日时，Moscow Mathematical Journal的一期特刊献给了西奈：-

西奈是我们这个时代最伟大的数学家之一。为表彰他的科学贡献而授予他的国际奖项清单极其长，他的基本成果清单甚至更长。他对数学的持久兴趣和他非凡的科学热情激励了全世界几代科学家。他仅仅出现在研讨会或会议上，就使科学生活更加明亮和令人兴奋。

1956年，西奈 Grigorievich 西奈与他的同学Elena Bentsionovna Vul结婚，她是著名物理学家Bentsion Moiseevich Vul（1903-1985）的女儿，后者对半导体和电介质物理学做出了重大贡献。Elena是一位数学家和物理学家，她与丈夫合写了许多论文；其中七篇列在[29]中。他们有一个儿子。

西奈在数学之外的兴趣是什么？小时候，他擅长国际象棋，但更喜欢足球和排球。后来他喜欢下坡滑雪和越野滑雪。他热爱户外，经常去远足和登山。

让我们以一些最了解他的人的引述作为结束。弗洛伦斯·南丁格尔·大卫，普林斯顿大学Hughes-Rogers数学讲席教授，在西奈被授予尼尔斯·阿贝尔奖[8]后说：-

我相信 西奈 无疑是20世纪和21世纪最伟大的数学家之一，当然也是最具有影响力的数学家之一。他对在他手下工作的年轻人也产生了巨大的影响。50年来，他一直在培养一流的学生。

普林斯顿大学负责研究的院长 Pablo Debenedetti 说 [8]：-

他被广泛认为是20世纪最有影响力的数学家之一，而这个奖项无疑是数学界最负盛名的奖项之一。这是对一段辉煌职业生涯的绝佳认可。

特拉维夫大学教授、埃尔德什 奖得主 Leonid Polterovich 说 [31]：-

我并不是很惊讶[西奈 获得了 尼尔斯·阿贝尔 奖]，因为我一直知道他是顶尖水平的。……像莫斯科国立大学的所有教授一样，西奈 没有个人办公室，而是与大约十位其他数学家共用一个小房间。我会在 西奈 的办公室里见到 西奈 和他其他的学生；西奈 讨论的话题从数学物理到几何都有。学生们有机会了解彼此的项目，这相当重要，因为 西奈 是一位非常广博的科学家。……西奈 的讨论班对我们来说是一扇通往科学世界的大门。……他是一位英俊且体格极佳的人，所以他从事一些体育运动，举止无可挑剔，社交能力高度发达。这些特点与一种善良、友好和人性化的待人方式结合在一起。

Both of Yakov Grigorevich Sinai's parents, Grigory Sinai and Nadezda Veniaminovna Kagan, were microbiologists with research careers. Yakov's mother Nadezda died when he was three years old having been infected by viral encephalitis while working in her own laboratory on making a vaccine. The family had strong mathematical connections since Yakov Grigorevich's grandfather (Nadezda Kagan's father) was Benjamin Fedorovich Kagan, the Head of the Department of Differential Geometry at Moscow State University where he founded an important School of Differential Geometry. It is also worth recording that the family was Jewish, and Kagan had a long struggle against anti-Semitism. It was, however, a family which had, over several generations, taken a leading role in Russian scientific and cultural life. Kagan had a large influence on his grandson. He retired from his chair at Moscow State University in 1952, the year in which his grandson Yakov Grigorevich entered the Faculty of Mechanics and Mathematics. There is one other member of the family we should mention, namely Grigory Isaakovich Barenblatt (1927-2018). He was the son of Isaak Grigorievich Barenblatt and Nadezda Veniaminovna Kagan, so was Yakov Sinai's half brother. He studied under Boris Moiseevich Levitan (1914-2004) and Andrei Nikolaevich Kolmogorov in the Department of Mechanics and Mathematics of Moscow State University and graduated in 1950. Two years later he married Iraida Nikolaevna Kochina, one of the two daughters of Nikolai Evgrafovich Kochin and Pelageia Polubarinova Kochina.

Talking about his school years, Sinai said [17]:-

I participated in many olympiads in mathematics during my school years but never had any success and never won any awards. I say this to young people who have never won in olympiads; there may be compensation in the future. At this time, my grandfather was of a great age and he did not have the energy to push me into mathematics. And I also have a half-brother, G I Barrenblatt, who worked at Moscow State University and who was convinced that I should pursue a career in mathematics.

German armies invaded the Soviet Union in May 1941 and came close to Moscow by October of that year. By this time Yakov Grigorevich was six years old and had started school but an evacuation of Moscow began. It was 1943 before the Sinai family could return to Moscow. Sinai said [17]:-

I entered school in 1943 after my family returned from the evacuation of Moscow. At that time boys and girls studied separately; at the end of each year, we had about ten exams. Before the evacuation, life was different. It was forbidden to leave windows open in the apartments in Moscow because it had to be dark. In 1943 windows were allowed to be open again. In Moscow there were no clear signs of war, but life was hard because of the time of Stalin.

By the time he was sixteen years old, he was fortunate to have an excellent mathematics teacher when he was at high school in Moscow [18]:-

We had a very good teacher in mathematics at our high school. His name was Vasily Alekseevich Efremov and he was a great old-style schoolteacher. He always brought us his problems in accurate handwriting on a piece of paper which he distributed among the students. Because of the well-organised and inspiring work, mathematics was very popular among us. We discussed and tried to solve his problems. At this time I was not among the best in the class. There were definitely other students who were much better than I.

Getting into university was not easy for Sinai since he was Jewish. At this time certain Soviet universities had a deliberate discriminatory policy to prevent Jews entering. Since Sinai was Jewish, when he took the entrance examination to Moscow State University, he was failed. Only the intervention of his grandfather, Benjamin Fedorovich Kagan, and that of the President of Moscow State University, Ivan Georgievich Petrovsky, saw the decision reversed and Sinai was allowed to begin his university studies.

Sinai took an analysis course from Mikhail Alekseevich Lavrentev, a classical mechanics course from Nikolai Guryevich Chetaev, and an algebra course from Eugene Borisovich Dynkin. His first advisor at Moscow State University was Chetaev who was an expert on analytical mechanics, particularly on stability of motion. Sinai quickly became interested in the dynamical systems on which Chetaev worked. However, he changed advisors and began to work with Dynkin. The problem which Dynkin suggested that Sinai work on, led to his first paper On the distribution of the first positive sum for a sequence of independent random variables (Russian) (1957). In 1957 Sinai was awarded his first degree from Moscow State University and he began to undertake research for his Master's Degree (equivalent to a Ph.D.) working with Andrei Nikolaevich Kolmogorov. His entry into the graduate school was not straightforward, however, since again he had to take entrance examinations. He was required to take an examination on the History of the Communist Party and, being a topic in which he had no interest, he failed. Pavel Sergeevich Aleksandrov was head of mathematics and he, together with Kolmogorov, went to see the Head of the History of the Party Department and asked that Sinai be allowed to resit. He took another History of the Communist Party examination and passed with grade B. It was deemed marginally good enough to let him begin graduate studies.

He was awarded a Master's Degree in 1960 and, in the same year, was appointed as a Scientific Researcher at the Laboratory of Probabilistic and Statistical Methods at Moscow State University. He continued to work towards his doctorate (equivalent to the German habilitation) under Kolmogorov. Other members of staff had a major influence on him at this time, particularly Israil Moiseevic Gelfand and Vladimir Abramovich Rokhlin who led the seminar on the metric theory of dynamical systems. Sinai's papers published around the time he was working for his Master's Degree include: On the concept of entropy for a dynamic system (Russian) (1959); Flows with finite entropy (1959) (Russian); The central limit theorem for geodesic flows on manifolds of constant negative curvature (1960) (Russian); and Dynamical systems and stationary Markov processes (1960) (Russian).

Already, in the first of these 1959 papers, Sinai gives theorems which make it possible to calculate the entropy for a large variety of dynamical systems. The term 'Kolmogorov-Sinai entropy' was quickly established [20]:-

Sinai's work deals with measuring dynamical systems, or systems that change over time, such as weather, the motion of planets and economic systems. These systems can be accurately measured in the short term (short term being relative to the issue at hand); but when analysed in the long term, the systems are difficult to understand and predict. Sinai was the first to come up with a mathematical foundation for determining the number that defines the complexity of a given dynamical system. His mathematical system is called Kolmogorov-Sinai entropy.

The high quality and importance of Sinai's papers led to him being invited to lecture at the International Congress of Mathematicians in Stockholm in 1962. Dynkin and Gelfand were both invited plenary speakers but did not attend. Kolmogorov did attend the Congress and read Dynkin's lecture. Sinai delivered the half-hour address Probabilistic ideas in ergodic theory on the invitation of the Organising Committee. He also read Dmitrii Viktorovich Anosov's Short Address, The roughness of geodesic currents in compact Riemannian manifolds of negative curvature.

In 1971, following Sergei Petrovich Novikov's advice, Sinai accepted a position as Senior Researcher at the L D Landau Institute of Theoretical Physics of the USSR Academy of Sciences. Novikov had just been appointed as head of the Mathematics Division at the Institute. Sinai continued to teach at Moscow State University but he did not become a professor there until 1981. The authors of [12] explain the reasons:-

His signing (together with many other mathematicians) in 1968 of the well-known letter in defence of A S Esenin-Vol'pin was for a long time a barrier preventing his becoming a Professor (he became a Professor only in 1981, 17 years after submitting his Ph.D. thesis).

Alexander Sergeyevich Esenin-Volpin was both a poet and a mathematician who led a human rights movement in the Soviet Union. Beginning in 1949, Volpin spent many years in prison for anti-Soviet poetry or in exile as a socially dangerous person. Sinai suffered much for his support of Volpin. For example in 1970 he was invited to lecture at the International Congress of Mathematicians in Nice. However, he was not allowed to go to Nice by the Soviet authorities. Many others were also prevented from attending the Nice Congress including Dynkin, Gelfand, Linnik, Manin, Shafarevich and Sergei Novikov who should have received a Fields Medal at the Congress. Sinai, however, was able to accept the invitation to deliver one of the plenary lectures at the International Congress of Mathematicians in Kyoto in 1990; he spoke on Hyperbolic Billiards. Continuing with his contributions to the International Congress of Mathematicians, we note that in 2001 he was appointed Chairman of the Fields Medal Committee of International Mathematical Union which decided on the awards of the Fields Medals at the Congress in Beijing in the following year.

In 1993 he was appointed Professor in the Department of Mathematics at Princeton University. He continued with his appointment at the L D Landau Institute of Theoretical Physics but gave up his position at Moscow State University. During 1997-1998 he was Thomas Jones Professor of Princeton University and in 2005 he was Moore Distinguished Scholar at the California Institute of Technology at Pasadena, California. He continued to hold his professorship at Princeton University until 2023 when he became professor emeritus. He continues (in 2023) to hold a professorship at the L D Landau Institute of Theoretical Physics in Moscow.

We have already looked at the deep contribution which was made by Sinai early in his career. Perhaps the best summary of his achievements up to the start of the 1990s is given in [5]:-

Sinai has done foundational, deep and highly influential work in the fields of ergodic theory, dynamical systems and statistical mechanics. Already in the sixties he had a deep understanding of the principles of what is now called chaos, and was among the first to recognise the significance of this phenomenon for dynamics. He has also done fundamental work in statistical mechanics. Besides his many major contributions to these subjects, he has had a very wide influence through a number of well-known expository texts and through his many research students.

Sinai's work centres round the grand aim of deriving the basic physical laws which describe the behaviour of many particle systems as a direct consequence of simple rules governing the interaction of individual particles. In this he has had some remarkable successes. In ergodic theory his work on hyperbolic systems, on billiards and the hard sphere gas has laid the foundation of many of the techniques presently used for proving that such systems are ergodic and for studying the finer statistical properties of their behaviour. He has influenced the general trend of ergodic theory away from the study of rather artificially constructed examples back to the problem which originally motivated the subject, namely the substantiation of Boltzmann's ergodic hypothesis.

The idea of applying the Kolmogorov theory of entropy to smooth dynamical systems was Sinai's. Previous work of the Russian school had studied entropy, as introduced by Kolmogorov, entirely in the context of probabilistic systems. His results in this direction were new and unexpected. He investigated the class of dynamical systems with transversal foliations, now known as stable and unstable manifolds, and proved that all systems in this class were ergodic, mixing and K. Subsequently he introduced the idea of Markov partitions and constructed such partitions for hyperbolic systems.

Sinai laid the foundations of the theory of billiards, for which he has more recently also constructed Markov partitions, and of the motion of a hard sphere gas. He has made many contributions to statistical mechanics, in particular to the theory of phase transition. His book on this topic is well known. In recent years, Sinai has made important contributions to KAM theory using renormalisation methods. He is currently developing some entirely new and very interesting ideas in quantum chaos.

It is remarkable, given the depth and originality of Sinai's papers that he has been so productive. In [29] there are 386 papers listed with Sinai as author or co-author. Yet Sinai finds writing papers the least interesting part of doing research. He considers it boring since he has already achieved his aim of solving the problem which he may have thought about for several years and spent periods in which everything else had to be put out of his mind.

Sinai has received many major awards, prizes and honours for his remarkable contributions. For example he has received the following medals and prizes: the Boltzmann Gold Medal from the Commission on Statistical Physics of the International Union of Pure and Applied Physics (1986); the Heineman Prize from the American Physical Society (1989); the Markov Prize from the USSR Academy of Sciences (1990); the Dirac Medal from the Abdus Salam International Centre for Theoretical Physics in Trieste (1992); the Wolf Prize in Mathematics (1997); the Brazilian Award of Merits in Sciences (2000); the Moser Prize from the Society for Industrial and Applied Mathematics (2001); the Frederic Esser Nemmers Prize in Mathematics (2002); the Kolmogorov Lecture and Medal, University of London (2007); the Lagrange Prize from the Institute for Scientific Interchange, Torino, Italy (2008); the Henri Poincaré Prize from the International Association of Mathematical Physics (2009); the Dobrushin International Prize from the Institute of Information Transmission of the USSR Academy of Sciences (2009), the Leroy P Steele Prize (2013), the Abel Prize (2014), and the Marcel GrossmannAward (2015).

Here are some extracts from the citations for these awards. The Wolf Prize (1997) [7]:-

Sinai received the prize for "his fundamental contributions to mathematically rigorous methods in statistical mechanics and the ergodic theory of dynamical systems and their applications in physics." Sinai brings to bear on the problems of mathematical physics the powerful tools of dynamical systems and probability theory, often developing new tools for this purpose. He is generally recognized as the world leader in the mathematics of statistical physics. Working in the tradition of the Kolmogorov school, he first formulated the rigorous definition of the invariant entropy for an arbitrary measure-preserving map. His subsequent work covers areas from the ergodicity of the motion of billiards to spectral properties of quasi-periodic Schrödinger operators. Statistical mechanics is one of the most active and rewarding areas of modern mathematics, and Yakov Sinai is its recognised leader today.

The 2002 Frederic Esser Nemmers Prize in Mathematics [20]:-

His work has revolutionised the study of dynamical systems and influenced statistical mechanics, probability theory and statistical physics.

The Henri Poincaré Prize (2009) was awarded to Sinai:-

... for his ground-breaking works concerning dynamical entropy, ergodic theory, chaotic dynamical systems, microscopic theory of phase transitions, and time evolution in statistical mechanics.

The Leroy P Steele Prize for Lifetime Achievement was presented to Sinai on Thursday, 10 January 2013, at the joint meeting of the American Mathematical Society and the Mathematical Association of America held in San Diego. The Prize was awarded to Sinai for [26]:-

... his pivotal role in shaping the theory of dynamical systems and for his ground-breaking contributions to ergodic theory, probability theory, statistical mechanics, and mathematical physics.

The Citation states:-

Sinai's research exhibits a unique combination of brilliant analytic technique, outstanding geometric intuition, and profound understanding of underlying physical phenomena. His work highlights deep and unexpected connections between dynamical systems and statistical mechanics. ... In the past fifteen years Sinai has brought novel tools and insights from dynamical systems and mathematical physics to statistical hydrodynamics, obtaining new results for the Navier-Stokes systems. Specifically, along with D Li, Sinai devised a new renormalisation scheme which allows the proof of existence of finite time singularities for complex solutions of the Navier-Stokes system in dimension three. Sinai's mathematical influence is overwhelming. During the past half-century he has written more than 250 research papers and a number of books. Sinai's famous monograph, 'Ergodic Theory' (with Cornfeld and Fomin), has been an introduction to the subject for several generations, and it remains a classic.

In 2014 Sinai was awarded, what many would say is the most prestigious mathematical prize of all, namely the Abel Prize for his [1]:-

... fundamental contributions to dynamical systems, ergodic theory, and mathematical physics.

The citation for the award ends with the words [28]:-

Sinai has trained and influenced a generation of leading specialists in his research fields. Much of his research has become a standard toolbox for mathematical physicists. His works had and continue to have a broad and profound impact on mathematics and physics, as well as on the ever-fruitful interaction of these two fields.

Stein Arne Nistad gives an interesting description of the award ceremony [32]:-

When Yakov Sinai entered the university Aula in Oslo to receive this year's Abel Prize, an award as rare and prestigious as a Nobel Prize in physics or medicine, the gathering of dignitaries and great minds was one of the smartest likely to attend an event in the Norwegian capital this year. On the walls, eleven monumental murals by Norwegian artist Edvard Munch illuminated the vast hall with images of northern light and the ages of man. The audience included academics from home and abroad, national and international press, and a broad selection of people all with an above-average interest in the field of mathematics. The musicians entered the scene and the youthful Crown Prince Haakon, representing his father, handed over the beautiful and weighty Abel prize almost deferentially to the slightly stooped, academic giant.

As part of the Abel Prize presentation, Arne B Sletsjøe wrote four elementary articles which illustrate ideas introduced by Yakov Sinai, which you can see at THIS LINK.

In 2015 Sinai received the Marcel Grossmann Award [10]:-

... for applying the mathematics of chaotic systems to physics and cosmology.

The Citation stresses his contributions relevant to the relativistic astrophysics community [10]:-

Particularly noteworthy for the general relativity community are his fundamental results on the stochastic nature of early cosmology obtained in his pioneering 1983 paper in collaboration with E M Lifshitz, I M Khalatnikov, K M Khanin, and L N Shchur. Landau had designated the problem of the initial cosmological singularity as one of the three fundamental problems of theoretical physics and the members of his school V Belinski, I Khalatnikov and E Lifshitz then found the general cosmological solution near a big bang or big crunch singularity in a series of papers from 1969 into the 1970s. This "BKL solution" gives rise to a chaotic dynamical system characterised by a positive Kolmogorov-Sinai entropy. The chaotic behaviour of the higher-dimensional analogues of the BKL solution has also been deciphered by T Damour, M Henneaux and H Nicolai. The results of the Kolmogorov-Sinai school have thus illuminated the stochastic nature of the BKL cosmological solution.

Lev Shchur, a leading computational physics researcher at the Landau Institute, explained Sinai's involvement in this 1983 paper came about [33]:-

Once we were working on a problem in the now fashionable field of cosmology, and in the process of solving it a strong suspicion arose that the answer could be obtained precisely, and not just a numerical approximation. We called Sinai and shared our guesses. He thought for two minutes and said: "if it can be solved, then only in this way." Two hours later the solution was ready. Among other things, this shows how well he can work in a team. When a young scientist approaches him at a seminar and talks about something, Sinai can easily answer: "Are you doing this? I have ideas here too, let's do it together."

Many mathematical societies and academies have elected Sinai to membership or honorary membership: the American Academy of Arts and Sciences (1983); the USSR Academy of Sciences (1991); the London Mathematical Society (1992); the Hungarian Academy of Sciences (1993); the United States National Academy of Sciences (1999); the Brazilian Academy of Sciences (2000); the Academia Europaea (2008); the Royal Society of London (2009); American Mathematical Society, Fellow (2013); and the Norwegian Academy of Science and Letters (2014). He has received honorary degrees from: Warsaw University (1993); Budapest University of Science and Technology (2002); the Hebrew University in Jerusalem (2005); and Warwick University (2010).

Sinai has also been invited to give many prestigious lectures or lecture courses including: Loeb Lecturer, Harvard University (1978); Plenary Speaker at the International Congress on Mathematical Physics in Berlin (1981); Plenary Speaker at the International Congress on Mathematical Physics in Marseilles (1986); Distinguished Lecturer, Israel (1989); Solomon Lefschetz Lectures, Mexico (1990); Plenary Speaker at the International Congress of Mathematicians, Kyoto (1990); Landau Lectures, Hebrew University of Jerusalem (1993); Plenary Speaker at the First Latin American Congress in Mathematics (2000); Plenary Speaker at the American Mathematical Society Meeting "Challenges in Mathematics" (2000); Andreevski Lectures, Berlin, Germany (2001); Bowen Lectures, University of California at Berkeley (2001); Leonidas Alaoglu Memorial Lecture, California Institute of Technology (2002); Joseph Fels Ritt Lectures, Columbia University (2004); Leonardo da Vinci Lecture, Milan, Italy (2006); Galileo Chair, Pisa, Italy (2006); John T Lewis Lecture Series, Dublin Institute for Advanced Studies and the Hamilton Mathematics Institute, Trinity College, Dublin, Ireland (2007); and Milton Brockett Porter Lecture Series, Rice University, Houston, Texas (2007).

For his seventieth birthday in 2005 a special issue of the Moscow Mathematical Journal was dedicated to Sinai:-

Yakov Grigorievich Sinai is one of the greatest mathematician of our days. The list of international prizes awarded to him as a sign of recognition of his scientific contributions is extremely long, the list of his fundamental results being even longer. His permanent interest in mathematics and his exceptional scientific enthusiasm inspires several generations of scientists all over the world. His mere presence at a seminar or at a conference makes scientific life brighter and more exciting.

In 1956 Yakov Grigorievich Sinai married his fellow student Elena Bentsionovna Vul, daughter of the famous physicist Bentsion Moiseevich Vul (1903-1985) who made a major contribution to the physics of semiconductors and dielectrics. Elena is a mathematician and physicist who has written a number of joint papers with her husband; seven are listed in [29]. They have one son.

What are Sinai's interests outside mathematics? As a young boy, he was good at chess but preferred football and volleyball. Later he liked both downhill and cross-country skiing. He loved the outdoors and often went hiking and mountaineering.

Let us end with some quotes from those who know him best. David Gabai, the Hughes-Rogers Professor of Mathematics at Princeton University, said after Sinai was awarded the Abel Prize [8]:-

I believe Sinai is definitely one of the great mathematicians of the 20th and 21st centuries and certainly one of the most influential mathematicians. He's also been a tremendous influence to the young people who have worked underneath him. For 50 years he's been producing stellar students.

The Dean for Research at Princeton University, Pablo Debenedetti, said [8]:-

He's widely considered to be one of the most influential mathematicians of the 20th century and this prize is unquestionably one of the most prestigious in mathematics. It's a wonderful recognition of a wonderful career.

Tel Aviv University professor and Erdős Prize winner Leonid Polterovich said [31]:-

I was not very surprised [Sinai received the Abel Prize] because I always knew that he was on the top level. ... Like all professors at Moscow State University, Sinai did not have a personal office, but shared a small room with about ten other mathematicians. I would meet in Sinai's office with Sinai and the rest of his advisees; topics discussed by Sinai ranged from mathematical physics to geometry. Students got the opportunity to learn about each others' projects, which was pretty important because Sinai was a very broad scientist. ... Sinai's seminar served for us as a door into the scientific world. ... He was a handsome man in an excellent physical shape, so he was doing some sports, had impeccable manners and highly developed social skills. These features were combined with a kind, friendly and human approach to people.