原文:Davide Castelvecchi
Michel Talagrand奠定的数学基础帮助其他人解决了涉及随机过程的问题。
Michel Talagrand专门研究随机过程,这种数学模型描述受随机性约束的现象。来源:Peter Bagde/Typos1/Abel Prize 2024
一位数学家因为提出了让随机过程更可预测的公式并帮助解决了一个复杂现象模型,被授予2024年阿贝尔奖(Abel Prize)。阿贝尔奖是数学界的最高荣誉之一。挪威科学与文学院3月20日在奥斯陆宣布,Michel Talagrand因其“对概率理论和泛函分析的贡献而得奖,其成果在数学物理学和统计学方面具有杰出应用”。
美国普林斯顿大学数学家Assaf Naor表示,Talagrand所做工作的影响力再怎么称赞也不为过。他说:“如今可能每天都有论文要加一句‘现在我们使用Talagrand的不等式’。”
Talagrand在听到获奖消息后感到难以置信。“我的大脑突然一片空白了至少4秒,”他说,“如果你和我说白宫前停了一艘外星飞船,我都不会这么震惊。”
阿贝尔奖以诺贝尔奖为参照,因为诺贝尔奖不含数学奖。阿贝尔奖首次于2003年颁奖,得奖者可以获得750万挪威克朗(约合70万美元)。
“像一件艺术品”
Talagrand专门研究概率论和随机过程,即描述受随机性约束的现象的数学模型。Talagrand说,一个典型例子是河流水位,河流水位高度易变,受到诸多独立因素的影响,包括雨、风和温度。他最自豪的成就是他的不等式,这是一组能对随机过程的变化加以约束的公式。他的公式表述了许多因素的贡献如何经常相互抵消,从而使整体结果的变化更少而不是更多。
“就像一件艺术品,”阿贝尔奖委员会主席、挪威科技大学的数学家Helge Holden说,“这里的魔法是找到一个好的估计,而不是一个粗略的估计。”
Naor说,多亏了Talagrand的方法,“许多看起来复杂又随机的事其实并不是那么随机。”他的估计值非常厉害,比如用来研究如何优化送货卡车路线这类问题。找到一个完美的解需要海量运算,而现在计算科学家只要计算有限数量的随机候选路线的长度再取平均值就可以了——Talagrand的不等式确保结果与最优解很接近。
Talagrand还完成了理论物理学家Giorgio Parisi提出的一个问题的解——这个工作最终帮助Parisi拿到了2021年诺贝尔物理学奖。1979年,现就职于罗马大学的Parisi提出了自旋玻璃结构的一个全解,在这个材料的抽象模型中,每个原子的磁化会根据相邻原子的磁化而向上或向下。
Talagrand说,Parisi的论证来自他对物理学的超强感知力,他遵循的是“数学家看来像巫术般”的步骤,比如取一个系统的
n个拷贝,
n为负数。许多研究人员质疑Parisi的证据在数学上是否严谨。但在2000年代初,这个问题被两项独立研究完全解决,一个来自Talagrand
[2],另一个来自同在罗马大学的数学物理学家Francesco Guerra
[3]。
发现动力
Talagrand成为杰出研究人员的道路有点非比寻常。他1952年出生于法国贝济耶,5岁时因为视网膜脱离的遗传倾向而右眼失明。他在里昂长大,小时候虽然对大众科学杂志爱不释手,但他学习成绩并不好,他对复杂的法语拼写规则特别不擅长。他在2019年的一次采访中表示,“我和正字法(orthography)从来没有和解过。”
15岁时,他迎来了人生的转折点。他因为左眼视网膜脱落而接受紧急治疗。为此他几乎停学一年。几近失明的可怕经历以及他父亲在他双眼被包扎时让他分心的努力,让他找到了新的人生焦点。他康复后开始非常主动地学习,逐渐在国家数学竞赛中崭露头角。
不过,Talagrand和法国大多数天赋型学生走了不同的道路——常见的道路是两年的预科班然后进入淘汰率很高的大学校(
grandes écoles) ,比如巴黎的高等师范学校
(École Normale Supérieure)。但Talagrand去了法国里昂大学,然后在法国国家科学研究中心
(CNRS)担任全职研究员——先在里昂后来去了巴黎,并在一个初级岗位上一干就是十多年。除了在加拿大工作过一小段时间,以及在美国遇到了他的妻子之外,他一直在CNRS工作到退休。
Talagrand喜欢向其他数学家发起挑战,给能解决他提出问题的人发现金奖励,他在自己的网站上给这些问题列了一张表。其中一些已经解决,并在主要的数学期刊上发表。但奖励也有条件:“我会发以下奖金,只要我还没有老到看不懂我收到的证明。但如果我看不懂,我是不会付钱的。”
参考文献:
Talagrand, M.
Publ. Math. IHES 81, 73–205, (1995).
Talagrand, M.
Ann. Math. 163, 221–263 (2006).
Guerra, F.,
Commun. Math. Phys. 233, 1–12 (2003).
原文以
Mathematician who tamed randomness wins Abel Prize标题发表在2024年3月20日《自然》的
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.6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media screen and (min-width:1024px){body:not(.pages_skin_pc) .wx-root[data-weui-theme=dark],body:not(.pages_skin_pc) body[data-weui-theme=dark]{--appmsgExtra-BG: #121212}}@media screen and (min-width:1024px){body:not(.pages_skin_pc)body:not(.pages_skin_pc){background:var(--weui-BG-2)}}@media screen and (min-width:1024px) and (prefers-color-scheme:dark){body:not(.pages_skin_pc) .wx-root[data-weui-mode=care]:not([data-weui-theme=light]),body:not(.pages_skin_pc) body[data-weui-mode=care]:not([data-weui-theme=light]){--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .85);--weui-FG-HALF: rgba(255, 255, 255, .65);--weui-FG-1: rgba(255, 255, 255, .55);--weui-FG-2: rgba(255, 255, 255, .35);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media screen and (min-width:1024px) and (prefers-color-scheme:dark){body:not(.pages_skin_pc) .wx-root:not([data-weui-theme=light]),body:not(.pages_skin_pc) body:not([data-weui-theme=light]){--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .8);--weui-FG-HALF: rgba(255, 255, 255, .6);--weui-FG-1: rgba(255, 255, 255, .5);--weui-FG-2: rgba(255, 255, 255, .3);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media screen and (min-width:1024px) and (prefers-color-scheme:dark){body:not(.pages_skin_pc) .wx-root:not([data-weui-theme=light]),body:not(.pages_skin_pc) body:not([data-weui-theme=light]){--appmsgExtra-BG: #121212}}@media(prefers-color-scheme:dark){body:not([data-weui-theme=light]).my_comment_empty_data{background-color:#111}}body,.wx-root{--weui-BG-6: rgba(0, 0, 0, .05);--weui-ACTIVE-MASK: rgba(0, 0, 0, .05)}body,.wx-root{--weui-REDORANGE: #ff6146;--weui-BG-0: #ededed;--weui-BG-1: #f7f7f7;--weui-BG-2: #fff;--weui-BG-3: #f7f7f7;--weui-BG-4: #4c4c4c;--weui-BG-5: #fff;--weui-FG-0: rgba(0, 0, 0, .9);--weui-FG-HALF: rgba(0, 0, 0, .9);--weui-FG-1: rgba(0, 0, 0, .55);--weui-FG-2: rgba(0, 0, 0, .3);--weui-FG-3: rgba(0, 0, 0, .1);--weui-FG-4: rgba(0, 0, 0, .15);--weui-FG-5: rgba(0, 0, 0, .05);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #fa9d3b;--weui-YELLOW: #ffc300;--weui-GREEN: #91d300;--weui-LIGHTGREEN: #95ec69;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1485ee;--weui-PURPLE: #6467f0;--weui-WHITE: #fff;--weui-LINK: #576b95;--weui-TEXTGREEN: #06ae56;--weui-FG: #000;--weui-BG: #fff;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: #fa9d3b;--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: #06ae56;--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: #10aeff;--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(0, 0, 0, .5);--weui-TAG-BACKGROUND-BLACK: rgba(0, 0, 0, .05)}body,.wx-root{--weui-BG-0: #ededed;--weui-BG-1: #f7f7f7;--weui-BG-2: #fff;--weui-BG-3: #f7f7f7;--weui-BG-4: #4c4c4c;--weui-BG-5: #fff;--weui-FG-0: rgba(0, 0, 0, .9);--weui-FG-HALF: rgba(0, 0, 0, .9);--weui-FG-1: rgba(0, 0, 0, .55);--weui-FG-2: rgba(0, 0, 0, .3);--weui-FG-3: rgba(0, 0, 0, .1);--weui-FG-4: rgba(0, 0, 0, .15);--weui-FG-5: rgba(0, 0, 0, .05);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #fa9d3b;--weui-YELLOW: #ffc300;--weui-GREEN: #91d300;--weui-LIGHTGREEN: #95ec69;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1485ee;--weui-PURPLE: #6467f0;--weui-WHITE: #fff;--weui-LINK: #576b95;--weui-TEXTGREEN: #06ae56;--weui-FG: #000;--weui-BG: #fff;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: #fa9d3b;--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: #06ae56;--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: #10aeff;--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(0, 0, 0, .5);--weui-TAG-BACKGROUND-BLACK: rgba(0, 0, 0, .05)}.wx-root,body{--weui-BTN-ACTIVE-MASK: rgba(0, 0, 0, .1)}.wx-root,body{--weui-BTN-DEFAULT-ACTIVE-BG: #e6e6e6}.wx-root,body{--weui-DIALOG-LINE-COLOR: rgba(0, 0, 0, .1)}.wx-root,body{--weui-BG-COLOR-ACTIVE: #ececec}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BTN-ACTIVE-MASK: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BTN-DEFAULT-ACTIVE-BG: rgba(255, 255, 255, .126)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-DIALOG-LINE-COLOR: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--APPMSGCARD-BG: #1E1E1E}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--APPMSGCARD-LINE-BG: rgba(255, 255, 255, .07)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-COLOR-ACTIVE: #373737}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-6: rgba(255, 255, 255, .1);--weui-ACTIVE-MASK: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-REDORANGE: #ff6146;--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .8);--weui-FG-HALF: rgba(255, 255, 255, .6);--weui-FG-1: rgba(255, 255, 255, .5);--weui-FG-2: rgba(255, 255, 255, .3);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--discussInput-BG: rgba(255, 255, 255, .03)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--nickName-FG: #959595}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .8);--weui-FG-HALF: rgba(255, 255, 255, .6);--weui-FG-1: rgba(255, 255, 255, .5);--weui-FG-2: rgba(255, 255, 255, .3);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--appmsgExtra-BG: #121212}}@media screen and (min-width:1024px){body:not(.pages_skin_pc) :root{--appmsgPageGap: 20px;--appmsgPageBottomGap: 40px}}:root{--articleFontsize: 17px}:root{--sab: env(safe-area-inset-bottom)}:root{--wxBorderAvatarRatio: 3}:root{--discussPageGap: 20px}:root{--immersive-safe-bottom: env(safe-area-inset-bottom)}:root{--appmsgPageGap: 20px;--appmsgPageBottomGap: 40px}
div.autoTypeSetting24psection > p,div.autoTypeSetting24psection > section{margin-bottom: 24px;}