<div dir="ltr">

<header id="gmail-story-header" class="gmail-story-header" style="display:block;margin-right:0px;margin-left:0px;color:rgb(51,51,51);font-family:cheltenham;font-size:16px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><div id="gmail-story-meta" class="gmail-story-meta" style="margin-bottom:20px"><h3 id="gmail-kicker" class="gmail-kicker" style="font-size:0.75rem;line-height:1rem;font-weight:300;font-style:normal;font-family:cheltenham-normal-300,georgia,"times new roman",times,serif;margin:0px 0px 32px;text-transform:uppercase;letter-spacing:0.075em;color:rgb(0,0,0)"><span class="gmail-kicker-label" style="font-size:0.8125rem;line-height:1rem;font-weight:700;font-style:normal;font-family:nyt-franklin,arial,helvetica,sans-serif;letter-spacing:0.05em"><a href="https://www.nytimes.com/section/science" style="text-decoration:none;color:rgb(0,0,0)">SCIENCE</a></span></h3><h1 id="gmail-headline" class="gmail-headline" style="font-size:2.125rem;line-height:2.375rem;font-weight:700;font-style:italic;font-family:cheltenham-italic-700,georgia,"times new roman",times,serif;margin:0px 0px 10px;font-feature-settings:'kern' 1;color:rgb(0,0,0)">Robert P. Langlands Is Awarded the Abel Prize, a Top Math Honor</h1><div id="gmail-story-meta-footer" class="gmail-story-meta-footer" style="border-top:1px solid rgb(226,226,226);padding-top:14px;border-bottom:1px solid rgb(226,226,226);padding-bottom:16px;display:flex"><p class="gmail-byline-dateline" style="margin:0px 45px 3px 0px;font-size:1rem;line-height:17px;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif"><span class="gmail-byline" style="font-size:0.6875rem;line-height:0.75rem;font-weight:700;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;margin-right:12px">By<span> </span><a href="https://www.nytimes.com/by/kenneth-chang" title="More Articles by KENNETH CHANG" style="text-decoration:none;color:rgb(0,0,0)"><span class="gmail-byline-author" style="white-space:nowrap">KENNETH CHANG</span></a></span><time class="gmail-dateline" datetime="2018-03-20T18:49:08-04:00" style="white-space:nowrap;font-size:0.6875rem;line-height:0.75rem;font-weight:300;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;color:rgb(0,0,0);margin-left:0px">MARCH 20, 2018</time></p><div class="gmail-story-meta-footer-sharetools" style="margin-top:0px;display:flex"><div id="gmail-sharetools-story-meta-footer" class="gmail-sharetools gmail-theme-classic gmail-sharetools-story-meta-footer"><a class="gmail-visually-hidden gmail-skip-to-text-link" href="https://www.nytimes.com/2018/03/20/science/robert-langlands-abel-prize-mathematics.html?hpw&rref=science&action=click&pgtype=Homepage&module=well-region&region=bottom-well&WT.nav=bottom-well#story-continues-1" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden;text-decoration:none;color:rgb(50,104,145)">Continue reading the main story</a><span class="gmail-sharetools-label gmail-visually-hidden" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Share This Page</span><ul class="gmail-sharetools-menu" style="margin:0px;list-style:none;padding-left:0px;display:flex"><li class="gmail-sharetool gmail-facebook-sharetool" style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;margin-right:15px"><a style="text-decoration:none;color:rgb(50,104,145);display:inline-block"><i class="gmail-icon gmail-sprite-icon" style="display:inline-block;line-height:0;vertical-align:middle;font-style:normal;background-image:url("/assets/article/20180316-205148/images/sprite/sprite-no-repeat.svg");background-repeat:no-repeat;background-position:-66px -54px;width:25px;height:25px"></i><span class="gmail-sharetool-text" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Share</span></a></li><li class="gmail-sharetool gmail-twitter-sharetool" style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;margin-right:15px"><a style="text-decoration:none;color:rgb(50,104,145);display:inline-block"><i class="gmail-icon gmail-sprite-icon" style="display:inline-block;line-height:0;vertical-align:middle;font-style:normal;background-image:url("/assets/article/20180316-205148/images/sprite/sprite-no-repeat.svg");background-repeat:no-repeat;background-position:-129px -297px;width:25px;height:25px"></i><span class="gmail-sharetool-text" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Tweet</span></a></li><li class="gmail-sharetool email-sharetool" style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;margin-right:15px"><a style="text-decoration:none;color:rgb(50,104,145);display:inline-block"><i class="gmail-icon gmail-sprite-icon" style="display:inline-block;line-height:0;vertical-align:middle;font-style:normal;background-image:url("/assets/article/20180316-205148/images/sprite/sprite-no-repeat.svg");background-repeat:no-repeat;background-position:-152px -21px;width:25px;height:25px"></i><span class="gmail-sharetool-text" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Email</span></a></li><li class="gmail-sharetool gmail-show-all-sharetool" style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;margin-right:15px"><a style="text-decoration:none;color:rgb(50,104,145);display:inline-block"><i class="gmail-icon gmail-sprite-icon" style="display:inline-block;line-height:0;vertical-align:middle;font-style:normal;background-image:url("/assets/article/20180316-205148/images/sprite/sprite-no-repeat.svg");background-repeat:no-repeat;background-position:-346px -243px;width:25px;height:25px"></i><span class="gmail-sharetool-text" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">More</span></a></li><li class="gmail-sharetool gmail-save-sharetool" style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;margin-right:15px;margin-left:15px"><a style="text-decoration:none;color:rgb(50,104,145);display:inline-block"><i class="gmail-icon gmail-sprite-icon" style="display:inline-block;line-height:0;vertical-align:middle;font-style:normal;background-image:url("/assets/article/20180316-205148/images/sprite/sprite-no-repeat.svg");background-repeat:no-repeat;background-position:-405px -210px;width:16px;height:25px"></i><span class="gmail-sharetool-text" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Save</span></a></li></ul></div></div></div></div></header><div class="gmail-story-body-supplemental" style="display:flex;color:rgb(51,51,51);font-family:cheltenham;font-size:16px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><div class="gmail-story-body gmail-story-body-1" style="width:630px"><figure id="gmail-media-100000005807262" class="gmail-media gmail-photo gmail-lede gmail-layout-large-horizontal" style="display:flex;margin:0px 0px 45px;clear:both;width:660px"><span class="gmail-visually-hidden" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Photo</span><div class="gmail-image" style="margin-bottom:7px"><img src="https://static01.nyt.com/images/2018/03/21/science/21MATH-2/21MATH-2-master768.jpg" alt="" class="gmail-media-viewer-candidate" style="height: auto; max-width: 100%; display: block; width: 660px;"><div class="gmail-media-action-overlay" style="border-radius:6px;opacity:0;border:1px solid rgba(200,200,200,0.8)"><i class="gmail-icon gmail-sprite-icon" style="display:inline-block;line-height:0;vertical-align:middle;font-style:normal;background-image:url("/assets/article/20180316-205148/images/sprite/sprite-no-repeat.svg");background-repeat:no-repeat;background-position:-256px -135px;width:38px;height:38px"></i></div></div><figcaption class="gmail-caption" style="display:block;font-size:0.8125rem;line-height:1.0625rem;font-weight:300;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;color:rgb(102,102,102);max-width:600px;margin-left:0px;margin-right:0px;margin-bottom:20px"><span class="gmail-caption-text">Robert P. Langlands, professor emeritus at the Institute for Advanced Study in Princeton, N.J., speaking in the fall of 2016 at a conference centered around his work.</span><span> </span><span class="gmail-credit" style="font-size:0.6875rem;line-height:1rem;font-weight:400;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;display:inline-block;color:rgb(153,153,153)"><span class="gmail-visually-hidden" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Credit</span>Dan Komoda/Institute for Advanced Study</span></figcaption></figure><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">In 1967, Robert P. Langlands set out a road map to prove a “grand unified theory” that would tie together disparate areas of mathematics.</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">The conjectures of Dr. Langlands, now 81 and an emeritus professor at the Institute for Advanced Study in Princeton, N.J., have proven fertile ground for mathematical advances in the past half-century. And although his suppositions remain far from fully proven, the Norwegian Academy of Science and Letters announced on Tuesday that Dr. Langlands was this year’s winner of<span> </span><a href="http://www.abelprize.no/" title="Website of the Abel Prize." style="text-decoration:underline;color:rgb(50,104,145)">the Abel Prize</a>, which many view as a Nobel Prize of mathematics.</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">“He’s a visionary,” said Sun-Yung Alice Chang, a mathematician at Princeton University who served on the five-member prize committee. The panel reviewed more than 100 candidates before selecting Dr. Langlands, Dr. Chang said.</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">There is no Nobel Prize in mathematics. (Contrary to myth, that is not because of an affair between a mathematician and Alfred Nobel’s wife. For one, Nobel never married.)</p><p class="gmail-story-body-text gmail-story-content" id="gmail-story-continues-1" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">For decades, the most prestigious math awards were the Fields Medals, but they are limited to mathematicians 40 years or younger, to recognize the promise of future discoveries as well as work already accomplished. The Fields medals are also only given out every four years.</p></div></div><div class="gmail-story-body-supplemental" style="display:flex;color:rgb(51,51,51);font-family:cheltenham;font-size:16px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><div class="gmail-story-body gmail-story-body-2" style="width:630px"><p class="gmail-story-body-text gmail-story-content" id="gmail-story-continues-3" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">The Abel Prize, first awarded in 2003, honors a lifetime of mathematical work and influence. It is named after Niels Hendrik Abel, a Norwegian mathematician. Previous winners include Andrew J. Wiles, a mathematician now at the University of Oxford<span> </span><a href="https://www.nytimes.com/1995/01/31/science/how-a-gap-in-the-fermat-proof-was-bridged.html" title=""How a Gap in the Fermat Proof Was Bridged," The New York Times." style="text-decoration:underline;color:rgb(50,104,145)">who proved Fermat’s Last Theorem</a>;<span> </span><a href="http://www.nytimes.com/2005/03/29/science/from-budapest-to-los-alamos-a-life-in-mathematics.html" title=""From Budapest to Los Alamos, a Life in Mathematics," The New York Times, March 29, 2005." style="text-decoration:underline;color:rgb(50,104,145)">Peter D. Lax</a><span> </span>of New York University; and<span> </span><a href="https://www.nytimes.com/2015/05/25/science/john-nash-a-beautiful-mind-subject-and-nobel-winner-dies-at-86.html" title=""John F. Nash Jr., Math Genius Defined by a ‘Beautiful Mind,’ Dies at 86," The New York Times, May 24, 2015." style="text-decoration:underline;color:rgb(50,104,145)">John F. Nash Jr.</a>, whose life was portrayed in the movie “A Beautiful Mind.”</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px"><a href="https://www.math.ubc.ca/Dept/Newsletters/Robert_Langlands_interview_2010.pdf" title="Interview of Robert Langlands at the University of British Columbia." style="text-decoration:underline;color:rgb(50,104,145)">In an interview in 2010</a>, Dr. Langlands, who was born in New Westminster, Canada, near Vancouver, recalled that even though he skipped a grade, he had no intention of going to college until a teacher “took up an hour of class time to explain to me, in the presence of all the other students, that it would be a betrayal of God-given talents for me not to attend university.”</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">At the age of 16, he enrolled at the University of British Columbia, and he later pursued his doctoral studies at Yale.</p><figure id="gmail-math-promotron" class="gmail-interactive gmail-interactive-embedded gmail-limit-small gmail-layout-sub-medium gmail-promotron gmail-default" style="display:block;margin:15px 0px 15px 60px;border-top:1px solid rgb(226,226,226);padding-top:15px;border-bottom:1px solid rgb(226,226,226);padding-bottom:15px;width:600px;overflow:hidden;max-width:495px;min-width:300px;clear:left"><figcaption class="gmail-interactive-caption" style="display:block;font-size:0.75rem;line-height:1rem;font-weight:400;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;color:rgb(102,102,102)"><h2 class="gmail-interactive-headline" style="font-size:13px;line-height:1;font-weight:700;font-style:normal;font-family:nyt-franklin,arial,helvetica,sans-serif;margin:0px 0px 3px;color:rgb(0,0,0);text-transform:uppercase">MORE REPORTING ON MATHEMATICS</h2></figcaption><div class="gmail-interactive-graphic" style="margin-bottom:10px"><div id="gmail-promotron-1501609160"><div class="gmail-promotron-embed"><ul class="gmail-promo-list" style="margin:0px;list-style:none;padding-left:0px;box-sizing:border-box;overflow:auto"><li style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;box-sizing:border-box;display:block;margin-top:20px;padding:0px 10px 0px 0px;vertical-align:top;float:left;width:247.5px;min-height:75px;clear:left"><article class="gmail-story gmail-theme-summary" style="display:block;box-sizing:border-box"><a class="gmail-story-link" href="https://www.nytimes.com/2017/07/25/science/marina-ratner-dead-mathematician.html?module=Promotron&region=Body&action=click&pgtype=article" style="display:block;color:rgb(50,104,145);box-sizing:border-box;text-decoration:none"><div class="gmail-thumb" style="box-sizing:border-box;float:left;clear:left;margin:0px 10px 0px 0px;width:75px;height:75px"><img src="https://static01.nyt.com/images/2017/07/26/obituaries/26ratner/26ratner-thumbStandard-v2.jpg" alt="" style="height: 75px; max-width: 100%; border: none; box-sizing: border-box; display: block; width: 75px;"><div class="gmail-media-action-overlay" style="box-sizing:border-box"></div></div><h2 class="gmail-story-heading" style="font-size:0.8125rem;line-height:1.0625rem;font-weight:300;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;box-sizing:border-box;color:rgb(51,51,51)"><span class="gmail-story-heading-text" style="box-sizing:border-box;padding-right:0.75em;color:rgb(50,104,145)">Marina Ratner, Émigré Mathematician Who Found Midlife Acclaim, Dies at 78</span><time class="gmail-dateline" datetime="2015-04-09" style="box-sizing:border-box;display:inline-block;font-size:0.625rem;line-height:1.0625rem;font-weight:400;font-family:nyt-franklin,arial,helvetica,sans-serif;color:rgb(153,153,153);white-space:nowrap;text-transform:uppercase">JULY 26, 2017</time></h2></a></article></li><li style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;box-sizing:border-box;display:block;margin-top:20px;padding:0px 0px 0px 10px;vertical-align:top;float:right;width:247.5px;min-height:75px"><article class="gmail-story gmail-theme-summary" style="display:block;box-sizing:border-box"><a class="gmail-story-link" href="https://www.nytimes.com/2017/07/16/us/maryam-mirzakhani-dead.html?module=Promotron&region=Body&action=click&pgtype=article" style="display:block;color:rgb(50,104,145);box-sizing:border-box;text-decoration:none"><div class="gmail-thumb" style="box-sizing:border-box;float:left;clear:left;margin:0px 10px 0px 0px;width:75px;height:75px"><img src="https://static01.nyt.com/images/2017/07/17/obituaries/17xp-Mirzakhani-obit/17xp-Mirzakhani-obit-thumbStandard.jpg" alt="" style="height: 75px; max-width: 100%; border: none; box-sizing: border-box; display: block; width: 75px;"><div class="gmail-media-action-overlay" style="box-sizing:border-box"></div></div><h2 class="gmail-story-heading" style="font-size:0.8125rem;line-height:1.0625rem;font-weight:300;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;box-sizing:border-box;color:rgb(51,51,51)"><span class="gmail-story-heading-text" style="box-sizing:border-box;padding-right:0.75em;color:rgb(50,104,145)">Maryam Mirzakhani, Only Woman to Win a Fields Medal, Dies at 40</span><time class="gmail-dateline" datetime="2015-04-09" style="box-sizing:border-box;display:inline-block;font-size:0.625rem;line-height:1.0625rem;font-weight:400;font-family:nyt-franklin,arial,helvetica,sans-serif;color:rgb(153,153,153);white-space:nowrap;text-transform:uppercase">JULY 16, 2017</time></h2></a></article></li><li style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;box-sizing:border-box;display:block;margin-top:20px;padding:0px 10px 0px 0px;vertical-align:top;float:left;width:247.5px;min-height:75px;clear:left"><article class="gmail-story gmail-theme-summary" style="display:block;box-sizing:border-box"><a class="gmail-story-link" href="http://www.nytimes.com/2016/01/22/science/new-biggest-prime-number-mersenne-primes.html?module=Promotron&region=Body&action=click&pgtype=article" style="display:block;color:rgb(50,104,145);box-sizing:border-box;text-decoration:none"><div class="gmail-thumb" style="box-sizing:border-box;float:left;clear:left;margin:0px 10px 0px 0px;width:75px;height:75px"><img src="https://static01.nyt.com/images/2016/01/22/science/22PRIME/22PRIME-thumbStandard.jpg" alt="" style="height: 75px; max-width: 100%; border: none; box-sizing: border-box; display: block; width: 75px;"><div class="gmail-media-action-overlay" style="box-sizing:border-box"></div></div><h2 class="gmail-story-heading" style="font-size:0.8125rem;line-height:1.0625rem;font-weight:300;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;box-sizing:border-box;color:rgb(51,51,51)"><span class="gmail-story-heading-text" style="box-sizing:border-box;padding-right:0.75em;color:rgb(50,104,145)">New Biggest Prime Number = 2 to the 74 Mil ... Uh, It’s Big</span><time class="gmail-dateline" datetime="2015-04-09" style="box-sizing:border-box;display:inline-block;font-size:0.625rem;line-height:1.0625rem;font-weight:400;font-family:nyt-franklin,arial,helvetica,sans-serif;color:rgb(153,153,153);white-space:nowrap;text-transform:uppercase">JAN. 22, 2016</time></h2></a></article></li><li style="font-size:1rem;line-height:1.4375rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;box-sizing:border-box;display:block;margin-top:20px;padding:0px 0px 0px 10px;vertical-align:top;float:right;width:247.5px;min-height:75px"><article class="gmail-story gmail-theme-summary" style="display:block;box-sizing:border-box"><a class="gmail-story-link" href="http://well.blogs.nytimes.com/2015/08/24/square-root-of-kids-math-anxiety-their-parents-help/?module=Promotron&region=Body&action=click&pgtype=article" style="display:block;color:rgb(50,104,145);box-sizing:border-box;text-decoration:none"><div class="gmail-thumb" style="box-sizing:border-box;float:left;clear:left;margin:0px 10px 0px 0px;width:75px;height:75px"><img src="https://static01.nyt.com/images/2015/08/25/science/25MATH/25MATH-thumbStandard.jpg" alt="" style="height: 75px; max-width: 100%; border: none; box-sizing: border-box; display: block; width: 75px;"><div class="gmail-media-action-overlay" style="box-sizing:border-box"></div></div><h2 class="gmail-story-heading" style="font-size:0.8125rem;line-height:1.0625rem;font-weight:300;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;box-sizing:border-box;color:rgb(51,51,51)"><span class="gmail-story-heading-text" style="box-sizing:border-box;padding-right:0.75em;color:rgb(50,104,145)">Square Root of Kids’ Math Anxiety: Their Parents’ Help</span><time class="gmail-dateline" datetime="2015-04-09" style="box-sizing:border-box;display:inline-block;font-size:0.625rem;line-height:1.0625rem;font-weight:400;font-family:nyt-franklin,arial,helvetica,sans-serif;color:rgb(153,153,153);white-space:nowrap;text-transform:uppercase">AUG. 24, 2015</time></h2></a></article></li></ul></div></div></div><div class="gmail-footer"></div></figure><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">As a professor at Princeton, Dr. Langlands started investigating ideas that connected the mathematics of integers with a generalization of the theory of periodic functions. Periodic functions are repeating patterns like the undulations of a sine wave in trigonometry. More than two centuries ago, mathematicians developed a method called Fourier analysis for describing, for example, the vibrations of a guitar string as the combination of multiple sine waves.</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">Dr. Langlands made use of this type of analysis in curved spaces of higher dimensions (that is, more than the three dimensions of the world we live in) to address fundamental problems in the theory of numbers.</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">In 1967, Dr. Langlands spoke with André Weil, a prominent French mathematician then at the nearby Institute for Advanced Study, who told him to put his thoughts in writing.</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">The result was 17 pages, handwritten. “After I wrote it I realized there was hardly a statement in it of which I was certain,” Dr. Langlands wrote apologetically. “If you are willing to read it as pure speculation I would appreciate that; if not — I am sure you have a wastebasket handy.”</p><figure id="gmail-media-100000005807415" class="gmail-media gmail-photo embedded gmail-layout-large-vertical gmail-media-100000005807415" style="display:flex;margin:45px 60px;clear:both;max-width:none;width:540px"><span class="gmail-visually-hidden" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Photo</span><div class="gmail-image" style="margin-bottom:0px;width:360px"><img src="https://static01.nyt.com/images/2018/03/21/science/21math-3/21math-3-blog427.jpg" alt="" class="gmail-media-viewer-candidate" style="height: auto; max-width: 100%; display: block; width: 360px;"><div class="gmail-media-action-overlay" style="border-radius:6px;opacity:0;border:1px solid rgba(200,200,200,0.8)"><i class="gmail-icon gmail-sprite-icon" style="display:inline-block;line-height:0;vertical-align:middle;font-style:normal;background-image:url("/assets/article/20180316-205148/images/sprite/sprite-no-repeat.svg");background-repeat:no-repeat;background-position:-256px -135px;width:38px;height:38px"></i></div></div><figcaption class="gmail-caption" style="display:block;font-size:0.8125rem;line-height:1.0625rem;font-weight:300;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;color:rgb(102,102,102);max-width:100%;margin-left:15px;margin-right:0px;margin-bottom:30px"><span class="gmail-caption-text">First page of the handwritten 1967 letter from Prof. Langlands to Prof. Weil.</span><span class="gmail-credit" style="font-size:0.6875rem;line-height:1rem;font-weight:400;font-style:normal;font-family:nyt-cheltenham-sh,georgia,"times new roman",times,serif;display:inline-block;color:rgb(153,153,153)"><span class="gmail-visually-hidden" style="width:1px;height:1px;padding:0px;border:0px;overflow:hidden">Credit</span>Shelby White and Leon Levy Archives Center, Institute for Advanced Study</span></figcaption></figure><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">Dr. Weil had the letter typed up, and it circulated among other mathematicians, becoming what was known as the “Langlands program.” Dr. Langlands proved a few pieces of it; others have solved additional special cases.</p><p class="gmail-story-body-text gmail-story-content" id="gmail-story-continues-4" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">Dr. Langlands’s work, for instance, served as one of the starting points in the proof of Fermat’s Last Theorem by Dr. Wiles of Oxford. Pierre de Fermat, a 17th century French mathematician, had asserted that equations of the form<span> </span><em>aⁿ</em><span> </span>+<span> </span><em>b</em>ⁿ<span> </span>=<span> </span><em>cⁿ</em>, where<span> </span><em>a</em>,<span> </span><em>b</em>,<span> </span><em>c<span> </span></em>and<span> </span><em>n<span> </span></em>are integers, have no solutions when<span> </span><em>n<span> </span></em>is greater than two.</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">“He never got a Fields medal,” said Peter C. Sarnak, a mathematician at the institute said of Dr. Langlands. “But many people have got Fields Medals for settling special cases of his conjectures, relying on his tools to start off.”</p><div class="gmail-newsletter-signup gmail-auto-newsletter" id="gmail-newsletter-promo" style="border-top:1px solid rgb(226,226,226);padding-top:15px;border-bottom:1px solid rgb(226,226,226);padding-bottom:15px;width:300px;margin:7px 30px 15px 60px;float:left;clear:left"><h2 class="gmail-visually-hidden" id="gmail-newsletter-promo-heading" style="font-size:1.25rem;line-height:1.375rem;font-weight:700;font-style:normal;font-family:cheltenham-normal-700,georgia,"times new roman",times,serif;width:1px;height:1px;padding:0px;border:0px;overflow:hidden">NThe Abel committee contacted Dr. Sarnak a few days ago as a sort of spy to check that Dr. Langlands would be around to receive the news on Monday morning, a day before the official announcement. “It seems like they do this kind of detective work, I guess,” Dr. Sarnak said.</h2></div><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">Even though the conjectures have not been proven in general, Dr. Sarnak was sure they would be eventually. “There’s no question about the truth,” he said. “It’s so intellectually compelling, it cannot not be true. God would never make the world in which that was not true.”</p><p class="gmail-story-body-text gmail-story-content" style="margin:0px 0px 1em 60px;font-size:1.0625rem;line-height:1.625rem;font-weight:400;font-style:normal;font-family:georgia,"times new roman",times,serif;max-width:none;width:540px">King Harald V of Norway is to present the prize, accompanied by $764,000, to Dr. Langlands at a ceremony in Oslo on May 22.<br></p></div><div class="gmail-supplemental" id="gmail-supplemental-2" style="display:flex;width:360px"><div class="gmail-supplemental-items" style="margin-bottom:45px;height:900px;display:flex"><div id="gmail-medium-rectangle-ad-3" class="gmail-ad gmail-ad-placeholder gmail-medium-rectangle-ad gmail-marginalia-item gmail-nocontent gmail-robots-nocontent" style="width:300px"><div id="gmail-google_ads_iframe_/29390238/NYT/science_9__container__" style="border:0pt none;display:inline-block;width:300px;height:250px"></div></div></div><div class="gmail-supplemental-items" style="margin-bottom:45px;height:900px;display:flex"><div id="gmail-medium-rectangle-ad-4" class="gmail-ad gmail-ad-placeholder gmail-medium-rectangle-ad gmail-marginalia-item gmail-nocontent gmail-robots-nocontent" style="width:300px"><div id="gmail-google_ads_iframe_/29390238/NYT/science_10__container__" style="border:0pt none;display:inline-block;width:300px;height:250px"></div></div></div><div class="gmail-supplemental-items" style="margin-bottom:45px;height:auto;max-height:900px;display:flex"><div id="gmail-marketing-ad" class="gmail-ad gmail-marketing-ad gmail-marginalia-anchor-ad gmail-marginalia-item gmail-nocontent gmail-robots-nocontent" style="width:300px;margin-bottom:45px"><div id="gmail-google_ads_iframe_/29390238/NYT/science_11__container__" style="border:0pt none;display:inline-block;width:300px;height:250px"></div></div></div></div></div>

<br></div>