A major ingredient of the proof is a stronger version of the bombieri. A cooperative team, polymath8, collaborating only online, has been able to lower the value of bto 4680, and it seems. He worked as a laborer for ten years and was unable to attend high school. Download limit exceeded you have exceeded your daily download allowance. By thomas lin as a boy in shanghai, china, yitang zhang believed he would someday solve a great problem in mathematics.
In 20, yitang zhang, member 2014 in the school of mathematics, submitted his paper small gaps between primes, which set off a series of rapid developments around the twin prime problem. Yitang zhang and the mystery of numbers quanta magazine. May 29, 20 to complete the story started as a rumour report in primes gotta stick together and confirmed in primes really do stick together, here we report that annals of mathematics has posted the pdf of bounded gaps between primes by yitang zhang on its to appear in forthcoming issues page. I want to do my undergrad thesis about yitang zhang proof, how much math do i need to understand the proof i think it can be a good topic for my undergraduate thesis, that is, a brief history of the problem ending in the landmark paper of zhang. May 19, 20 on april 17, a paper arrived in the inbox of annals of mathematics, one of the disciplines preeminent journals. Renowned mathematician yitang zhang will be joining uc santa barbaras mathematics faculty this fall, a development many hope will add further prestige to the university. For the undergraduate thesis i have about 250 hours. I think it might have made him a candidate, but i doubt that it would be a sure thing that he would get the award. Written by a mathematician virtually unknown to the experts in his field a 50something lecturer at the university of new hampshire named yitang zhang the paper. Apr 02, 2015 as a boy in shanghai, china, yitang zhang believed he would someday solve a great problem in mathematics.
Yitang zhang and the twin prime conjecture chronicles a string of mathematical discoveries that began with a solution to the twin prime conjecture. A major ingredient of the proof is a stronger version of the bombierivinogradov theorem that is applicable when the moduli are free from large prime divisors only, but it is adequate for our purpose. Pdf document information annals of mathematics fine hall. Ten mathematical landmarks, 1967 2017 maa sections. Yitang zhangs pursuit of beauty in math the new yorker. On april 17, a paper arrived in the inbox of annals of mathematics, one of the disciplines preeminent journals. A primenumber proof and a world of persistence an exciting breakthrough by an academic little known before last year is firing up mathematicians. It concerned another famous problem, the landausiegel zeros conjecture, and he left it up because he hopes to correct it.
Are there any experts here who can explain the proof. As a boy in shanghai, china, yitang zhang believed he would someday solve a great problem in mathematics. Celebrity mathematician joins ucsb faculty the daily nexus. To some extent i feel an unwarranted amount of closeness to this story. While working for the university of new hampshire as a lecturer, zhang submitted an article to the annals of mathematics in 20 which established the first finite bound on the least gap between consecutive primes that is attained infinitely.
Zhangs work also set off a flurry of followup activity in the mathematics community, including a collaboration of a dozen or so mathematicians called the polymath8 project, which is attempting to reduce the maximum separation between primes in zhangs proof to something less than 70 million. If you have additional information or corrections regarding this mathematician, please use the update form. Why did seemingly nobody notice yitang zhang before the prime. First proof that infinitely many prime numbers come in pairs. While a proof of this conjecture seems to be out of reach by present methods, recently goldston, pintz and yildirim 7 have made signi cant progress toward. Now his surprise solution to a major problem in number theory has catapulted him to mathematical stardom. Counting from infinity yitang zhang and the twin prime conjecture a film by george csicsery in april 20, a lecturer at the university of new hampshire submi ed a paper to the annals of mathema cs within weeks word spread.
A major ingredient of the proof is a stronger version of the bombierivinogradov theorem that is applicable when the moduli are free from large prime divisors only see theorem 2, but it is adequate for our purpose. He was a math instructor, not a tenuretrack professor, at the university of new hampshire from 1999 to 20, teaching prealgebra and calculus yitang zhang on rat. The lead article in this weeks new yorker feb2, 2015 is on yitang zhang, the unh professor who appeared from obscurity last year to prove the first real result in the direction of the twinprimes conjecture specifically, a concrete repeating bounded gap between primes. By yitang zhang abstract it is proved that liminf n.
Pdf document information annals of mathematics fine hall washington road princeton university princeton, nj 08544, usa phone. Yitang zhang department of mathematics and statistics. Since yitang zhang has given talks in the public, he probably did all he could have done. While working for the university of new hampshire as a lecturer, zhang submitted an article to the annals of mathematics in 20 which established the first finite bound on gaps between prime numbers. Zhang became famous in 20 when he submitted a proof to the annals of mathematics which established the first finite bound on gaps between twin prime numbers, a feat many. Aperiodic to complete the story started as a rumour report in primes gotta stick together and confirmed in primes really do stick together, here we report that annals of mathematics has posted the pdf. In 1964, at around the age of nine, he found a proof of the pythagorean theorem, which describes the relationship. Appel and hakens proof was later re ned and simpli ed, and we now call it the fourcolor theorem.
While working for the university of new hampshire as a lecturer, zhang submitted an article to the annals of mathematics in 20 which established the first finite bound on gaps between prime numbers, which lead to a 2014 macarthur award and his. Yitang zhang proves landmark theorem in distribution of. Ketika bekerja di universitas new hampshire, zhang membuat sebuah artikel untuk annals of mathematics pada 20, yang membuatnya mendapatkan penghargaan macarthur 2014. And when news leaked out about yitang zhangs solution to an ageold problem, the reaction was swift. While working for the university of new hampshire as a lecturer, zhang submitted an article to the annals of mathematics in 20 which established the first finite bound on gaps between prime numbers, which lead to a 2014. Counting from infinity yitang zhang and the twin prime conjecture 2015 documentary duration.
The unassuming mathematician, who spends pretty much every free waking momentand many sleeping ones as wellpondering intractable math problems, became famous overnight. Bounded gaps between primes by yitang zhang now available. To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 16848 for the advisor id. Zhang yitang born 1955 is a chineseborn american mathematician working in the area of number theory. While his proof did kick off a temporary flurry of progress in sieving techniques, im not sure i can say tha. Zhang yitang is proof that for mathematicians, life begins at.
To submit students of this mathematician, please use the new data form, noting this. Bounded gaps between primes annals of mathematics princeton. Bounded gaps between primes yitang zhang abstract it is proved that liminf n. Zhangs paper was not quite the final proof of the twin. Yitang zhang bounded gaps between primes 2014 youtube. Mathematician yitang zhang, 2014 macarthur fellow youtube. Yitang zhang was born on february 5, 1955 in shanghai, china, and lived there until he was years old.
After prime proof, an unlikely star rises two years ago, yitang zhang was virtually unknown. We provide a proof of a variant of the landausiegel zeros conjecture. As of 2018, i believe the proof is incomplete in lemma x. Written by a mathematician virtually unknown to the experts in his field a 50something lecturer at the university of new hampshire named yitang zhang the paper claimed to have taken a huge step forward in understanding one of mathematics oldest.
Zhang yitang made a major advancement to the twin prime conjecture as veri ed by prof. Please join the simons foundation and our generous member organizations in supporting arxiv during our giving campaign september 2327. Pdf proof of twin prime conjecture original and final edition. Jul 18, 2016 counting from infinity yitang zhang and the twin prime conjecture 2015 documentary duration. Sep 16, 2014 yitang zhang is a mathematician tackling truly hard questions in number theory leading to the first finite bound on a gap between prime numbers and the best possible qualitative approximation of. Bounded gaps between primes by yitang zhang, in annals of mathematics. They had not only been more careful in several difficult arguments in zhang s original paper, they had also developed zhang s techniques to be both more powerful and to allow a much simpler proof and forms the basis for the proof presented herein. Here zhang relies on a result of birch and bombieri that depends on delignes proof of the weil conjectures.
Written by a mathematician virtually unknown to the experts in his field a 50something lecturer at the university of new hampshire named yitang zhang the paper claimed to have taken a huge step forward in understanding one of mathematics oldest problems, the twin. Math needed to understand yitang zhang proof i want to do my undergrad thesis about yitang zhang proof, how much math do i need to understand the proof i think it can be a good topic for my undergraduate thesis, that is, a brief history of the problem ending in the landmark paper of zhang. May 14, 20 the new result, from yitang zhang of the university of new hampshire in durham, finds that there are infinitely many pairs of primes that are less than 70 million units apart without relying on. Unheralded mathematician bridges the prime gap by erica klarreich on april 17, a paper arrived in the inbox of annals of mathematics, one of the disciplines preeminent journals. The most delicate part of the proof involves the type iii sums. In 20, an imp ortant breakthrough was made by yitang zhang who. Is the outline in the annals the preprint or the full accepted paper. In april 20, yitang zhang 21 proved a weaker version of elliott. In 1964, at around the age of nine, he found a proof of the pythagorean theorem, which describes the relationship between the lengths of the sides of any right triangle. Zhang posted a paper in 2007 that fell short of a proof. Yitang zhang wikipedia bahasa indonesia, ensiklopedia bebas.
Because zhang was a nobody at a relatively unknown researchwise us university. They had not only been more careful in several difficult arguments in zhangs original paper, they had also developed zhangs techniques to be both more powerful and to allow a much simpler proof and forms the basis for the proof presented herein. Sutherland mit new bounds on gaps between primes october 17, 20 12 28. Yitang zhang is a mathematician tackling truly hard questions in number theory leading to the first finite bound on a gap between prime numbers and the best possible qualitative approximation of. In 20, yitang zhang, member 2014 in the school of mathematics, submitted his paper small gaps between primes, which set off a series of rapid developments around the twin prime. During the cultural revolution, he and his parents were sent to the countryside to work in the fields. How yitang tom zhang proved a theorem that had stumped. Zhang, yitang i i 2s i zhang, yitang 1955 yitang zhang is a chinese american mathematician who catapulted from obscurity into professional and public prominence in 20 with the publication of his research related to the famous twin primes conjec ture in number theory. Why did seemingly nobody notice yitang zhang before the. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext.
1214 812 549 529 1640 888 513 331 143 369 957 1274 1178 690 144 650 1414 1378 1159 1205 1235 1556 947 200 521 504 700 774 585 1236 1650 1171 1269 769 918 970 239 262 257 1153 1111 731 648