Terence Chi-Shen Tao is an Australian-American mathematician who has worked in various areas of mathematics. He focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory; as of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao was the 2014 Breakthrough Prize in Mathematics, he is the second ethnic Chinese person to win the Fields medal after Shing-Tung Yau, the first Australian mathematician to win the Fields medal. Tao's father, Dr. Billy Tao, was a pediatrician, born in Shanghai and earned his medical degree from the University of Hong Kong in 1969. Tao's mother, Grace, is from Hong Kong, she was a secondary school teacher of physics in Hong Kong. Billy and Grace met as students at the University of Hong Kong, they emigrated from Hong Kong to Australia. Tao has two brothers and Trevor, living in Australia. Both represented Australia at the International Mathematical Olympiad.
Tao's wife, Laura, is an engineer at NASA's Jet Propulsion Laboratory. They live with their daughter in Los Angeles, California. Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9, he and Lenhard Ng are the only two children in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just nine years old. Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten, he remains the youngest winner of each of the three medals in the Olympiad's history, winning the gold medal shortly after his thirteenth birthday. At age 14, Tao attended the Research Science Institute; when he was 15, he published his first assistant paper. In 1991, he received his bachelor's and master's degrees at the age of 16 from Flinders University under Garth Gaudry. In 1992, he won a Postgraduate Fulbright Scholarship to undertake research in Mathematics at Princeton University in the United States.
From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his PhD at the age of 21. He joined the faculty of the University of California, Los Angeles. In 1999, when he was 24, he was promoted to full professor at UCLA and remains the youngest person appointed to that rank by the institution. Within the field of mathematics, Tao is known for his collaboration with Ben J. Green of Oxford University. Known for his collaborative mindset, by 2006, Tao had worked with over 30 others in his discoveries, reaching 68 co-authors by October 2015. In a book review, the mathematician Timothy Gowers remarked on Tao's accomplishments: Tao's mathematical knowledge has an extraordinary combination of breadth and depth: he can write confidently and authoritatively on topics as diverse as partial differential equations, analytic number theory, the geometry of 3-manifolds, nonstandard analysis, group theory, model theory, quantum mechanics, ergodic theory, harmonic analysis, image processing, functional analysis, many others.
Some of these are areas. Others are areas that he appears to understand at the deep intuitive level of an expert despite not working in those areas. How he does all this, as well as writing papers and books at a prodigious rate, is a complete mystery, it has been said that David Hilbert was the last person to know all of mathematics, but it is not easy to find gaps in Tao's knowledge, if you do you may well find that the gaps have been filled a year later. Tao has won numerous awards over the years, he is a Fellow of the Royal Society, the Australian Academy of Science, the National Academy of Sciences, the American Academy of Arts and Sciences, the American Mathematical Society. In 2006 he received the Fields Medal "for his contributions to partial differential equations, harmonic analysis and additive number theory", was awarded the MacArthur Fellowship, he has been featured in The New York Times, CNN, USA Today, Popular Science, many other media outlets. By 2016, Tao had published about 17 books.
He has an Erdős number of 2. In 2018, Tao proved Bounding the de Bruijn-Newman constant. In 2004, Ben Green and Tao released a preprint proving; this theorem states. The New York Times described it this way: In 2004, Dr. Tao, along with Ben Green, a mathematician now at the University of Cambridge in England, solved a problem related to the Twin Prime Conjecture by looking at prime number progressions—series of numbers spaced. Dr. Tao and Dr. Green proved that it is always possible to find, somewhere in the infinity of integers, a progression of prime numbers of equal spacing and any length. For this and other work Tao was awarded the Australian Mathematical Society Medal of 2004, he was awarded a Fields Medal in August 2006 at the 25th International Cong
South Africa the Republic of South Africa, is the southernmost country in Africa. It is bounded to the south by 2,798 kilometres of coastline of Southern Africa stretching along the South Atlantic and Indian Oceans. South Africa is the largest country in Southern Africa and the 25th-largest country in the world by land area and, with over 57 million people, is the world's 24th-most populous nation, it is the southernmost country on the mainland of the Eastern Hemisphere. About 80 percent of South Africans are of Sub-Saharan African ancestry, divided among a variety of ethnic groups speaking different African languages, nine of which have official status; the remaining population consists of Africa's largest communities of European and multiracial ancestry. South Africa is a multiethnic society encompassing a wide variety of cultures and religions, its pluralistic makeup is reflected in the constitution's recognition of 11 official languages, the fourth highest number in the world. Two of these languages are of European origin: Afrikaans developed from Dutch and serves as the first language of most coloured and white South Africans.
The country is one of the few in Africa never to have had a coup d'état, regular elections have been held for a century. However, the vast majority of black South Africans were not enfranchised until 1994. During the 20th century, the black majority sought to recover its rights from the dominant white minority, with this struggle playing a large role in the country's recent history and politics; the National Party imposed apartheid in 1948. After a long and sometimes violent struggle by the African National Congress and other anti-apartheid activists both inside and outside the country, the repeal of discriminatory laws began in 1990. Since 1994, all ethnic and linguistic groups have held political representation in the country's liberal democracy, which comprises a parliamentary republic and nine provinces. South Africa is referred to as the "rainbow nation" to describe the country's multicultural diversity in the wake of apartheid; the World Bank classifies South Africa as an upper-middle-income economy, a newly industrialised country.
Its economy is the second-largest in Africa, the 34th-largest in the world. In terms of purchasing power parity, South Africa has the seventh-highest per capita income in Africa; however and inequality remain widespread, with about a quarter of the population unemployed and living on less than US$1.25 a day. South Africa has been identified as a middle power in international affairs, maintains significant regional influence; the name "South Africa" is derived from the country's geographic location at the southern tip of Africa. Upon formation, the country was named the Union of South Africa in English, reflecting its origin from the unification of four separate British colonies. Since 1961, the long form name in English has been the "Republic of South Africa". In Dutch, the country was named Republiek van Zuid-Afrika, replaced in 1983 by the Afrikaans Republiek van Suid-Afrika. Since 1994, the Republic has had an official name in each of its 11 official languages. Mzansi, derived from the Xhosa noun umzantsi meaning "south", is a colloquial name for South Africa, while some Pan-Africanist political parties prefer the term "Azania".
South Africa contains human-fossil sites in the world. Archaeologists have recovered extensive fossil remains from a series of caves in Gauteng Province; the area, a UNESCO World Heritage site, has been branded "the Cradle of Humankind". The sites include one of the richest sites for hominin fossils in the world. Other sites include Gondolin Cave Kromdraai, Coopers Cave and Malapa. Raymond Dart identified the first hominin fossil discovered in Africa, the Taung Child in 1924. Further hominin remains have come from the sites of Makapansgat in Limpopo Province and Florisbad in the Free State Province, Border Cave in KwaZulu-Natal Province, Klasies River Mouth in Eastern Cape Province and Pinnacle Point and Die Kelders Cave in Western Cape Province; these finds suggest that various hominid species existed in South Africa from about three million years ago, starting with Australopithecus africanus. There followed species including Australopithecus sediba, Homo ergaster, Homo erectus, Homo rhodesiensis, Homo helmei, Homo naledi and modern humans.
Modern humans have inhabited Southern Africa for at least 170,000 years. Various researchers have located pebble tools within the Vaal River valley. Settlements of Bantu-speaking peoples, who were iron-using agriculturists and herdsmen, were present south of the Limpopo River by the 4th or 5th century CE, they displaced and absorbed the original Khoisan speakers, the Khoikhoi and San peoples. The Bantu moved south; the earliest ironworks in modern-day KwaZulu-Natal Province are believed to date from around 1050. The southernmost group was the Xhosa people, whose language incorporates certain linguistic traits from the earlier Khoisan people; the Xhosa reached the Great Fish River, in today's Eastern Cape Province. As they migrated, these larger Iron Age populations
Henryk Iwaniec is a Polish-American mathematician, since 1987 a professor at Rutgers University. Iwaniec studied at the University of Warsaw, where he got his Ph. D. in 1972 under Andrzej Schinzel. He held positions at the Institute of Mathematics of the Polish Academy of Sciences until 1983 when he left Poland, he held visiting positions at the Institute for Advanced Study, University of Michigan, University of Colorado Boulder before being appointed Professor of Mathematics at Rutgers University. He is a citizen of the United States, he and mathematician Tadeusz Iwaniec are twin brothers. Iwaniec studies both sieve methods and deep complex-analytic techniques, with an emphasis on the theory of automorphic forms and harmonic analysis. In 1997, Iwaniec and John Friedlander proved that there are infinitely many prime numbers of the form a2 + b4. Results of this strength had been seen as out of reach: sieve theory—used by Iwaniec and Friedlander in combination with other techniques—cannot distinguish between primes and products of two primes, say.
In 2001 Iwaniec was awarded the seventh Ostrowski Prize. The prize citation read, in part, "Iwaniec's work is characterized by depth, profound understanding of the difficulties of a problem, unsurpassed technique, he has made deep contributions to the field of analytic number theory in modular forms on GL and sieve methods." He became a fellow of the American Academy of Arts and Sciences in 1995. He was awarded the fourteenth Frank Nelson Cole Prize in Number Theory in 2002. In 2006, he became a member of the National Academy of Science, he received the Leroy P. Steele Prize for Mathematical Exposition in 2011. In 2012 he became a fellow of the American Mathematical Society. In 2015 he was awarded the Shaw Prize in Mathematics. In 2017 he was awarded the AMS Doob Prize for their book Opera de Cribro, about sieve theory. Iwaniec, Henryk. Topics in Classical Automorphic Forms. Providence: American Mathematical Society. ISBN 978-0-8218-0777-4. Iwaniec, Henryk. Spectral Methods of Automorphic Forms. Providence: American Mathematical Society.
ISBN 978-0-8218-3160-1. Iwaniec, Henryk. Analytic Number Theory. Providence: American Mathematical Society. ISBN 978-0-8218-3633-0. Iwaniec, Henryk. Friedlander. Analytic Number Theory: Lectures Given at the C. I. M. E. Summer School Held in Cetraro, July 11–18, 2002. Berlin: Springer. ISBN 978-3-540-36363-7. Friedlander, John. Opera de Cribro. Providence: American Mathematical Society. ISBN 978-0-8218-4970-5. List of Poles Cipra, Barry A.. "Sieving Prime Numbers From Thin Ore". Science. 279: 31. Bibcode:1998Sci...279...31C. doi:10.1126/science.279.5347.31.. Henryk Iwaniec at the Mathematics Genealogy Project "Henryk Iwaniec's results". International Mathematical Olympiad
Poland the Republic of Poland, is a country located in Central Europe. It is divided into 16 administrative subdivisions, covering an area of 312,696 square kilometres, has a temperate seasonal climate. With a population of 38.5 million people, Poland is the sixth most populous member state of the European Union. Poland's capital and largest metropolis is Warsaw. Other major cities include Kraków, Łódź, Wrocław, Poznań, Gdańsk, Szczecin. Poland is bordered by the Baltic Sea, Russia's Kaliningrad Oblast and Lithuania to the north and Ukraine to the east and Czech Republic, to the south, Germany to the west; the establishment of the Polish state can be traced back to AD 966, when Mieszko I, ruler of the realm coextensive with the territory of present-day Poland, converted to Christianity. The Kingdom of Poland was founded in 1025, in 1569 it cemented its longstanding political association with the Grand Duchy of Lithuania by signing the Union of Lublin; this union formed the Polish–Lithuanian Commonwealth, one of the largest and most populous countries of 16th and 17th century Europe, with a uniquely liberal political system which adopted Europe's first written national constitution, the Constitution of 3 May 1791.
More than a century after the Partitions of Poland at the end of the 18th century, Poland regained its independence in 1918 with the Treaty of Versailles. In September 1939, World War II started with the invasion of Poland by Germany, followed by the Soviet Union invading Poland in accordance with the Molotov–Ribbentrop Pact. More than six million Polish citizens, including 90% of the country's Jews, perished in the war. In 1947, the Polish People's Republic was established as a satellite state under Soviet influence. In the aftermath of the Revolutions of 1989, most notably through the emergence of the Solidarity movement, Poland reestablished itself as a presidential democratic republic. Poland is regional power, it has the fifth largest economy by GDP in the European Union and one of the most dynamic economies in the world achieving a high rank on the Human Development Index. Additionally, the Polish Stock Exchange in Warsaw is the largest and most important in Central Europe. Poland is a developed country, which maintains a high-income economy along with high standards of living, life quality, safety and economic freedom.
Having a developed school educational system, the country provides free university education, state-funded social security, a universal health care system for all citizens. Poland has 15 UNESCO World Heritage Sites. Poland is a member state of the European Union, the Schengen Area, the United Nations, NATO, the OECD, the Three Seas Initiative, the Visegrád Group; the origin of the name "Poland" derives from the West Slavic tribe of Polans that inhabited the Warta river basin of the historic Greater Poland region starting in the 6th century. The origin of the name "Polanie" itself derives from the early Slavic word "pole". In some languages, such as Hungarian, Lithuanian and Turkish, the exonym for Poland is Lechites, which derives from the name of a semi-legendary ruler of Polans, Lech I. Early Bronze Age in Poland begun around 2400 BC, while the Iron Age commenced in 750 BC. During this time, the Lusatian culture, spanning both the Bronze and Iron Ages, became prominent; the most famous archaeological find from the prehistory and protohistory of Poland is the Biskupin fortified settlement, dating from the Lusatian culture of the early Iron Age, around 700 BC.
Throughout the Antiquity period, many distinct ancient ethnic groups populated the regions of what is now Poland in an era that dates from about 400 BC to 500 AD. These groups are identified as Celtic, Slavic and Germanic tribes. Recent archeological findings in the Kujawy region, confirmed the presence of the Roman Legions on the territory of Poland; these were most expeditionary missions sent out to protect the amber trade. The exact time and routes of the original migration and settlement of Slavic peoples lacks written records and can only be defined as fragmented; the Slavic tribes who would form Poland migrated to these areas in the second half of the 5th century AD. Up until the creation of Mieszko's state and his subsequent conversion to Christianity in 966 AD, the main religion of Slavic tribes that inhabited the geographical area of present-day Poland was Slavic paganism. With the Baptism of Poland the Polish rulers accepted Christianity and the religious authority of the Roman Church.
However, the transition from paganism was not a smooth and instantaneous process for the rest of the population as evident from the pagan reaction of the 1030s. Poland began to form into a recognizable unitary and territorial entity around the middle of the 10th century under the Piast dynasty. Poland's first documented ruler, Mieszko I, accepted Christianity with the Baptism of Poland in 966, as the new official religion of his subjects; the bulk of the population converted in the course of the next few centuries. In 1000, Boleslaw the Brave, continuing the policy of his father Mieszko, held a Congress of Gniezno and created the metropolis of Gniezno and the dioceses of Kraków, Kołobrzeg, Wrocław. However, the pagan unrest led to the transfer of the capital to Kraków in 1038 by Casimir I the Restorer. In 1109, Prince Bolesław III Wrymouth defeated the King of Germany Henry V at the Battle of Hundsfeld, stopping the Ge
Peter Clive Sarnak is a South African-born mathematician with dual South-African and American nationalities. He has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, is an editor of the Annals of Mathematics, he is known for his work in analytic number theory. Sarnak is on the permanent faculty at the School of Mathematics of the Institute for Advanced Study, he sits on the Board of Adjudicators and the selection committee for the Mathematics award, given under the auspices of the Shaw Prize. Sarnak graduated from the University of the Witwatersrand and Stanford University, under the direction of Paul Cohen. Sarnak's cited work applied deep results in number theory to Ramanujan graphs, with connections to combinatorics and computer science. Sarnak has made major contributions to number theory, he is recognised internationally as one of the leading analytic number theorists of his generation. His early work on the existence of cusp forms led to the disproof of a conjecture of Atle Selberg.
He has obtained the strongest known bounds towards the Ramanujan–Petersson conjectures for sparse graphs, he was one of the first to exploit connections between certain questions of theoretical physics and analytic number theory. There are fundamental contributions to arithmetical quantum chaos, a term which he introduced, to the relationship between random matrix theory and the zeros of L-functions, his work on subconvexity for Rankin–Selberg L-functions led to the resolution of Hilbert's eleventh problem. During his career he has held numerous appointments including: Assistant Professor, 1980–83. "Spectral Behavior of Quasi Periodic Potentials". Commun. Math. Phys. 84: 377–401. Doi:10.1007/bf01208483. Some Applications of Modular Forms, 1990 Extremal Riemann Surfaces, 1997 Random Matrices, Frobenius Eigenvalues and Monodromy, 1998 Peter Sarnak. "Some problems in Number Theory and Mathematical Physics". In V. I. Arnold, M. Atiyah, P. Lax, B. Mazur. Mathematics: frontiers and perspectives. American Mathematical Society.
Pp. 261–269. ISBN 978-0821826973. CS1 maint: Uses editors parameter Selected Works of Ilya Piatetski-Shapiro, 2000 Elementary Number Theory, Group Theory and Ramanujan Graphs, 2003 Selected Papers Volume I-Peter Lax, 2005 Automorphic Forms and Applications, 2007 Peter Sarnak was awarded the Polya Prize of Society of Industrial & Applied Mathematics in 1998, the Ostrowski Prize in 2001, the Levi L. Conant Prize in 2003, the Frank Nelson Cole Prize in Number Theory in 2005 and a Lester R. Ford Award in 2012, he is the recipient of the 2014 Wolf Prize in Mathematics. The University of the Witwatersrand conferred an honorary doctorate on Professor Peter Sarnak on 2 July 2014 for his distinguished contribution to the field of mathematics, he was elected as member of the National Academy of Sciences and Fellow of the Royal Society in 2002. He was awarded an honorary doctorate by the Hebrew University of Jerusalem in 2010, he was awarded an honorary doctorate by the University of Chicago in 2015. He was elected to the 2018 class of fellows of the American Mathematical Society.
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Royal Netherlands Academy of Arts and Sciences
The Royal Netherlands Academy of Arts and Sciences is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory and administrative functions it operates a number of research institutes and awards many prizes, including the Lorentz Medal in theoretical physics, the Dr Hendrik Muller Prize for Behavioural and Social Science and the Heineken Prizes; the academy advises the Dutch government on scientific matters. While its advice pertains to genuine scientific concerns, it counsels the government on such topics as policy on careers for researchers or the Netherlands' contribution to major international projects; the academy offers solicited and unsolicited advice to parliament, ministries and research institutes, funding agencies and international organizations. Advising the government on matters related to scientific research Assessing the quality of scientific research Providing a forum for the scientific world and promoting international scientific cooperation Acting as an umbrella organization for the institutes engaged in basic and strategic scientific research and disseminating information The members are appointed for life by co-optation.
Nominations for candidate membership by persons or organizations outside the academy are accepted. The acceptance criterion is delivered scientific achievements. Academy membership is therefore regarded as a great honor, prestigious. Besides regular members, there are corresponding members. Since a new membership system was introduced in 2011 there will be no new corresponding members; each year a maximum of sixteen members is appointed to the academy. The Royal Netherlands Academy of Arts and Sciences has long embraced the entire field of learning; the Royal Academy comprises two departments, consisting of around 500 members: Science Humanities and Social Sciences Both departments have their own board. The departments, in turn, are divided into sections; the highest organ in the academy is the general meeting of members, the united meeting of both departments. The president was Frits van Oostrom until 1 May 2008, after which he was succeeded by Robbert Dijkgraaf. Both van Oostrom in his leaving address and Dijkgraaf in his inaugural address have voiced their worries about the low level of funding in science in the Netherlands compared to all other western countries.
In March 2012, Hans Clevers was elected president and took office in June 2012. Latrer presidents were Wim van Saarloos. During the Kingdom of Holland, it was founded as the Koninklijk Instituut van Wetenschappen, Letterkunde en Schoone Kunsten by Lodewijk Napoleon on May 4, 1808. In 1816, after the occupation had ended, it was renamed to Koninklijk-Nederlandsch Instituut van Wetenschappen, Letteren en Schoone Kunsten. In 1851 it was disbanded and re-established as the Koninklijke Akademie van Wetenschappen and in 1938 obtained its present name. Since 1812 the academy has resided in the Trippenhuis in Amsterdam; the institute was awarded the Gouden Ganzenveer in 1955. The following Research institutes are associated with the KNAW: Centraalbureau voor Schimmelcultures Data Archiving and Networked Services Huygens Instituut Fryske Akademy Hubrecht Instituut Internationaal Instituut voor Sociale Geschiedenis Nederlands Herseninstituut Koninklijk Instituut voor Taal-, Land- en Volkenkunde Meertens Instituut Nederlands Instituut voor Ecologie Nederlands Instituut voor Oorlogsdocumentatie Nederlands Instituut voor Wetenschappelijke Informatiediensten Nederlands Interdisciplinair Demografisch Instituut Netherlands Institute for Advanced Study in the Humanities and Social Sciences Rathenau InstituutThe Netherlands Institute for Neuroscience was established in 2005 as a merger of the Netherlands Institute for Brain Research and the Netherlands Ophthalmic Research Institute.
De Jonge Akademie is a society of younger science researchers, founded in 2005 as part of the KNAW. Ten members are elected each year for a term of five years, it was modelled after the similar German Junge Akademie, both of these academies in turn were used as models for the Global Young Academy. Netherlands Organisation for Applied Scientific Research Netherlands Organisation for Scientific Research Koninklijke Hollandsche Maatschappij der Wetenschappen Royal Netherlands Academy of Arts and Sciences, official website
Yitang "Tom" Zhang is a Chinese-born American mathematician working in the area of number theory. While working for the University of New Hampshire as a lecturer, Zhang submitted an article to the Annals of Mathematics in 2013 which established the first finite bound on the least gap between consecutive primes, attained infinitely often; this work led to a 2014 MacArthur award and his appointment as a professor at the University of California, Santa Barbara. Zhang was lived there until he was 13 years old. At around the age of nine, he found a proof of the Pythagorean theorem, he first learned about Fermat’s last theorem and the Goldbach conjecture when he was 10. During the Cultural Revolution, he and his mother were sent to the countryside to work in the fields, he was unable to attend high school. After the Cultural Revolution ended, Zhang entered Peking University in 1978 as an undergraduate student and received his B. Sc. degree in mathematics in 1982. He became a graduate student of Professor Pan Chengbiao, a number theorist at Peking University, obtained his M.
Sc. degree in mathematics in 1984. After receiving his master's degree in mathematics, with recommendations from Professor Ding Shisun, the President of Peking University, Professor Deng Donggao, Chair of the university's Math Department, Zhang was granted a full scholarship at Purdue University. Zhang arrived at Purdue in January 1985, studied there for six and a half years, obtained his Ph. D. in mathematics in December 1991. Zhang's Ph. D. work was on the Jacobian conjecture. After graduation, Zhang had a hard time finding an academic position. In a 2013 interview with Nautilus magazine, Zhang said. "During that period it was difficult to find a job in academics. That was a job market problem. My advisor did not write me letters of recommendation." The reason behind this is that Zhang's research pointed out the mistakes made by his advisor Tzuong-Tsieng Moh's previous work. Moh was unhappy with this and refused to write the job recommendation letter for Zhang. Zhang made this claim again in George Csicsery’s documentary film Counting From Infinity while discussing his difficulties at Purdue and in the years that followed.
Tzuong-Tsieng Moh, his Ph. D. advisor at Purdue, said that Zhang never came back to him requesting recommendation letters. In a detailed profile published in The New Yorker magazine in February 2015, Alec Wilkinson wrote Zhang "parted unhappily" with Moh, that Zhang "left Purdue without Moh’s support, having published no papers, was unable to find an academic job". After some years, Zhang managed to find a position as a lecturer at the University of New Hampshire, where he was hired by Kenneth Appel in 1999. Prior to getting back to academia, he worked for several years as an accountant and a delivery worker for a New York City restaurant, he worked in a motel in Kentucky and in a Subway sandwich shop. A profile published in the Quanta Magazine reports that Zhang used to live in his car during the initial job-hunting days, he served as lecturer at UNH from 1999 until around January 2014, when UNH appointed him to a full professorship as a result of his breakthrough on prime numbers. Zhang stayed for a semester in Princeton University in 2014, in Fall 2015, Zhang joined the University of California, Santa Barbara.
On April 17, 2013, Zhang announced a proof that states there are infinitely many pairs of prime numbers that differ by 70 million or less. This result implies the existence of an infinitely repeatable prime 2-tuple, thus establishing a theorem akin to the twin prime conjecture. Zhang's paper was accepted by Annals of Mathematics in early May 2013, his first publication since his last paper in 2001; the proof was refereed by leading experts in analytic number theory. Zhang's result set off a flurry of activity in the field, such as the Polymath8 project. If P stands for the proposition that there is an infinitude of pairs of prime numbers that differ by N Zhang's result is equivalent to the statement that there exists at least one integer k < 70,000,000 such that P is true. The classical form of the twin prime conjecture is equivalent to P. While these stronger conjectures remain unproven, a result due to James Maynard in November 2013, employing a different technique, showed that P holds for some k ≤ 600.
Subsequently, in April 2014, the Polymath project 8 lowered the bound to k ≤ 246. With current methods k ≤ 6 is the best attainable, in fact k ≤ 12 and k ≤ 6 follow using current methods if the Elliott–Halberstam conjecture and its generalisation hold. Zhang was awarded the 2013 Morningside Special Achievement Award in Mathematics, the 2013 Ostrowski Prize, the 2014 Frank Nelson Cole Prize in Number Theory, the 2014 Rolf Schock Prize in Mathematics, he is a recipient of the 2014 MacArthur award, was elected as an Academia Sinica Fellow during the same year. He was an invited speaker at the 2014 International Congress of Mathematicians. In 1989 Zhang joined a group interested in Chinese democracy. In a 2013 interview, he affirmed. Lu Jiaxi, a Chinese self-taught mathematician unknown to the mathematical community until he solved a major problem in combinatorics. Alec Wilkinson, The Pursuit of Beauty, Yitang Zhang solves a pure-math mystery, The New Yorker, February 2, 2015 issue Discover Magazine article by Steve Nadis, "Prime Solver" Gaps between Primes – Numberphile - University of Nottingham video Gaps between Primes – Numberphil