Paul Erdős was a renowned Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century, he was known both for his eccentric lifestyle. He devoted his waking hours to mathematics into his years—indeed, his death came only hours after he solved a geometry problem at a conference in Warsaw. Erdős pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, probability theory. Much of his work centered around discrete mathematics, cracking many unsolved problems in the field, he championed and contributed to Ramsey theory, which studied the conditions in which order appears. Overall, his work leaned towards solving open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed, he believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathematicians.
Erdős's prolific output with co-authors prompted the creation of the Erdős number, the number of steps in the shortest path between a mathematician and Erdős in terms of co-authorships. Paul Erdős was born in Budapest, Austria-Hungary, on 26 March 1913, he was the only surviving child of Lajos Erdős. His two sisters, aged 3 and 5, both died of scarlet fever a few days, his parents were both Jewish mathematics teachers. His fascination with mathematics developed early—he was left home by himself because his father was held captive in Siberia as an Austro-Hungarian POW during 1914–1920, causing his mother to have to work long hours to support their household, he taught himself to read through mathematics texts. By the age of four, given a person's age, he could calculate in his head how many seconds they had lived. Due to his sisters' deaths, he had a close relationship with his mother, with the two of them sharing the same bed until he left for college. Both of Erdős's parents were high school mathematics teachers, Erdős received much of his early education from them.
Erdős always remembered his parents with great affection. At 16, his father introduced him to two of his lifetime favorite subjects—infinite series and set theory. During high school, Erdős became an ardent solver of the problems proposed each month in KöMaL, the Mathematical and Physical Monthly for Secondary Schools. Erdős entered the University of Budapest at the age of 17. By the time he was 20, he had found a proof for Chebyshev's Theorem. In 1934, at the age of 21, he was awarded a doctorate in mathematics. Erdős's thesis advisor was Lipót Fejér, the thesis advisor for John von Neumann, George Pólya, Paul Turán; because he was a Jew, Erdős decided. Many members of Erdős' family, including two of his aunts, two of his uncles, his father, died in Budapest during the Holocaust, his mother survived in hiding. He was working at the Princeton Institute for Advanced Study at the time. Described by his biographer, Paul Hoffman, as "probably the most eccentric mathematician in the world," Erdős spent most of his adult life living out of a suitcase.
Except for some years in the 1950s, when he was not allowed to enter the United States based on the pretense that he was a Communist sympathizer, his life was a continuous series of going from one meeting or seminar to another. During his visits, Erdős expected his hosts to lodge him, feed him, do his laundry, along with anything else he needed, as well as arrange for him to get to his next destination. On 20 September 1996, at the age of 83, he had a heart attack and died while attending a conference in Warsaw; these circumstances were close to the way. He once said, I want to be giving a lecture, finishing up an important proof on the blackboard, when someone in the audience shouts out,'What about the general case?'. I'll turn to the audience and smile,'I'll leave that to the next generation,' and I'll keel over. Erdős never had no children, he is buried next to his father in grave 17A-6-29 at Kozma Utcai Temető in Budapest. For his epitaph, he suggested "I've stopped getting dumber.". His life was documented in the film N Is a Number: A Portrait of Paul Erdős, made while he was still alive, posthumously in the book The Man Who Loved Only Numbers.
Erdős' name contains the Hungarian letter "ő", but is incorrectly written as Erdos or Erdös either "by mistake or out of typographical necessity". Possessions meant little to Erdős. Awards and other earnings were donated to people in need and various worthy causes, he spent most of his life traveling between scientific conferences and the homes of colleagues all over the world. He earned enough in stipends from universities as a guest lecturer, from various mathematical awards, to fund his travels and basic needs, he would show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the c
The Erdős number describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers. Paul Erdős was an influential Hungarian mathematician who in the latter part of his life spent a great deal of time writing papers with a large number of colleagues, working on solutions to outstanding mathematical problems, he published more papers during his lifetime than any other mathematician in history. Erdős spent a large portion of his life living out of a suitcase, visiting his over 500 collaborators around the world; the idea of the Erdős number was created by the mathematician's friends as a tribute to his enormous output. It gained prominence as a tool to study how mathematicians cooperate to find answers to unsolved problems. Several projects are devoted to studying connectivity among researchers, using the Erdős number as a proxy.
For example, Erdős collaboration graphs can tell us how authors cluster, how the number of co-authors per paper evolves over time, or how new theories propagate. Several studies have shown that leading mathematicians tend to have low Erdős numbers; the median Erdős number of Fields Medalists is 3. Only 7,097 have an Erdős number of lower; as time passes, the smallest Erdős number that can still be achieved will increase, as mathematicians with low Erdős numbers die and become unavailable for collaboration. Still, historical figures can have low Erdős numbers. For example, renowned Indian mathematician Srinivasa Ramanujan has an Erdős number of only 3 though Paul Erdős was only 7 years old when Ramanujan died. To be assigned an Erdős number, someone must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is k + 1; the American Mathematical Society provides a free online tool to determine the Erdős number of every mathematical author listed in the Mathematical Reviews catalogue.
Erdős wrote around 1,500 mathematical articles in his lifetime co-written. He had 511 direct collaborators; the people who have collaborated with them have an Erdős number of 2, those who have collaborated with people who have an Erdős number of 2 have an Erdős number of 3, so forth. A person with no such coauthorship chain connecting to Erdős has an Erdős number of infinity. Since the death of Paul Erdős, the lowest Erdős number that a new researcher can obtain is 2. There is room for ambiguity over; the American Mathematical Society collaboration distance calculator uses data from Mathematical Reviews, which includes most mathematics journals but covers other subjects only in a limited way, which includes some non-research publications. The Erdős Number Project web site says:... Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional co-authors is permitted... but they do not include non-research publications such as elementary textbooks, joint editorships and the like.
The “Erdős number of the second kind” restricts assignment of Erdős numbers to papers with only two collaborators. The Erdős number was most first defined in print by Casper Goffman, an analyst whose own Erdős number is 2. Goffman published his observations about Erdős' prolific collaboration in a 1969 article entitled "And what is your Erdős number?" See some comments in an obituary by Michael Golomb. The median Erdős number among Fields medalists is as low as 3. Fields medalists with Erdős number 2 include Atle Selberg, Kunihiko Kodaira, Klaus Roth, Alan Baker, Enrico Bombieri, David Mumford, Charles Fefferman, William Thurston, Shing-Tung Yau, Jean Bourgain, Richard Borcherds, Manjul Bhargava, Jean-Pierre Serre and Terence Tao. There are no Fields medalists with Erdős number 1, however Endre Szemerédi is an Abel Prize Laureate with Erdős number 1. While Erdős collaborated with hundreds of co-authors, there were some individuals with whom he co-authored dozens of papers; this is a list of the ten persons who most co-authored with Erdős and their number of papers co-authored with Erdős.
As of 2016, all Fields Medalists have a finite Erdős number, with values that range between 2 and 6, a median of 3. In contrast, the median Erdős number across all mathematicians is 5, with an extreme value of 13; the table below summarizes the Erdős number statistics for Nobel prize laureates in Physics, Chemistry and Economics. The first column counts the number of laureates; the second column counts the number of winners with a finite Erdős number. The third column is the percentage of winners with a finite Erdős number; the remaining columns report the minimum, maximum and median Erdős numbers among those laureates. Among the Nobel Prize laureates in Physics, Albert Einstein and Sheldon Lee Glashow have an Erdős number of 2. Nobel Laureates with an Erdős number of 3 include Enrico Fermi, Otto Stern, Wolfgang Pauli, Max Born, Willis E. Lamb, Eugene Wigner, Richard P. Feynman, Hans A. Bethe, Murray Gell-Mann, Abdus
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns
University of Memphis
The University of Memphis, colloquially known as U of M, is a public research university in Memphis, Tennessee. Founded in 1912, the university has an enrollment of more than 21,000 students; the university maintains The Center for Earthquake Research and Information, The Cecil C. Humphreys School of Law, the former Lambuth University campus, The Loewenberg College of Nursing, The School of Public Health, The College of Communication and Fine Arts, The FedEx Institute of Technology, The Advanced Distributed Learning Workforce Co-Lab, The Institute of Egyptian Art and Archaeology; the University of Memphis is associated with the Tennessee Board of Regents system, consisting of 18 Board Members. However, as of May 2017, it is governed by an institutional Board of Trustees. Within this framework, the President of the University of Memphis is the day-to-day administrator of the university; the University of Memphis today comprises a number of different colleges and schools: College of Arts and Sciences Fogelman College of Business and Economics College of Communication and Fine Arts College of Education Herff College of Engineering University College Loewenberg College of Nursing Kemmons Wilson School of Hospitality and Resort Management School of Communication Sciences and Disorders Cecil C.
Humphreys School of Law Graduate School School of Public Health Rudi E. Scheidt School of Music Helen Hardin Honors CollegeThe University of Memphis is host to several centers of advanced research: FedEx Institute of Technology Center for Earthquake Research and Information Institute for Intelligent Systems Advanced Distributed Learning Workforce Co-Lab The Sparks Bureau of Business and Economic Research Mobile Sensor Data-To-Knowledge Center The University of Memphis Foundation, founded in 1964, manages the university endowment and accepts and disburses private support to the university. In 1909, the Tennessee Legislature enacted the General Education Bill; this bill stated that three colleges be established, one within each grand division of the state and one additional school for African-American students. After much bidding and campaigning, the state had to choose between two sites to build the new college for West Tennessee: Jackson and Memphis. Memphis was chosen, one of the main reasons being the proximity of the rail line to the site proposed to build the new college for West Tennessee.
This would allow students to go home and visit their relatives. The other three schools established through the General Education Act evolved into East Tennessee State University, Middle Tennessee State University, Tennessee State University. Prior to the establishment of the West Tennessee Normal School pursuant to the General Education Bill, a number of higher education departments existed in Memphis under the banner of the University of Memphis; this earlier University of Memphis was formed in 1909 by adding to an existing medical school's departments of pharmacy and law. On September 10, 1912, West Tennessee Normal School opened in Memphis. By 1913 all departments of the earlier University of Memphis, except the law school, had been taken over by West Tennessee Normal School. After Mynders' death in 1913, John Willard Brister was chosen to take his place. After Brister's resignation in 1918, Andrew A. Kincannon became president. In 1924, Brister returned to his post as president of the school.
The name changed in 1925 to West Tennessee State Teachers College. In 1931, the campus' first newspaper, The Tiger Rag, was established. In 1939, Richard C. Jones became president of WTSTC. In 1941, the name was changed to Memphis State College, when the college expanded its liberal arts curriculum. In 1943, Dr. Jennings B. Sanders succeeded Jones as president. Three years the first alumnus to become president, J. Millard Smith, was appointed. In 1951 MSC awarded its first B. A. degrees. In 1957 the school received full University status and changed its name accordingly to Memphis State University. In 1959, five years after Brown v. Board of Education the university admitted its first black students. Racial segregation was the norm throughout the South at the time; the Memphis State Eight, as they were known, were admitted to Memphis State University. Their presence on campus was the focus not only of intense media scrutiny, but severe criticism from much of the local public. Ostensibly for the black students' safety and to maintain an air of calm on the campus, University administrators placed certain restrictions on where and when the black students could be on campus.
They were to go only to their classes, not to any of the public places on campus, such as the cafeteria. These limitations were lifted after the novelty of their presence on campus had subsided and the public's focus on their presence there had lessened, as more and more black students were admitted to the university. Today, black students make up more than one-third of the campus student body and participate in all campus activities. Cecil C. Humphreys became president of MSU, succeeding Smith, in 1960. In 1966, the school began awarding doctoral degrees. Humphreys resigned as MSU president to become the first chancellor of the newly formed State University and Community College System renamed the Tennessee Board of Regents. John Richardson was appointed interim president. In 1973, Dr. Billy Mac Jones became president; that year, the Memphis State Tiger men's basketball team reached the finals of the NCAA tournament, only to fall at the hands of a UCLA team led by future NBA superstar and Hall of Famer Bill Walton in The NCAA Bas
Système universitaire de documentation
The système universitaire de documentation or SUDOC is a system used by the libraries of French universities and higher education establishments to identify and manage the documents in their possession. The catalog, which contains more than 10 million references, allows students and researcher to search for bibliographical and location information in over 3,400 documentation centers, it is maintained by the Bibliographic Agency for Higher Education. Official website
Virtual International Authority File
The Virtual International Authority File is an international authority file. It is a joint project of several national libraries and operated by the Online Computer Library Center. Discussion about having a common international authority started in the late 1990s. After a series of failed attempts to come up with a unique common authority file, the new idea was to link existing national authorities; this would present all the benefits of a common file without requiring a large investment of time and expense in the process. The project was initiated by the US Library of Congress, the German National Library and the OCLC on August 6, 2003; the Bibliothèque nationale de France joined the project on October 5, 2007. The project transitioned to being a service of the OCLC on April 4, 2012; the aim is to link the national authority files to a single virtual authority file. In this file, identical records from the different data sets are linked together. A VIAF record receives a standard data number, contains the primary "see" and "see also" records from the original records, refers to the original authority records.
The data are available for research and data exchange and sharing. Reciprocal updating uses the Open Archives Initiative Protocol for Metadata Harvesting protocol; the file numbers are being added to Wikipedia biographical articles and are incorporated into Wikidata. VIAF's clustering algorithm is run every month; as more data are added from participating libraries, clusters of authority records may coalesce or split, leading to some fluctuation in the VIAF identifier of certain authority records. Authority control Faceted Application of Subject Terminology Integrated Authority File International Standard Authority Data Number International Standard Name Identifier Wikipedia's authority control template for articles Official website VIAF at OCLC