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84-509: Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician , electrical engineer , computer scientist , cryptographer and inventor known as the "father of information theory " and as the "father of the Information Age ". Shannon was the first to describe the Boolean gates (electronic circuits) that are essential to all digital electronic circuits, and was one of

168-553: A Roman numeral computer called THROBAC, and juggling machines . He built a device that could solve the Rubik's Cube puzzle. Shannon also invented flame-throwing trumpets , rocket-powered frisbees , and plastic foam shoes for navigating a lake, and which to an observer, would appear as if Shannon was walking on water. Shannon designed the Minivac 601 , a digital computer trainer to teach business people about how computers functioned. It

252-483: A paper which is considered one of the foundational pieces of modern cryptography, with his work described as "a turning point, and marked the closure of classical cryptography and the beginning of modern cryptography." The work of Shannon is the foundation of secret-key cryptography , including the work of Horst Feistel , the Data Encryption Standard (DES) , Advanced Encryption Standard (AES) , and more. As

336-408: A (uniform) discrete set of samples. This theory was essential in enabling telecommunications to move from analog to digital transmissions systems in the 1960s and later. He further wrote a paper in 1956 regarding coding for a noisy channel, which also became a classic paper in the field of information theory. Claude Shannon's influence has been immense in the field, for example, in a 1973 collection of

420-473: A complicated problem and find the right way to look at it, so that things become very simple." In an obituary by Neil Sloane and Robert Calderbank , they stated that "Shannon must rank near the top of the list of major figures of twentieth century science". Due to his work in multiple fields, Shannon is also regarded as a polymath . Historian James Gleick noted the importance of Shannon, stating that "Einstein looms large, and rightly so. But we’re not living in

504-426: A digital 4-bit full adder. His work differed significantly from the work of previous engineers such as Akira Nakashima , who still relied on the existent circuit theory of the time and took a grounded approach. Shannon's idea were more abstract and relied on mathematics, thereby breaking new ground with his work, with his approach dominating modern-day eletrical engineering. Using electrical switches to implement logic

588-569: A few months in the summer of 1937, and returned there to work on fire-control systems and cryptography during World War II , under a contract with section D-2 (Control Systems section) of the National Defense Research Committee (NDRC). Shannon is credited with the invention of signal-flow graphs , in 1942. He discovered the topological gain formula while investigating the functional operation of an analog computer. For two months early in 1943, Shannon came into contact with

672-471: A financial economist might study the structural reasons why a company may have a certain share price , a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock ( see: Valuation of options ; Financial modeling ). According to the Dictionary of Occupational Titles occupations in mathematics include

756-419: A footnote near the beginning of the classified report, Shannon announced his intention to "develop these results … in a forthcoming memorandum on the transmission of information." While he was at Bell Labs, Shannon proved that the cryptographic one-time pad is unbreakable in his classified research that was later published in 1949. The same article also proved that any unbreakable system must have essentially

840-892: A general expression for the distribution of several linked traits in a population after multiple generations under a random mating system, which was original at the time, with the new theorem unworked out by other population geneticists of the time. In 1940, Shannon became a National Research Fellow at the Institute for Advanced Study in Princeton, New Jersey . In Princeton, Shannon had the opportunity to discuss his ideas with influential scientists and mathematicians such as Hermann Weyl and John von Neumann , and he also had occasional encounters with Albert Einstein and Kurt Gödel . Shannon worked freely across disciplines, and this ability may have contributed to his later development of mathematical information theory. Shannon had worked at Bell Labs for

924-540: A machine can be made to simulate it. An attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves. We think that a significant advance can be made in one or more of these problems if a carefully selected group of scientists work on it together for a summer. The proposal goes on to discuss computers , natural language processing , neural networks , theory of computation , abstraction and creativity (these areas within

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1008-400: A manner which will help ensure that the plans are maintained on a sound financial basis. As another example, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while

1092-469: A mechanical mouse could move through. Below the surface were sensors that followed the path of a mechanical mouse through the maze. After much trial and error, this device would learn the shortest path through the maze, and direct the mechanical mouse through the maze. The pattern of the maze could be changed at will. Mazin Gilbert stated that Theseus "inspired the whole field of AI. This random trial and error

1176-766: 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 (some say roofing tiles). Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily 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

1260-493: A radio-controlled model boat and a barbed-wire telegraph system to a friend's house a half-mile away. While growing up, he also worked as a messenger for the Western Union company. Shannon's childhood hero was Thomas Edison , whom he later learned was a distant cousin. Both Shannon and Edison were descendants of John Ogden (1609–1682), a colonial leader and an ancestor of many distinguished people. In 1932, Shannon entered

1344-484: A result, Shannon has been called the "founding father of modern cryptography". His mathematical theory of communication laid the foundations for the field of information theory, with his famous paper being called the " Magna Carta of the Information Age" by Scientific American , along with his work being described as being at "the heart of today's digital information technology ". Robert G. Gallager referred to

1428-557: A science of intelligent machines, but also held a broader view of viable approaches in automata studies, such as neural nets, Turing machines, cybernetic mechanisms, and symbolic processing by computer. Shannon co-organized and participated in the Dartmouth workshop of 1956, alongside John McCarthy, Marvin Minsky and Nathaniel Rochester , and which is considered the founding event of the field of artificial intelligence. In 1956 Shannon joined

1512-560: A science." It has also been called the "birth certificate of the digital revolution ", and it won the 1939 Alfred Noble Prize . Shannon then graduated with a PhD in mathematics from MIT in 1940, with his thesis focused on genetics , with it deriving important results, but it went unpublished. Shannon contributed to the field of cryptanalysis for national defense of the United States during World War II , including his fundamental work on codebreaking and secure telecommunications , writing

1596-406: A sender wants to transmit. Shannon developed information entropy as a measure of the information content in a message, which is a measure of uncertainty reduced by the message. In so doing, he essentially invented the field of information theory . The book The Mathematical Theory of Communication reprints Shannon's 1948 article and Warren Weaver 's popularization of it, which is accessible to

1680-498: A summer seminar at Dartmouth for about 10 participants. In June, he and Claude Shannon , a founder of information theory then at Bell Labs , met with Robert Morison, Director of Biological and Medical Research to discuss the idea and possible funding, though Morison was unsure whether money would be made available for such a visionary project. On September 2, 1955, the project was formally proposed by McCarthy , Marvin Minsky , Nathaniel Rochester and Claude Shannon . The proposal

1764-420: Is mathematics that studies entirely abstract concepts . From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics , and at variance with the trend towards meeting the needs of navigation , astronomy , physics , economics , engineering , and other applications. Another insightful view put forth is that pure mathematics

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1848-419: Is " Communication Theory of Secrecy Systems ", a declassified version of his wartime work on the mathematical theory of cryptography, in which he proved that all theoretically unbreakable cyphers must have the same requirements as the one-time pad. He is credited with the introduction of sampling theorem , which he had derived as early as 1940, and which is concerned with representing a continuous-time signal from

1932-451: Is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science , engineering , business , and other areas of mathematical practice. Pure mathematics

2016-399: Is a conceptual descendant of Shannon's publication in 1948: "He's one of the great men of the century. Without him, none of the things we know today would exist. The whole digital revolution started with him." The cryptocurrency unit shannon (a synonym for gwei) is named after him. Shannon is credited by many as single-handedly creating information theory and for laying the foundations for

2100-478: Is about communication itself, Warren Weaver communicated his ideas in such a way that those not acclimated to complex theory and mathematics could comprehend the fundamental laws he put forth. The coupling of their unique communicational abilities and ideas generated the Shannon-Weaver model , although the mathematical and theoretical underpinnings emanate entirely from Shannon's work after Weaver's introduction. For

2184-467: Is credited with introducing the term 'artificial intelligence'. The Proposal states: We propose that a 2-month, 10-man study of artificial intelligence be carried out during the summer of 1956 at Dartmouth College in Hanover, New Hampshire . The study is to proceed on the basis of the conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that

2268-400: Is not necessarily applied mathematics : it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing

2352-704: Is subject to change when the group gets together." The actual participants came at different times, mostly for much shorter times. Trenchard More replaced Rochester for three weeks and MacKay and Holland did not attend—but the project was set to begin. Around June 18, 1956, the earliest participants (perhaps only Ray Solomonoff, maybe with Tom Etter) arrived at the Dartmouth campus in Hanover, N.H., to join John McCarthy who already had an apartment there. Solomonoff and Minsky stayed at Professors' apartments, but most would stay at

2436-508: Is the foundation of artificial intelligence." Shannon wrote multiple influential papers on artificial intelligence, such as his 1950 paper titled "Programming a Computer for Playing Chess", and his 1953 paper titled "Computers and Automata". Alongside John McCarthy , he co-edited a book titled Automata Studies , which was published in 1956. The categories in the articles within the volume were influenced by Shannon's own subject headings in his 1953 paper. Shannon shared McCarthy’s goal of creating

2520-425: Is the fundamental concept that underlies all electronic digital computers . Shannon's work became the foundation of digital circuit design, as it became widely known in the electrical engineering community during and after World War II . The theoretical rigor of Shannon's work superseded the ad hoc methods that had prevailed previously. Howard Gardner hailed Shannon's thesis "possibly the most important, and also

2604-566: The Cold Spring Harbor Laboratory , in order to develop a mathematical formulation for Mendelian genetics . This research resulted in Shannon's PhD thesis, called An Algebra for Theoretical Genetics . However, the thesis went unpublished after Shannon lost interest, but it did contain important results. Notably, he was one of the first to apply an algebraic framework to study theoretical population genetics. In addition, Shannon devised

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2688-530: The Digital Age . The artificial intelligence large language model family Claude (language model) was named in Shannon's honor. A Mind at Play , a biography of Shannon written by Jimmy Soni and Rob Goodman, was published in 2017. They described Shannon as "the most important genius you’ve never heard of, a man whose intellect was on par with Albert Einstein and Isaac Newton ". Consultant and writer Tom Rutledge, writing for Boston Review , stated that "Of

2772-634: 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", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( c.  AD 350 – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of

2856-656: The Schock Prize , and the Nevanlinna Prize . The American Mathematical Society , Association for Women in Mathematics , and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics. Several well known mathematicians have written autobiographies in part to explain to a general audience what it is about mathematics that has made them want to devote their lives to its study. These provide some of

2940-725: The University of California, San Diego ; one at Bell Labs; and another at AT&T Shannon Labs . The statue in Gaylord is located in the Claude Shannon Memorial Park. After the breakup of the Bell System , the part of Bell Labs that remained with AT&T Corporation was named Shannon Labs in his honor. In June 1954, Shannon was listed as one of the top 20 most important scientists in America by Fortune . In 2013, information theory

3024-495: The University of Michigan , where he was introduced to the work of George Boole . He graduated in 1936 with two bachelor's degrees : one in electrical engineering and the other in mathematics. In 1936, Shannon began his graduate studies in electrical engineering at the Massachusetts Institute of Technology (MIT), where he worked on Vannevar Bush 's differential analyzer , which was an early analog computer that

3108-478: The graduate level . In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation . 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

3192-576: The Hanover Inn. The Dartmouth Workshop is said to have run for six weeks in the summer of 1956. Ray Solomonoff's notes written during the Workshop, however, say it ran for roughly eight weeks, from about June 18 to August 17. Solomonoff's Dartmouth notes start on June 22; June 28 mentions Minsky, June 30 mentions Hanover, N.H., July 1 mentions Tom Etter. On August 17, Solomonoff gave a final talk. Initially, McCarthy lost his list of attendees. Instead, after

3276-578: The Italian and German universities, but as they already 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 even German universities, which were subject to state authority. Overall, science (including mathematics) became

3360-592: The MIT faculty, holding an endowed chair. He worked in the Research Laboratory of Electronics (RLE). He continued to serve on the MIT faculty until 1978. Shannon developed Alzheimer's disease and spent the last few years of his life in a nursing home ; he died in 2001, survived by his wife, a son and daughter, and two granddaughters. Outside of Shannon's academic pursuits, he was interested in juggling , unicycling , and chess . He also invented many devices, including

3444-503: The best glimpses into what it means to be a mathematician. The following list contains some works that are not autobiographies, but rather essays on mathematics and mathematicians with strong autobiographical elements. Dartmouth workshop The project lasted approximately six to eight weeks and was essentially an extended brainstorming session. Eleven mathematicians and scientists originally planned to attend; not all of them attended, but more than ten others came for short times. In

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3528-647: The cafeteria. Turing showed Shannon his 1936 paper that defined what is now known as the " universal Turing machine ". This impressed Shannon, as many of its ideas complemented his own. In 1945, as the war was coming to an end, the NDRC was issuing a summary of technical reports as a last step prior to its eventual closing down. Inside the volume on fire control, a special essay titled Data Smoothing and Prediction in Fire-Control Systems , coauthored by Shannon, Ralph Beebe Blackman , and Hendrik Wade Bode , formally treated

3612-696: The close of the war, he prepared a classified memorandum for Bell Telephone Labs entitled "A Mathematical Theory of Cryptography", dated September 1945. A declassified version of this paper was published in 1949 as " Communication Theory of Secrecy Systems " in the Bell System Technical Journal . This paper incorporated many of the concepts and mathematical formulations that also appeared in his A Mathematical Theory of Communication . Shannon said that his wartime insights into communication theory and cryptography developed simultaneously, and that "they were so close together you couldn't separate them". In

3696-400: The computer pioneers who drove the mid-20th-century information technology revolution—an elite men’s club of scholar-engineers who also helped crack Nazi codes and pinpoint missile trajectories—Shannon may have been the most brilliant of them all." Electrical engineer Robert Gallager stated about Shannon that "He had this amazing clarity of vision. Einstein had it, too – this ability to take on

3780-500: The earliest known mathematicians was Thales of Miletus ( c.  624  – c.  546 BC ); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry , by deriving four corollaries to Thales's theorem . The number of known mathematicians grew when Pythagoras of Samos ( c.  582  – c.  507 BC ) established

3864-414: The early 1950s, there were various names for the field of "thinking machines": cybernetics , automata theory , and complex information processing . The variety of names suggests the variety of conceptual orientations. In 1955, John McCarthy , then a young Assistant Professor of Mathematics at Dartmouth College , decided to organize a group to clarify and develop ideas about thinking machines. He picked

3948-429: The essential operators of Boolean algebra . Then he proved that his switching circuits could be used to simplify the arrangement of the electromechanical relays that were used during that time in telephone call routing switches . Next, he expanded this concept, proving that these circuits could solve all problems that Boolean algebra could solve. In the last chapter, he presented diagrams of several circuits, including

4032-400: The field of artificial intelligence are considered still relevant to the work of the field). On May 26, 1956, McCarthy notified Robert Morison of the planned 11 attendees: For the full period: For four weeks: For the first two weeks: He noted, "we will concentrate on a problem of devising a way of programming a calculator to form concepts and to form generalizations. This of course

4116-400: The first examples of artificial intelligence. He also co-organized and participated in the Dartmouth workshop of 1956, considered the founding event of the field of artificial intelligence. Rodney Brooks declared that Shannon was the 20th century engineer who contributed the most to 21st century technologies, and Solomon W. Golomb described the intellectual achievement of Shannon as "one of

4200-442: The focus of universities in the 19th and 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

4284-992: The following. There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the Abel Prize , the Chern Medal , the Fields Medal , the Gauss Prize , the Nemmers Prize , the Balzan Prize , the Crafoord Prize , the Shaw Prize , the Steele Prize , the Wolf Prize ,

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4368-585: The founding fathers of artificial intelligence . Shannon is credited with laying the foundations of the Information Age . At the University of Michigan , Shannon dual degreed , graduating with a Bachelor of Science in both electrical engineering and mathematics in 1936. A 21-year-old master's degree student at the Massachusetts Institute of Technology (MIT) in electrical engineering, his thesis concerned switching circuit theory , demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship, thereby establishing

4452-464: The greatest of the twentieth century". His achievements are considered to be on par with those of Albert Einstein , Sir Isaac Newton , and Charles Darwin . The Shannon family lived in Gaylord, Michigan , and Claude was born in a hospital in nearby Petoskey . His father, Claude Sr. (1862–1934), was a businessman and, for a while, a judge of probate in Gaylord. His mother, Mabel Wolf Shannon (1880–1945),

4536-629: The imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models . Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers. The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics"

4620-504: The key papers in the field of information theory, he was author or coauthor of 12 of the 49 papers cited, while no one else appeared more than three times. Even beyond his original paper in 1948, he is still regarded as the most important post-1948 contributor to the theory. In May 1951, Mervin Kelly , received a request from the director of the CIA , general Walter Bedell Smith , regarding Shannon and

4704-569: 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, teaching and study." Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education , and then proceed to specialize in topics of their own choice at

4788-470: The king of Prussia , Fredrick William III , to build a university in Berlin based on Friedrich Schleiermacher 's liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve. British universities of this period adopted some approaches familiar to

4872-499: The layman, Weaver's introduction better communicates The Mathematical Theory of Communication , but Shannon's subsequent logic, mathematics, and expressive precision was responsible for defining the problem itself. Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems . Mathematicians are concerned with numbers , data , quantity , structure , space , models , and change . One of

4956-575: The leading British mathematician Alan Turing . Turing had been posted to Washington to share with the U.S. Navy 's cryptanalytic service the methods used by the British Government Code and Cypher School at Bletchley Park to break the cyphers used by the Kriegsmarine U-boats in the north Atlantic Ocean . He was also interested in the encipherment of speech and to this end spent time at Bell Labs. Shannon and Turing met at teatime in

5040-546: The main math classroom where someone might lead a discussion focusing on his ideas, or more frequently, a general discussion would be held. It was not a directed group research project; discussions covered many topics, but several directions are considered to have been initiated or encouraged by the Workshop: the rise of symbolic methods, systems focused on limited domains (early expert systems ), and deductive systems versus inductive systems. One participant, Arthur Samuel, said, "It

5124-496: The most noted, master's thesis of the century." One of the reviewers of his work commented that "To the best of my knowledge, this is the first application of the methods of symbolic logic to so practical an engineering problem. From the point of view of originality I rate the paper as outstanding." Shannon's master thesis won the 1939 Alfred Noble Prize . Shannon received his PhD in mathematics from MIT in 1940. Vannevar Bush had suggested that Shannon should work on his dissertation at

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5208-479: The name 'Artificial Intelligence' for the new field. He chose the name partly for its neutrality; avoiding a focus on narrow automata theory, and avoiding cybernetics which was heavily focused on analog feedback, as well as him potentially having to accept the assertive Norbert Wiener as guru or having to argue with him. In early 1955, McCarthy approached the Rockefeller Foundation to request funding for

5292-454: The need for him, as Shannon was regarded as, based on "the best authority" the "most eminently qualified scientist in the particular field concerned". As a result of the request, Shannon became part of the CIA's Special Cryptologic Advisory Group or SCAG. In 1950, Shannon, designed, and built with the help of his wife, a learning machine named Theseus. It consisted of a maze on a surface, through which

5376-549: The non-specialist. Weaver pointed out that the word "information" in communication theory is not related to what you do say, but to what you could say. That is, information is a measure of one's freedom of choice when one selects a message. Shannon's concepts were also popularized, subject to his own proofreading, in John Robinson Pierce 's Symbols, Signals, and Noise . Information theory's fundamental contribution to natural language processing and computational linguistics

5460-489: The paper as a "blueprint for the digital era". Regarding the influence that Shannon had on the digital age, Solomon W. Golomb remarked "It's like saying how much influence the inventor of the alphabet has had on literature." Shannon's theory is widely used and has been fundamental to the success of many scientific endeavors, such as the invention of the compact disc , the development of the Internet , feasibility of mobile phones,

5544-531: The probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in

5628-408: The problem of smoothing the data in fire-control by analogy with "the problem of separating a signal from interfering noise in communications systems." In other words, it modeled the problem in terms of data and signal processing and thus heralded the coming of the Information Age . Shannon's work on cryptography was even more closely related to his later publications on communication theory . At

5712-484: The real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research. Many professional mathematicians also engage in the teaching of mathematics. Duties may include: Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate

5796-435: The relativity age, we’re living in the information age. It’s Shannon whose fingerprints are on every electronic device we own, every computer screen we gaze into, every means of digital communication. He’s one of these people who so transform the world that, after the transformation, the old world is forgotten." Gleick further noted that "he created a whole field from scratch, from the brow of Zeus ". On April 30, 2016, Shannon

5880-519: The same characteristics as the one-time pad: the key must be truly random, as large as the plaintext, never reused in whole or part, and kept secret. In 1948, the promised memorandum appeared as "A Mathematical Theory of Communication", an article in two parts in the July and October issues of the Bell System Technical Journal . This work focuses on the problem of how best to encode the message

5964-403: The seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle , and 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[ing] productive thinking." In 1810, Alexander von Humboldt convinced

6048-461: The theory behind digital computing and digital circuits . The thesis has been claimed to be the most important master's thesis of all time, as in 1985, Howard Gardner described it as "possibly the most important, and also the most famous, master's thesis of the century", while Herman Goldstine described it as "surely   ... one of the most important master's theses ever written   ... It helped to change digital circuit design from an art to

6132-417: The understanding of black holes , and more, and is at the intersection of numerous important fields. Shannon also formally introduced the term " bit ". Shannon made numerous contributions to the field of artificial intelligence, writing papers on programming a computer for chess, which have been immensely influential. His Theseus machine was the first electrical device to learn by trial and error, being one of

6216-530: The workshop, McCarthy sent Solomonoff a preliminary list of participants and visitors plus those interested in the subject. There were 47 people listed. Solomonoff, however, made a complete list in his notes of the summer project: Shannon attended Solomonoff's talk on July 10 and Bigelow gave a talk on August 15. Solomonoff doesn't mention Bernard Widrow, but apparently he visited, along with W.A. Clark and B.G. Farley. Trenchard mentions R. Culver and Solomonoff mentions Bill Shutz. Herb Gelernter didn't attend, but

6300-938: Was Al-Khawarizmi . A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics , maths and astronomy of Ibn al-Haytham . The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting ); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer). As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in

6384-580: Was a language teacher, who also served as the principal of Gaylord High School . Claude Sr. was a descendant of New Jersey settlers , while Mabel was a child of German immigrants. Shannon's family was active in their Methodist Church during his youth. Most of the first 16 years of Shannon's life were spent in Gaylord, where he attended public school, graduating from Gaylord High School in 1932. Shannon showed an inclination towards mechanical and electrical things. His best subjects were science and mathematics. At home, he constructed such devices as models of planes,

6468-475: Was a numerical analyst at Bell Labs. They were married in 1949. Betty assisted Claude in building some of his most famous inventions. They had three children. Shannon presented himself as apolitical and an atheist . There are six statues of Shannon sculpted by Eugene Daub : one at the University of Michigan ; one at MIT in the Laboratory for Information and Decision Systems ; one in Gaylord, Michigan; one at

6552-480: Was composed of electromechanical parts and could solve differential equations . While studying the complicated ad hoc circuits of this analyzer, Shannon designed switching circuits based on Boole's concepts . In 1937, he wrote his master's degree thesis, A Symbolic Analysis of Relay and Switching Circuits , with a paper from this thesis published in 1938. A revolutionary work for switching circuit theory , Shannon diagramed switching circuits that could implement

6636-481: Was further established in 1951, in his article "Prediction and Entropy of Printed English", showing upper and lower bounds of entropy on the statistics of English – giving a statistical foundation to language analysis. In addition, he proved that treating space as the 27th letter of the alphabet actually lowers uncertainty in written language, providing a clear quantifiable link between cultural practice and probabilistic cognition. Another notable paper published in 1949

6720-622: Was honored with a Google Doodle to celebrate his life on what would have been his 100th birthday. The Bit Player , a feature film about Shannon directed by Mark Levinson premiered at the World Science Festival in 2019. Drawn from interviews conducted with Shannon in his house in the 1980s, the film was released on Amazon Prime in August 2020. Shannon's The Mathematical Theory of Communication, begins with an interpretation of his own work by Warren Weaver . Although Shannon's entire work

6804-470: Was influenced later by what Rochester learned. Ray Solomonoff, Marvin Minsky, and John McCarthy were the only three who stayed for the full-time. Trenchard took attendance during two weeks of his three-week visit. From three to about eight people would attend the daily sessions. They had the entire top floor of the Dartmouth Math Department to themselves, and most weekdays they would meet at

6888-406: Was listed as one of the top 10 revolutionary scientific theories by Science News . According to Neil Sloane , an AT&T Fellow who co-edited Shannon's large collection of papers in 1993, the perspective introduced by Shannon's communication theory (now called "information theory") is the foundation of the digital revolution , and every device containing a microprocessor or microcontroller

6972-431: Was ongoing throughout the reign of certain caliphs, and 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

7056-599: Was sold by the Scientific Development Corp starting in 1961. He is also considered the co-inventor of the first wearable computer along with Edward O. Thorp . The device was used to improve the odds when playing roulette . Shannon married Norma Levor , a wealthy, Jewish, left-wing intellectual in January 1940. The marriage ended in divorce after about a year. Levor later married Ben Barzman . Shannon met his second wife, Mary Elizabeth Moore (Betty), when she

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