Charles Babbage | British inventor and mathematician | Britannica.com British inventor and mathematician Charles Babbage, (born December 26, 1791, London , England —died October 18, 1871, London), English mathematician and inventor who is credited with having conceived the first automatic digital computer . Charles Babbage, detail of an oil painting by Samuel Lawrence, 1845; in the National Portrait … Courtesy of the National Portrait Gallery, London In 1812 Babbage helped found the Analytical Society, whose object was to introduce developments from the European continent into English mathematics . In 1816 he was elected a fellow of the Royal Society of London. He was instrumental in founding the Royal Astronomical (1820) and Statistical (1834) societies. The idea of mechanically calculating mathematical tables first came to Babbage in 1812 or 1813. Later he made a small calculator that could perform certain mathematical computations to eight decimals. Then in 1823 he obtained government support for the design of a projected machine , the Difference Engine , with a 20-decimal capacity.

Its construction required the development of mechanical engineering techniques, to which Babbage of necessity devoted himself. In the meantime (1828–39), he served as Lucasian Professor of Mathematics at the University of Cambridge . The Difference Engine Science Museum London During the mid-1830s Babbage developed plans for the Analytical Engine , the forerunner of the modern digital computer. In that device he envisioned the capability of performing any arithmetical operation on the basis of instructions from punched cards, a memory unit in which to store numbers, sequential control, and most of the other basic elements of the present-day computer. In 1843 Babbage’s friend mathematician Ada Lovelace translated a French paper about the Analytical Engine and, in her own annotations , published how it could perform a sequence of calculations, the first computer program. The Analytical Engine, however, was never completed. Babbage’s design was forgotten until his unpublished notebooks were discovered in 1937. In 1991 British scientists built Difference Engine No. 2—accurate to 31 digits—to Babbage’s specifications, and in 2000 the printer for the Difference Engine was also built.

Babbage made notable contributions in other areas as well. He assisted in establishing the modern postal system in England and compiled the first reliable actuarial tables. He also invented a type of speedometer and the locomotive cowcatcher. Learn More in these related articles: Who invented the computer? | eNotes Who invented the computer? thanatassa | College Teacher | (Level 3) Educator Emeritus Posted on August 6, 2011 at 8:21 PM Paper tapes, used as information storage for control purposes were first employed in the 1720s by Basile Bouchon and Jean-Baptiste Falcon to control looms. By changing tapes, one could quickly reprogram the loom to weave different patterns. Joseph Jacquard more fully automated loom control with punched cards in 1801. These cards were used by Babbage in his computing machines to order the sequence of calculations. Charles Babbage (1791-1871) is considered by many to be the inventor of the computer. He designed two machines, a "difference engine" and an "analytical engine" which used algorithms to calculate complex equations algorithmically.

The first programmer was Ada Byron, Lady Lovelace (1815-1852), daughter of the famous Romantic poet Lord Byron. In 1843, Ada developed a plan for how his machines could calculate Bernoulli numbers; this plan is normally credited as the first computer program. More complex calculating and tabulating machines evolved in the early twentieth century, until the first general purpose electronic computer, the ENIAC (Electronic Numerical Integrator and Computer), was developed in 1941-1945. Soon after the invention of the computer was the discovery by Grace Hopper of the first computer bug, a moth trapped in a relay of the Harvard University Mark II Aiken Relay Calculator on 9 September, 1945. It could be argued that the abacus is the first device for ‘computing, invented in Chine between 2600 BC and 300 BC- it was used for tabulating numbers and The "difference engine" conceived in 1786 by J.H. Müllerr is arguably the first of device like a computer.

Müllerr’s devices was never built, and the plans were discovered by Charles Babbage in 1822, who is credited as creating the first computer. Babbage’s device used a crank handle and a number system, sort of like a massive calculator, and was part funded by the British Government. It was later improved as a general analytical engine but later returned and produced an improved design (his "Difference Engine No. 2") between 1834 and 1869. If you mean Electronic Computer that would be recognisable by modern standards then Alan Turing from Cambridge UK, in the employ of the British Governent created a machine to crack the enigma codes named Colossus, which was the worlds first digital, electronic computing device. Much of Turing’s work was top secret until recently. like 4 dislike 3 October 10, 2011 at 4:00 PM English mathematician Charles Babbage (1792–1871) designed a mechanical computing machine called the "analytical engine." It is considered the forerunner of the digital computer, a programmable electronic device that stores, retrieves, and processes data.

While attending Cambridge University in 1812, Babbage conceived of the idea of a machine that could calculate data more rapidly than existing computing methods, and without human error. The Industrial Revolution (a period of technological development; c. 1750–c. 1850) had been underway for more than half a century, and the world was becoming increasingly complex. Human errors in mathematical tables posed serious problems for many rapidly growing industries. After graduating from Cambridge, Babbage returned to the idea of developing a device to facilitate computation. Beginning work in 1834, he spent the rest of his life and much of his fortune trying to build such a machine. Babbage's device used punch cards to store data, and was intended to print answers. Although he was unable to complete his invention, the "analytical engine" was the forerunner of the modern digital computer. More than one hundred years later the first fully automatic calculator was invented—development began in 1939 at Harvard University in Cambridge, Massachusetts. Under the direction of mathematician Howard Aiken (1900–73), the first electronic digital computer, called Mark I, was invented in 1944.

(The Mark II followed in 1947.) In 1946 scientists at the University of Pennsylvania completed ENIAC (Electronic Numerical Integrator And Calculator), the first all-purpose electronic digital computer. ENIAC was operated by 18,000 vacuum tubes, which required a great deal of power and generated a considerable amount of heat. The first computer to handle both numeric and alphabetical data with equal facility was the UNIVAC (UNIVersal Automatic Computer), developed between 1946 and 1951, also at the University of Pennsylvania. Further Information: Aspray, William, ed. Computing Before Computers. Ames, Ia.: Iowa State University Press, 1990; Campbell-Kelly, Martin, and William Aspray. Computer: A History of the Information Machine. New York: Basic Books, 1996; "Charles Babbage." MSN Encarta. [Online] Available , November 8, 2000. Source: UXL History Fact Finder, ©2001 Gale Cengage. All Rights Reserved. Full copyright .

like 20 dislike 3 Mathematics - 2 | Britannica.com Mathematics the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. Browse Subcategories: (10) Displaying 1 - 100 of 800 results abacus calculating device, probably of Babylonian origin, that was long important in commerce. It is the ancestor of the modern calculating machine and computer. The earliest “abacus” likely was a board or slab on which a Babylonian spread sand so he could... Abel, Niels Henrik Norwegian mathematician, a pioneer in the development of several branches of modern mathematics. Abel’s father was a poor Lutheran minister who moved his family to the parish of Gjerstad, near the town of Risør in southeast Norway, soon after Niels Henrik... Abel’s test in analysis (a branch of mathematics), a test for determining if an infinite series converges to some finite value. The test is named for the Norwegian mathematician Niels Henrik Abel (1802–29). Starting with any known convergent series, say Σ a n (i.e.,...

Abraham bar Hiyya Spanish Jewish philosopher, astronomer, astrologer, and mathematician whose writings were among the first scientific and philosophical works to be written in Hebrew. He is sometimes known as Savasorda, a corruption of an Arabic term indicating that he... Abūʾl-Wafāʾ a distinguished Muslim astronomer and mathematician, who made important contributions to the development of trigonometry. Abūʾl-Wafāʾ worked in a private observatory in Baghdad, where he made observations to determine, among other astronomical parameters,... Adams, John Couch British mathematician and astronomer, one of two people who independently discovered the planet Neptune. On July 3, 1841, Adams had entered in his journal: “Formed a design in the beginning of this week of investigating, as soon as possible after taking... Aepinus, Franz Maria Ulrich Theodor Hoch physicist who discovered (1756) pyroelectricity in the mineral tourmaline and published (1759) the first mathematical theory of electric and magnetic phenomena. Aepinus studied medicine and briefly taught mathematics at the University of Rostock, where...

Agnesi, Maria Gaetana Italian mathematician and philosopher, considered to be the first woman in the Western world to have achieved a reputation in mathematics. Agnesi was the eldest child of a wealthy silk merchant who provided her with the best tutors available. She was... Ahlfors, Lars Valerian Finnish mathematician who was awarded one of the first two Fields Medals in 1936 for his work with Riemann surfaces. He also won the Wolf Prize in 1981. Ahlfors received his Ph.D. from the University of Helsinki in 1932. He held an appointment there... Aiken, Howard mathematician who invented the Harvard Mark I, forerunner of the modern electronic digital computer. Aiken did engineering work while he attended the University of Wisconsin, Madison. After completing his doctorate at Harvard University in 1939, he remained... al-Ḥanafī, ʿAlam al-Dīn Egyptian mathematician, astronomer, and engineer. He wrote a treatise on Euclid’s postulates, built water mills and fortifications on the Orontes River, and constructed the second-oldest existing Arabic celestial globe.

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(Solutions in two and three dimensions are first covered in plane and solid analytic geometry, respectively.) Algebraic geometry emerged... algebraic number real number for which there exists a polynomial equation with integer coefficients such that the given real number is a solution. Algebraic numbers include all of the natural numbers, all rational numbers, some irrational numbers, and complex numbers... algebraic surface in three-dimensional space, a surface the equation of which is f (x, y, z) = 0, with f (x, y, z) a polynomial in x, y, z. The order of the surface is the degree of the polynomial equation. If the surface is of the first order, it is a plane. If the... algebraic topology Field of mathematics that uses algebraic structures to study transformations of geometric objects. It uses function s (often called maps in this context) to represent continuous transformations (see topology). Taken together, a set of maps and objects... algorithm systematic procedure that produces—in a finite number of steps—the answer to a question or the solution of a problem. The name derives from the Latin translation, Algoritmi de numero Indorum, of the 9th-century Muslim mathematician al-Khwarizmi ’s arithmetic...

algorithms, analysis of Basic computer-science discipline that aids in the development of effective programs. Analysis of algorithms provides proof of the correctness of algorithms, allows for the accurate prediction of program performance, and can be used as a measure of computational... American Philosophical Society oldest extant learned society in the United States, founded under the impetus of Benjamin Franklin in 1743. At the beginning of the 21st century, it had more than 850 members, elected for their scholarly and scientific accomplishments in any of five... ʿĀmilī, Bahāʾ ad-Dīn Muḥammad ibn Ḥusayn al- theologian, mathematician, jurist, and astronomer who was a major figure in the cultural revival of Ṣafavid Iran. Al-ʿĀmilī was educated by his father, Shaykh Ḥusayn, a Shīʿite theologian, and by excellent teachers of mathematics and medicine. After... analysis a branch of mathematics that deals with continuous change and with certain general types of processes that have emerged from the study of continuous change, such as limits, differentiation, and integration. Since the discovery of the differential and...

analytic geometry mathematical subject in which algebraic symbolism and methods are used to represent and solve problems in geometry. The importance of analytic geometry is that it establishes a correspondence between geometric curves and algebraic equations. This correspondence... Analytical Engine generally considered the first computer, designed and partly built by the English inventor Charles Babbage in the 19th century (he worked on it until his death in 1871). While working on the Difference Engine, a simpler calculating machine commissioned... Apollonius of Perga mathematician, known by his contemporaries as “the Great Geometer,” whose treatise Conics is one of the greatest scientific works from the ancient world. Most of his other treatises are now lost, although their titles and a general indication of their... Archimedes the most-famous mathematician and inventor in ancient Greece. Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. He is known for his formulation of a hydrostatic... Archytas of Tarentum Greek scientist, philosopher, and major Pythagorean mathematician.

Plato, a close friend, made use of his work in mathematics, and there is evidence that Euclid borrowed from him for the treatment of number theory in Book VIII of his Elements. Archytas... arithmetic branch of mathematics in which numbers, relations among numbers, and observations on numbers are studied and used to solve problems. Arithmetic (a term derived from the Greek word arithmos, “number”) refers generally to the elementary aspects of the... arithmetic function any mathematical function defined for integers (…, −3, −2, −1, 0, 1, 2, 3, …) and dependent upon those properties of the integer itself as a number, in contrast to functions that are defined for other values (real numbers, complex numbers, or even other... Arnold, Vladimir Igorevich Soviet mathematician who made significant contributions to mathematics that had application in such diverse fields as celestial mechanics, fluid dynamics, and weather forecasting. While still an undergraduate (1954–59) at Moscow State University, Arnold... Artin, Emil Austro-German mathematician who made fundamental contributions to class field theory, notably the general law of reciprocity.

After one year at the University of Göttingen, Artin joined the staff of the University of Hamburg in 1923. He emigrated to... Aryabhata astronomer and the earliest Indian mathematician whose work and history are available to modern scholars. He is also known as Aryabhata I or Aryabhata the Elder to distinguish him from a 10th-century Indian mathematician of the same name. He flourished... associative law in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + (b + c) = (a + b) + c, and a (bc) = (ab) c; that is, the terms or factors may be associated in any way desired. While associativity... Atanasoff, John V. U.S. physicist. He received his Ph.D. from the University of Wisconsin. With Clifford Berry, he developed the Atanasoff-Berry Computer (1937–42), a machine capable of solving differential equations using binary arithmetic. In 1941 he joined the Naval...

Atiyah, Sir Michael Francis British mathematician who was awarded the Fields Medal in 1966 primarily for his work in topology. Atiyah received a knighthood in 1983 and the Order of Merit in 1992. He also served as president of the Royal Society (1990–95). Atiyah’s father was Lebanese... Aumann, Robert J. Israeli mathematician, who shared the 2005 Nobel Prize for Economics with Thomas C. Schelling. Aumann’s primary contribution to economics involved the analysis of repeated noncooperative encounters, a subject in the mathematical discipline of game theory.... austausch coefficient in fluid mechanics, particularly in its applications to meteorology and oceanography, the proportionality between the rate of transport of a component of a turbulent fluid and the rate of change of density of the component. In this context, the term... automata theory body of physical and logical principles underlying the operation of any electromechanical device (an automaton) that converts information from one form into another according to a definite procedure. Real or hypothetical automata of varying complexity...

axiom in logic, an indemonstrable first principle, rule, or maxim, that has found general acceptance or is thought worthy of common acceptance whether by virtue of a claim to intrinsic merit or on the basis of an appeal to self-evidence. An example would be:... axiom of choice statement in the language of set theory that makes it possible to form sets by choosing an element simultaneously from each member of an infinite collection of sets even when no algorithm exists for the selection. The axiom of choice has many mathematically... Babbage, Charles English mathematician and inventor who is credited with having conceived the first automatic digital computer. In 1812 Babbage helped found the Analytical Society, whose object was to introduce developments from the European continent into English mathematics.... Bacon, Roger English Franciscan philosopher and educational reformer who was a major medieval proponent of experimental science. Bacon studied mathematics, astronomy, optics, alchemy, and languages. He was the first European to describe in detail the process of making... Baire, René-Louis French mathematician whose study of irrational numbers and the concept of continuity of functions that approximate them greatly influenced the French school of mathematics.

The son of a tailor, Baire won a scholarship in 1886 that enabled him to attend... Baker, Alan British mathematician who was awarded the Fields Medal in 1970 for his work in number theory. Baker attended University College, London (B.S., 1961), and Trinity College, Cambridge (M.A. and Ph.D., 1964). He held an appointment at University College... Balmer, Johann Jakob Swiss mathematician who discovered a formula basic to the development of atomic theory and the field of atomic spectroscopy. A secondary-school teacher in Basel from 1859 until his death, Balmer also lectured (1865–90) on geometry at the University of... Banach, Stefan Polish mathematician who founded modern functional analysis and helped develop the theory of topological vector spaces. Banach was given the surname of his mother, who was identified as Katarzyna Banach on his birth certificate, and the first name of... Banneker, Benjamin mathematician, astronomer, compiler of almanacs, inventor, and writer, one of the first important African American intellectuals.

Banneker, a freeman, was raised on a farm near Baltimore that he would eventually inherit from his father. Although he periodically... Barlow, Peter optician and mathematician who invented two varieties of achromatic (non-colour-distorting) telescope lenses known as Barlow lenses. Self-educated, he became assistant mathematics master at the Royal Military Academy, Woolwich, in 1801. He published... Barrow, Isaac English classical scholar, theologian, and mathematician who was the teacher of Isaac Newton. He developed a method of determining tangents that closely approached the methods of calculus, and he first recognized that what became known as the processes... Bartholin, Erasmus Danish physician, mathematician, and physicist who discovered the optical phenomenon of double refraction. While professor of medicine (1657–98) at the University of Copenhagen, Bartholin observed that images seen through Icelandic feldspar (calcite)... base in mathematics, an arbitrarily chosen whole number greater than 1 in terms of which any number can be expressed as a sum of that base raised to various powers. See numerals and numeral systems.

Battānī, al- Arab astronomer and mathematician who refined existing values for the length of the year and of the seasons, for the annual precession of the equinoxes, and for the inclination of the ecliptic. He showed that the position of the Sun’s apogee, or farthest... Bayes, Thomas English Nonconformist theologian and mathematician who was the first to use probability inductively and who established a mathematical basis for probability inference (a means of calculating, from the frequency with which an event has occurred in prior... Bayesian analysis a method of statistical inference (named for English mathematician Thomas Bayes) that allows one to combine prior information about a population parameter with evidence from information contained in a sample to guide the statistical inference process.... Bayes’s theorem in probability theory, a means for revising predictions in light of relevant evidence, also known as conditional probability or inverse probability. The theorem was discovered among the papers of the English Presbyterian minister and mathematician Thomas... Bell, Eric Temple Scottish American mathematician, educator, and writer who made significant contributions to analytic number theory.

Bell emigrated to the United States at the age of 19 and immediately enrolled at Stanford University, where after only two years he earned... Beltrami, Eugenio Italian mathematician known for his description of non-Euclidean geometry and for his theories of surfaces of constant curvature. Following his studies at the University of Pavia (1853–56) and later in Milan, Beltrami was invited to join the faculty... Bernays, Paul Isaak Swiss mathematician whose work in proof theory and axiomatic set theory helped create the new discipline of mathematical logic. After obtaining his doctorate from the University of Göttingen in Germany under Edmund Landau in 1912, Bernays taught for... Bernoulli, Daniel the most distinguished of the second generation of the Bernoulli family of Swiss mathematicians. He investigated not only mathematics but also such fields as medicine, biology, physiology, mechanics, physics, astronomy, and oceanography. Bernoulli’s... Bernoulli family Two generations of distinguished Swiss mathematicians.

Jakob (1655–1705) and Johann (1667–1748) were the sons of a pharmacist who wanted one boy to study theology and the other medicine. Over his objections, both pursued careers in mathematics, making... Bernoulli, Jakob first of the Bernoulli family of Swiss mathematicians. He introduced the first principles of the calculus of variation. Bernoulli numbers, a concept that he developed, were named for him. The scion of a family of drug merchants, Jakob Bernoulli was compelled... Bernoulli, Johann major member of the Bernoulli family of Swiss mathematicians. He investigated the then new mathematical calculus, which he applied to the measurement of curves, to differential equations, and to mechanical problems. The son of a pharmacist, Johann studied... Bertrand, Joseph French mathematician and educator remembered for his elegant applications of differential equations to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability and the theory of curves and surfaces. The nephew...

Bessel function any of a set of mathematical functions systematically derived around 1817 by the German astronomer Friedrich Wilhelm Bessel during an investigation of solutions of one of Kepler’s equations of planetary motion. Particular functions of the set had been... Betti, Enrico mathematician who wrote a pioneering memoir on topology, the study of surfaces and higher-dimensional spaces, and wrote one of the first rigorous expositions of the theory of equations developed by the noted French mathematician Évariste Galois (1811–32).... Bhaskara I Indian astronomer and mathematician who helped to disseminate the mathematical work of Aryabhata (born 476). Little is known about the life of Bhaskara; I is appended to his name to distinguish him from a 12th-century Indian astronomer of the same name.... Bhāskara II the leading mathematician of the 12th century, who wrote the first work with full and systematic use of the decimal number system. Bhāskara II was the lineal successor of the noted Indian mathematician Brahmagupta (598– c. 665) as head of an astronomical...

Bigelow, Julian Himely American engineer and mathematician who engineered one of the earliest computers. In 1946 John von Neumann hired Bigelow as the engineer on his project, based at the Institute for Advanced Study, Princeton, to create a stored-program computer. Bigelow... binary number system in mathematics, positional numeral system employing 2 as the base and so requiring only two different symbols for its digits, 0 and 1, instead of the usual 10 different symbols needed in the decimal system. The numbers from 0 to 10 are thus in binary... binomial distribution in statistics, a common distribution function for discrete processes in which a fixed probability prevails for each independently generated value. First studied in connection with games of pure chance, the binomial distribution is now widely used to... binomial theorem statement that for any positive integer n, the n th power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form in the sequence of terms, the index r takes on the successive values 0, 1, 2,…, n. The coefficients, called...

Birch and Swinnerton-Dyer conjecture in mathematics, the conjecture that an elliptic curve (a type of cubic curve, or algebraic curve of order 3, confined to a region known as a torus) has either an infinite number of rational points (solutions) or a finite number of rational points, according... Birkhoff, George David foremost American mathematician of the early 20th century, who formulated the ergodic theorem. Birkhoff attended the Lewis Institute (now the Illinois Institute of Technology) in Chicago from 1896 to 1902 and then spent a year at the University of Chicago... Black, Max American Analytical philosopher who was concerned with the nature of clarity and meaning in language. Black studied at the Universities of Cambridge (B.A., 1930), Göttingen (1930–31), and London (Ph.D., 1939). He immigrated to the United States in 1940...

Blackwell, David Harold American statistician and mathematician who made significant contributions to game theory, probability theory, information theory, and Bayesian statistics and broke racial barriers when he was named (1965) the first African American member of the U.S.... Blaschke, Wilhelm Johann Eugen German mathematician whose major contributions to geometry concerned kinematics and differential and integral geometry. Blaschke became extraordinary professor of mathematics at the Deutsche Technische Hochschule (German Technical University), Prague,... Bliss, Gilbert Ames U.S. mathematician and educator known for his work on the calculus of variations. He received his B.S. degree in 1897 from the University of Chicago and remained to study mathematical astronomy under F.R. Moulton. He received his M.S. degree in 1898... Bôcher, Maxime American mathematician and educator whose teachings and writings influenced many mathematical researchers. Bôcher graduated from Harvard University in 1888 and received his doctorate from the University of Göttingen in 1891. Within months of acquiring...

Bochner, Salomon Galician-born American mathematician who made profound contributions to harmonic analysis, probability theory, differential geometry, and other areas of mathematics. Fearful of a Russian invasion in 1914, Bochner’s family moved to Berlin, Germany. Bochner... Bohr, Harald August Danish mathematician who devised a theory that concerned generalizations of functions with periodic properties, the theory of almost periodic functions. The brother of the noted physicist Niels Bohr, he became professor at the Polytechnic Institute in... Bolyai, János Hungarian mathematician and one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines. The discovery of a consistent alternative geometry that might correspond to the structure... Bolza, Oskar German mathematician and educator who was particularly noted for his work on the reduction of hyperelliptic to elliptic integrals and for his original contributions to the calculus of variations. Bolza studied at the University of Berlin and received...

Bolzano, Bernhard Bohemian mathematician and theologian who provided a more detailed proof for the binomial theorem in 1816 and suggested the means of distinguishing between finite and infinite classes. Bolzano graduated from the University of Prague as an ordained priest... Bombieri, Enrico Italian mathematician who was awarded the Fields Medal in 1974 for his work in number theory. Between 1979 and 1982 Bombieri served on the executive committee of the International Mathematical Union. Bombieri received a Ph.D. from the University of Milan... Bondi, Sir Hermann Austrian-born British mathematician and cosmologist who, with Fred Hoyle and Thomas Gold, formulated the steady-state theory of the universe. Bondi received an M.A. from Trinity College, Cambridge. During World War II he worked in the British Admiralty... Boole, George English mathematician who helped establish modern symbolic logic and whose algebra of logic, now called Boolean algebra, is basic to the design of digital computer circuits. Boole was given his first lessons in mathematics by his father, a tradesman,...

Borcherds, Richard Ewen British mathematician who won the Fields Medal in 1998 for his work in algebra. Borcherds studied undergraduate mathematics at the University of Cambridge and went on to finish his doctorate there in 1983. Afterward he held teaching and research positions... Borda, Jean-Charles de French mathematician and nautical astronomer noted for his studies of fluid mechanics and his development of instruments for navigation and geodesy, the study of the size and shape of the Earth. Borda entered the French army at an early age and later... Borel, Émile French mathematician who created the first effective theory of the measure of sets of points and who shares credit with René-Louis Baire and Henri Lebesgue of France for launching the modern theory of functions of a real variable. The son of a Protestant... Boscovich, Ruggero Giuseppe astronomer and mathematician who gave the first geometric procedure for determining the equator of a rotating planet from three observations of a surface feature and for computing the orbit of a planet from three observations of its position. Boscovich’s...

Bose, Satyendra Nath Indian mathematician and physicist noted for his collaboration with Albert Einstein in developing a theory regarding the gaslike qualities of electromagnetic radiation (see Bose-Einstein statistics). Bose, a graduate of the University of Calcutta, taught... Bott, Raoul Hungarian American mathematician who was the winner of the 2000 Wolf Prize in Mathematics for his contributions in topology and differential geometry, especially applications to mathematical physics. His early life was filled with tragedy; his parents... boundary value condition accompanying a differential equation in the solution of physical problems. In mathematical problems arising from physical situations, there are two considerations involved when finding a solution: (1) the solution and its derivatives must satisfy... Who Invented the Digital Computer? Who Invented the Digital Computer? Who Invented the Digital Computer? I want to take you back to 1830, and tell you an amazing story from the time of the industrial revolution. Charles Babbage A well known British mathematician, named Charles Babbage, came up with the idea of a machine that could compute polynomials of a variable, i.e. functions like a0 + a1x + a2x2+…+anxn.

By that time the importance of such functions had already been demonstrated in the work of the French physicist J.B. Fourier (1822). Fourier was studying the problem of heat propagation. He discovered what is now referred to in the fields of physics and mathematics as the ‘Fourier series’ or ‘Fourier transform’. His discovery was that one can approximate a general function using sums of periodic functions like sin(nx) and cos(nx), in which n is an integer. In a sense, these periodic functions serve as a basis for the approximation. It was well known then, that polynomial functions may be used in a similar way. Therefore, a machine that computes polynomial functions could be used to compute an approximation for almost any function. In the machine’s design, Babbage used a method of differences.

For example, to compute f(x)= 2x2 +3x +1 for any x, it is enough to compute the value of the function for some low x’s like f(1), f(2), f(3) and f(4), the differences between those values: f(2)-f(1), f(3)-f(2), f(4)-f(3), and the differences of the differences: (f(3)-f(2))-(f(2)- f(1)) and (f(4)-f(3))- (f(3)-f(2)). In this way, it is possible to compute the value of the function at any high x. To compute f(15), the machine works through 15 cycles, at each cycle only adding ‘differences’. The machine is activated by a crank, the operator rotating a handle the necessary amount of times (in this example, 15 times). In the spirit of his time, Babbage thought of using a steam engine to work the crank and handle, so to make the operation of the machine easier.

In order to help clarify this principle, we bring the following table for our function f(x)= 2x2 +3x +1 : 4 The machine has three cogwheels. The operator places the left wheel at state 6, the middle wheel at state 9 and the right wheel at state 4 (this corresponds to the upper diagonal in the table above). At the first half cycle, a clutch (like the one in your car) joins the left and middle wheels. The machine turns the middle wheel to zero position, that is, 9 steps clockwise, moving the left wheel 9 steps counterclockwise – bringing the left wheel to state 15. At this point, the clutch is drawn back and a spring returns the middle wheel back to its original position – state 9. At the next half cycle, the clutch joins the middle and right wheels. The machine turns the right wheel 4 steps clockwise, moving the middle wheel 4 steps counterclockwise to position 13. A spring now returns the right wheel to its original position – state 4. This completes a full cycle and brings each of the cogwheels to its next position (the second diagonal from the top).

A portion of a reconstructed Difference Engine, built from Babbage’s working drawings in 1991 Babbage called the machine a “difference engine “. He made a small model of it and presented it at his evening cocktail parties, as the “thinking machine”. However, he could not build the complete machine. At the time, even the most advanced technology available was far from satisfactory for the needs of such a machine. Babbage himself manufactured some of the parts necessary for the machine. In addition to a generous fund granted to him by the British government for the purpose of building such a machine, Babbage also invested all of his savings in the project. In 1832, Babbage was a highly influential scientist in England, a well known professor at Cambridge, a member of Parliament, a member of the Royal Society (of sciences), and a famous figure in the world of economy. The next machine he was about to invent, the ‘analytical engine’, was an information- processing machine, which reflected his background in economy. Babbage was thinking about the principle of ‘division of labor’, an economic term that had been in use since the time of Adam Smith (see the “Wealth of Nations”, 1776).

According to this principle, the most efficient way to manufacture a product is to divide the work between several workers, each specializing in a certain aspect of the process. The worst, least efficient way is to let each one of the workers do the whole job. A portion of the ‘mill’ of the analytical engine built in 1871 by Henry Babbage in honor of his father Towards the end of the 18th century this idea was taken seriously by Gaspard de Prony, who was in charge of the new tax and measurement system in France. De Prony conceived the idea of building a huge information ‘machine’. This ‘machine’ was based on distributing the mathematical work necessary for computing between three groups of people. At the top of the computing pyramid De Prony placed several famous French mathematicians of that period, including Legendre and Carno, who gave the mathematical formulas and instructions for the computing process. At the middle of the pyramid he placed less famous mathematicians, whose task was to interpret the formulas to simple computations, and to collect results from the computing section. At the bottom of the pyramid were the ‘human computers’, whose main task was to compute, mainly adding numbers.

At that time, the word ‘computer’ referred to a person whose job was to compute, not to a machine. Babbage learned about the project during a visit to France. But De Prony’s information machine was not one of a kind. 19th century banks used ‘Clearing Houses’. These were rooms to which agents from every branch of each bank in London would arrive in at the end of each day in order to balance checks and transfer money. Babbage was visiting one of these clearing houses just before he came up with the idea of the analytic engine. This gave him a strong sense that computation includes also manipulation of symbols. In the analytic engine, the labor of computing is divided between several parts. There is the ‘mill’, where the machine actually calculates. Babbage used notions from the cotton industry. He was inspired by the automatic looming machines of his time, especially the Jacquard loom. Another part in the analytical engine is the ‘store’ where numbers are stored, waiting to be used by the machine. A third part of the machine includes a drum. On top of the drum there is a roll of punched cards. The cards include codes of operations and codes for the places in the ‘store’ where the variables lie.

Suppose now the first card includes a code of an operation, such as subtraction or multiplication, and the second card includes a code for the locations of the variables in the ‘store’. Having read the first card, the machine tunes itself to the appropriate mode (subtraction or multiplication). After reading the second card, the machine looks for the correct place in the ‘store’. Using the cogwheels, the machine reads numbers from the ‘store’ and multiplies (or subtracts) them. The next card tells the machine where to store the result. The ‘mill’ uses the cogwheels to write the result in the ‘store’… Looking at the machine from a distance, one could see the drum revolving and the ‘mill’ moving to and fro in front of the ‘store’. When the computation was completed the result could be read from a certain point at the ‘store’. Babbage’s analytical engine includes all the components of a modern computer. There is the memory- the ‘store’, the central processing unit- the ‘mill’, and the program or software- the punched cards. Babbage understood that one can use numbers as codes or as data. He spent two years figuring out this scheme of computations.

Lady Lovelace It was a struggle to build the difference engine at that time, so you can imagine how building the analytical engine was virtually impossible. The British government stopped financing the project but Babbage was obsessed by his invention and seeked recognition outside England. In 1840 he traveled to Italy in order to deliver a lecture about his engines. In Italy Babbage met a mathematician named Luigi Federico Menabrea, later to become the Italian Prime Minister. Menabrea wrote a paper describing Babbage’s analytical machine, and Babbage’s old friend Ada Lovelace, a mathematician and daughter of Lord Byron, translated Menabrea’s paper into English and added a mathematical appendix (longer than the paper itself) explaining the operation of the engine. In the appendix Lovelace wrote that Babbage’s machine weaves numbers like a loom (you may have heard the name ADA, it’s a programming language named after Lady Lovelace). I would like to conclude with Menabrea’s vision about the future role of the analytical engine, probably quoting Babbage: “Again, who can foresee the consequences of such an invention?

In truth, how many precious observations remain practically barren for the progress of the sciences, because there are not powers sufficient for computing the results! And what discouragement does the perspective of a long and arid computation cast into the mind of a man of genius, who demands time exclusively for meditation, and who beholds it snatched from him by the material routine of operations! Yet it is by the laborious rout of analysis that he must reach truth: but he cannot pursue this unless guided by numbers; for without numbers it is not given us to raise the veil which envelopes the mysteries of nature. Thus the idea of constructing an apparatus capable of aiding human weakness in such researches, is a conception which, being realized, would mark a glorious epoch in the history of the sciences.” Babbage never lost his interest in the machine, but became angry, bitter, and frustrated with the British government for what he called a loss of sight. Well, I guess he was right! Digital computers were forgotten for about a hundred years, from the failure of Babbage’s project to their resurrection in the 1940’s.

Further reading: The difference engine, Charles Babbage and the quest to build the first computer, by Doron Swade, Penguin Group, 2000. Jacquard’s web, How a hand loom led to the birth of the information age, by James Essinger, Oxford University Press, 2004. About the author: Boaz Tamir holds a Ph.D. degree in Mathematics from the Weizmann Institute of Science. In 2008 he recived a second Ph.D. from the department of History and Philosophy of Science at the Bar Ilan University. Related Posts . : Computer Science : . Charles Babbage ______________________________________________________________ Babbage, Charles (b. Dec. 26, 1791, London, Eng.--d. Oct. 18, 1871, London), English mathematician and inventor who is credited with having conceived the first automatic digital computer. In 1812 Babbage helped found the Analytical Society, whose object was to introduce developments from the European continent into English mathematics. In 1816 he was elected a fellow of the Royal Society of London.

He was instrumental in founding the Royal Astronomical (1820) and Statistical (1834) societies. The idea of mechanically calculating mathematical tables first came to Babbage in 1812 or 1813. Later he made a small calculator that could perform certain mathematical computations to eight decimals. Then in 1823 he obtained government support for the design of a projected machine with a 20-decimal capacity. Its construction required the development of mechanical engineering techniques, to which Babbage of necessity devoted himself. In the meantime (1828-39) he served as Lucasian professor of mathematics at the University of Cambridge. During the mid-1830s Babbage developed plans for the so-called analytical engine, the forerunner of the modern digital computer. In this device he envisioned the capability of performing any arithmetical operation on the basis of instructions from punched cards, a memory unit in which to store numbers, sequential control, and most of the other basic elements of the present-day computer. The analytical engine, however, was never completed. Babbage's design was forgotten until his unpublished notebooks were discovered in 1937.

In 1991 British scientists built Difference Engine No. 2--accurate to 31 digits--to Babbage's specifications. Babbage made notable contributions in other areas as well. He assisted in establishing the modern postal system in England and compiled the first reliable actuarial tables. He also invented a type of speedometer and the locomotive cowcatcher. 1000+ images about Ada Lovelace & Charles Babbage on Pinterest | Engine, Mathematicians and Computers Forward Not Less Than Gods by Kage Baker Today’s book is the ninth book in a series that is not a steampunk series, yet I think it qualifies for inclusion here. The trick is that the series is about time travel and in this one the travel is to a steampunk Victorian England. The result is a lighthearted steampunk James Bond-style adventure using what Publisher’s Weekly called “Charles-Babbage-meets-Maxwell-Smart technologia”.

Whether the much-loved late Kage Baker would have explored the steampunk… See More Babbage, Charles | Short Biography Babbage, Charles Sorry, there was a problem with our biography API Related links to Babbage, Charles Charles Babbage - Wikipedia, the free… Charles Babbage, FRS (26 December 1791 – 18 October 1871) was an English polymath. He was a mathematician, philosopher, inventor and mechanical engineer, who is ... Charles Babbage Biography, Computer models… Charles Babbage (Dec. 1791 – Oct. 1871) Mathematician, philosopher and (proto-) computer scientist who originated the idea of a programmable computer. Charles Babbage A biography by J.A.N. Lee. looking at him as a philosopher, politician, Newtonian, and industrialist. Charles Babbage (British inventor and… English mathematician and inventor who is credited with having conceived the first automatic digital computer. In 1812 Babbage helped found the Analytical Society ... BBC - History - Charles Babbage Read a concise life history of Charles Babbage, a pioneer of computer science. Discover facts about his inventions.

Charles Babbage Biography - YouTube Charles Babbage 1791 - 1871 Charles Babbage is considered to be the father of the first programmable computer. All content is either in the public domain ... Charles Babbage - Mathematician Biography,… Charles Babbage Biography - Early Life Charles Babbage was a Mathematician, inventor, philosopher and mechanical engineer. His place of birth is not confirmed but ... Charles Babbage - MacTutor History of… Biography of Charles Babbage (1791-1871) ... Both the date and place of Charles Babbage's birth were uncertain but have now been firmly established. Charles Babbage Biography: The Inventor of… 06/04/2010 · A prolific inventor, mathematician, scientist and political economist, Charles Babbage is widely known as the father of the computer. Charles Babbage ... Ada Byron, Lady Lovelace - Agnes Scott… Brief biography, by Dr. Betty Toole, along with a portrait and links. World-Information.Org The 19th Century: First Programmable Computing Devices Until the 19th century "early computers", probably better described as calculating machines, were basically mechanical devices and operated by hand.

Early calculators like the abacus worked with a system of sliding beads arranged on a rack and the centerpiece of Leibniz's multiplier was a stepped-drum gear design. Therefore Charles Babbage's proposal of the Difference Engine (1822), which would have (it was never completed) a stored program and should perform calculations and print the results automatically, was a major breakthrough, as it for the first time suggested the automation of computers. The construction of the Difference Engine, which should perform differential equations, was inspired by Babbage's idea to apply the ability of machines to the needs of mathematics. Machines, he noted, were best at performing tasks repeatedly without mistakes, while mathematics often required the simple repetition of steps. After working on the Difference Engine for ten years Babbage was inspired to build another machine, which he called Analytical Engine. Its invention was a major step towards the design of modern computers, as it was conceived the first general-purpose computer. Instrumental to the machine's design was his assistant, Augusta Ada King, Countess of Lovelace, the first female computer programmer. The second major breakthrough in the design of computing machines in the 19th century may be attributed to the American inventor Herman Hollerith.

He was concerned with finding a faster way to compute the U.S. census, which in 1880 had taken nearly seven years. Therefore Hollerith invented a method, which used cards to store data information which he fed into a machine that compiled the results automatically. The punch cards not only served as a storage method and helped reduce computational errors, but furthermore significantly increased speed. Of extraordinary importance for the evolution of digital computers and artificial intelligence have furthermore been the contributions of the English mathematician and logician George Boole . In his postulates concerning the Laws of Thought (1854) he started to theorize about the true/false nature of binary numbers. His principles make up what today is known as Boolean algebra, the collection of logic concerning AND, OR, NOT operands, on which computer switching theory and procedures are grounded. Boole also assumed that the human mind works according to these laws, it performs logical operations that could be reasoned. Ninety years later Boole's principles were applied to circuits , the blueprint for electronic computers, by Claude Shannon. TEXTBLOCK 1/1 // URL:

Question: Which mathematician and inventor conceived the first automatic digital computer?
Answer: Charles Babbage