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Benjamin Franklin (January 17, 1706 [O.S. January 6, 1705] – April 17, 1790) was an American polymath and one of the Founding Fathers of the United States. Franklin was a leading writer, printer, political philosopher, politician, Freemason, postmaster, scientist, inventor, humorist, civic activist, statesman, and diplomat. As a scientist, he was a major figure in the American Enlightenment and the history of physics for his discoveries and theories regarding electricity. As an inventor, he is known for the lightning rod, bifocals, and the Franklin stove, among other inventions. He founded many civic organizations, including the Library Company, Philadelphia's first fire department and the University of Pennsylvania.

Franklin earned the title of "The First American" for his early and indefatigable campaigning for colonial unity, initially as an author and spokesman in London for several colonies. As the first United States Ambassador to France, he exemplified the emerging American nation. Franklin was foundational in defining the American ethos as a marriage of the practical values of thrift, hard work, education, community spirit, self-governing institutions, and opposition to authoritarianism both political and religious, with the scientific and tolerant values of the Enlightenment. In the words of historian Henry Steele Commager, "In a Franklin could be merged the virtues of Puritanism without its defects, the illumination of the Enlightenment without its heat." To Walter Isaacson, this makes Franklin "the most accomplished American of his age and the most influential in inventing the type of society America would become."

Franklin became a successful newspaper editor and printer in Philadelphia, the leading city in the colonies, publishing the Pennsylvania Gazette at the age of 23. He became wealthy publishing this and Poor Richard's Almanack, which he authored under the pseudonym "Richard Saunders". After 1767, he was associated with the Pennsylvania Chronicle, a newspaper that was known for its revolutionary sentiments and criticisms of British policies.

He pioneered and was the first president of Academy and College of Philadelphia which opened in 1751 and later became the University of Pennsylvania. He organized and was the first secretary of the American Philosophical Society and was elected president in 1769. Franklin became a national hero in America as an agent for several colonies when he spearheaded an effort in London to have the Parliament of Great Britain repeal the unpopular Stamp Act. An accomplished diplomat, he was widely admired among the French as American minister to Paris and was a major figure in the development of positive Franco-American relations. His efforts proved vital for the American Revolution in securing shipments of crucial munitions from France.

He was promoted to deputy postmaster-general for the British colonies in 1753, having been Philadelphia postmaster for many years, and this enabled him to set up the first national communications network. During the revolution, he became the first United States Postmaster General. He was active in community affairs and colonial and state politics, as well as national and international affairs. From 1785 to 1788, he served as governor of Pennsylvania. He initially owned and dealt in slaves but, by the late 1750s, he began arguing against slavery and became an abolitionist.

His life and legacy of scientific and political achievement, and his status as one of America's most influential Founding Fathers, have seen Franklin honored more than two centuries after his death on coinage and the $100 bill, warships, and the names of many towns, counties, educational institutions, and corporations, as well as countless cultural references.

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Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer.

Considered by some to be a father of the computer, Babbage is credited with inventing the first mechanical computer that eventually led to more complex electronic designs, though all the essential ideas of modern computers are to be found in Babbage's Analytical Engine. His varied work in other fields has led him to be described as "pre-eminent" among the many polymaths of his century.

Parts of Babbage's incomplete mechanisms are on display in the Science Museum in London. In 1991, a functioning difference engine was constructed from Babbage's original plans. Built to tolerances achievable in the 19th century, the success of the finished engine indicated that Babbage's machine would have worked.

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Muḥammad ibn Mūsā al-Khwārizmī (Persian: Muḥammad Khwārizmī محمد بن موسی خوارزمی‎; c. 780 – c. 850), Arabized as al-Khwarizmi with al- and formerly Latinized as Algorithmi, was a Persian polymath who produced works in mathematics, astronomy, and geography. Around 820 CE he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad.

Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813–833 CE) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The term algebra itself comes from the title of his book (specifically the word al-jabr meaning "completion" or "rejoining"). His name gave rise to the terms algorism and algorithm. His name is also the origin of (Spanish) guarismo and of (Portuguese) algarismo, both meaning digit.

In the 12th century, Latin translations of his textbook on arithmetic (Algorithmo de Numero Indorum) which codified the various Indian numerals, introduced the decimal positional number system to the Western world. The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities.

In addition to his best-known works, he revised Ptolemy's Geography, listing the longitudes and latitudes of various cities and localities. He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial. He also made important contributions to trigonometry, producing accurate sine and cosine tables, and the first table of tangents.