Germany the Federal Republic of Germany, is a country in Central and Western Europe, lying between the Baltic and North Seas to the north, the Alps to the south. It borders Denmark to the north and the Czech Republic to the east and Switzerland to the south, France to the southwest, Luxembourg and the Netherlands to the west. Germany includes 16 constituent states, covers an area of 357,386 square kilometres, has a temperate seasonal climate. With 83 million inhabitants, it is the second most populous state of Europe after Russia, the most populous state lying in Europe, as well as the most populous member state of the European Union. Germany is a decentralized country, its capital and largest metropolis is Berlin, while Frankfurt serves as its financial capital and has the country's busiest airport. Germany's largest urban area is the Ruhr, with its main centres of Essen; the country's other major cities are Hamburg, Cologne, Stuttgart, Düsseldorf, Dresden, Bremen and Nuremberg. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity.
A region named Germania was documented before 100 AD. During the Migration Period, the Germanic tribes expanded southward. Beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation. After the collapse of the Holy Roman Empire, the German Confederation was formed in 1815; the German revolutions of 1848–49 resulted in the Frankfurt Parliament establishing major democratic rights. In 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the revolution of 1918–19, the Empire was replaced by the parliamentary Weimar Republic; the Nazi seizure of power in 1933 led to the establishment of a dictatorship, the annexation of Austria, World War II, the Holocaust. After the end of World War II in Europe and a period of Allied occupation, Austria was re-established as an independent country and two new German states were founded: West Germany, formed from the American and French occupation zones, East Germany, formed from the Soviet occupation zone.
Following the Revolutions of 1989 that ended communist rule in Central and Eastern Europe, the country was reunified on 3 October 1990. Today, the sovereign state of Germany is a federal parliamentary republic led by a chancellor, it is a great power with a strong economy. As a global leader in several industrial and technological sectors, it is both the world's third-largest exporter and importer of goods; as a developed country with a high standard of living, it upholds a social security and universal health care system, environmental protection, a tuition-free university education. The Federal Republic of Germany was a founding member of the European Economic Community in 1957 and the European Union in 1993, it is part of the Schengen Area and became a co-founder of the Eurozone in 1999. Germany is a member of the United Nations, NATO, the G7, the G20, the OECD. Known for its rich cultural history, Germany has been continuously the home of influential and successful artists, musicians, film people, entrepreneurs, scientists and inventors.
Germany has a large number of World Heritage sites and is among the top tourism destinations in the world. The English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine; the German term Deutschland diutisciu land is derived from deutsch, descended from Old High German diutisc "popular" used to distinguish the language of the common people from Latin and its Romance descendants. This in turn descends from Proto-Germanic *þiudiskaz "popular", derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- "people", from which the word Teutons originates; the discovery of the Mauer 1 mandible shows that ancient humans were present in Germany at least 600,000 years ago. The oldest complete hunting weapons found anywhere in the world were discovered in a coal mine in Schöningen between 1994 and 1998 where eight 380,000-year-old wooden javelins of 1.82 to 2.25 m length were unearthed. The Neander Valley was the location where the first non-modern human fossil was discovered.
The Neanderthal 1 fossils are known to be 40,000 years old. Evidence of modern humans dated, has been found in caves in the Swabian Jura near Ulm; the finds included 42,000-year-old bird bone and mammoth ivory flutes which are the oldest musical instruments found, the 40,000-year-old Ice Age Lion Man, the oldest uncontested figurative art discovered, the 35,000-year-old Venus of Hohle Fels, the oldest uncontested human figurative art discovered. The Nebra sky disk is a bronze artefact created during the European Bronze Age attributed to a site near Nebra, Saxony-Anhalt, it is part of UNESCO's Memory of the World Programme. The Germanic tribes are thought to date from the Pre-Roman Iron Age. From southern Scandinavia and north Germany, they expanded south and west from the 1st century BC, coming into contact with the Celtic tribes of Gaul as well
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, measure, infinite series, analytic functions. These theories are studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary techniques of analysis. Analysis may be distinguished from geometry. Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy. Greek mathematicians such as Eudoxus and Archimedes made more explicit, but informal, use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids; the explicit use of infinitesimals appears in Archimedes' The Method of Mechanical Theorems, a work rediscovered in the 20th century.
In Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would be called Cavalieri's principle to find the volume of a sphere in the 5th century; the Indian mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolle's theorem in the 12th century. In the 14th century, Madhava of Sangamagrama developed infinite series expansions, like the power series and the Taylor series, of functions such as sine, cosine and arctangent. Alongside his development of the Taylor series of the trigonometric functions, he estimated the magnitude of the error terms created by truncating these series and gave a rational approximation of an infinite series, his followers at the Kerala School of Astronomy and Mathematics further expanded his works, up to the 16th century. The modern foundations of mathematical analysis were established in 17th century Europe. Descartes and Fermat independently developed analytic geometry, a few decades Newton and Leibniz independently developed infinitesimal calculus, which grew, with the stimulus of applied work that continued through the 18th century, into analysis topics such as the calculus of variations and partial differential equations, Fourier analysis, generating functions.
During this period, calculus techniques were applied to approximate discrete problems by continuous ones. In the 18th century, Euler introduced the notion of mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the modern definition of continuity in 1816, but Bolzano's work did not become known until the 1870s. In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra used in earlier work by Euler. Instead, Cauchy formulated calculus in terms of geometric infinitesimals. Thus, his definition of continuity required an infinitesimal change in x to correspond to an infinitesimal change in y, he introduced the concept of the Cauchy sequence, started the formal theory of complex analysis. Poisson, Liouville and others studied partial differential equations and harmonic analysis; the contributions of these mathematicians and others, such as Weierstrass, developed the -definition of limit approach, thus founding the modern field of mathematical analysis.
In the middle of the 19th century Riemann introduced his theory of integration. The last third of the century saw the arithmetization of analysis by Weierstrass, who thought that geometric reasoning was inherently misleading, introduced the "epsilon-delta" definition of limit. Mathematicians started worrying that they were assuming the existence of a continuum of real numbers without proof. Dedekind constructed the real numbers by Dedekind cuts, in which irrational numbers are formally defined, which serve to fill the "gaps" between rational numbers, thereby creating a complete set: the continuum of real numbers, developed by Simon Stevin in terms of decimal expansions. Around that time, the attempts to refine the theorems of Riemann integration led to the study of the "size" of the set of discontinuities of real functions. "monsters" began to be investigated. In this context, Jordan developed his theory of measure, Cantor developed what is now called naive set theory, Baire proved the Baire category theorem.
In the early 20th century, calculus was formalized using an axiomatic set theory. Lebesgue solved the problem of measure, Hilbert introduced Hilbert spaces to solve integral equations; the idea of normed vector space was in the air, in the 1920s Banach created functional analysis. In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. Much of analysis happens in some metric space. Examples of analysis without a metric include functional analysis. Formally, a metric space is an ordered pair where M is a set
The Bible is a collection of sacred texts or scriptures. Varying parts of the Bible are considered to be a product of divine inspiration and a record of the relationship between God and humans by Christians, Jews and Rastafarians. What is regarded as canonical text differs depending on traditions and groups; the Hebrew Bible overlaps with the Christian Old Testament. The Christian New Testament is a collection of writings by early Christians, believed to be Jewish disciples of Christ, written in first-century Koine Greek. Among Christian denominations there is some disagreement about what should be included in the canon about the Apocrypha, a list of works that are regarded with varying levels of respect. Attitudes towards the Bible differ among Christian groups. Roman Catholics, high church Anglicans and Eastern Orthodox Christians stress the harmony and importance of the Bible and sacred tradition, while Protestant churches, including Evangelical Anglicans, focus on the idea of sola scriptura, or scripture alone.
This concept arose during the Protestant Reformation, many denominations today support the use of the Bible as the only infallible source of Christian teaching. The Bible has been a massive influence on literature and history in the Western World, where the Gutenberg Bible was the first book printed using movable type. According to the March 2007 edition of Time, the Bible "has done more to shape literature, history and culture than any book written, its influence on world history is unparalleled, shows no signs of abating." With estimated total sales of over 5 billion copies, it is considered to be the most influential and best-selling book of all time. As of the 2000s, it sells 100 million copies annually; the English word Bible is from the Latin biblia, from the same word in Medieval Latin and Late Latin and from Koinē Greek: τὰ βιβλία, translit. Ta biblia "the books". Medieval Latin biblia is short for biblia sacra "holy book", while biblia in Greek and Late Latin is neuter plural, it came to be regarded as a feminine singular noun in medieval Latin, so the word was loaned as a singular into the vernaculars of Western Europe.
Latin biblia sacra "holy books" translates Greek τὰ βιβλία τὰ ἅγια tà biblía tà ágia, "the holy books". The word βιβλίον itself had the literal meaning of "paper" or "scroll" and came to be used as the ordinary word for "book", it is the diminutive of βύβλος byblos, "Egyptian papyrus" so called from the name of the Phoenician sea port Byblos from whence Egyptian papyrus was exported to Greece. The Greek ta biblia was "an expression. Christian use of the term can be traced to c. 223 CE. The biblical scholar F. F. Bruce notes that Chrysostom appears to be the first writer to use the Greek phrase ta biblia to describe both the Old and New Testaments together. By the 2nd century BCE, Jewish groups began calling the books of the Bible the "scriptures" and they referred to them as "holy", or in Hebrew כִּתְבֵי הַקֹּדֶשׁ, Christians now call the Old and New Testaments of the Christian Bible "The Holy Bible" or "the Holy Scriptures"; the Bible was divided into chapters in the 13th century by Stephen Langton and it was divided into verses in the 16th century by French printer Robert Estienne and is now cited by book and verse.
The division of the Hebrew Bible into verses is based on the sof passuk cantillation mark used by the 10th-century Masoretes to record the verse divisions used in earlier oral traditions. The oldest extant copy of a complete Bible is an early 4th-century parchment book preserved in the Vatican Library, it is known as the Codex Vaticanus; the oldest copy of the Tanakh in Hebrew and Aramaic dates from the 10th century CE. The oldest copy of a complete Latin Bible is the Codex Amiatinus. Professor John K. Riches, Professor of Divinity and Biblical Criticism at the University of Glasgow, says that "the biblical texts themselves are the result of a creative dialogue between ancient traditions and different communities through the ages", "the biblical texts were produced over a period in which the living conditions of the writers – political, cultural and ecological – varied enormously". Timothy H. Lim, a professor of Hebrew Bible and Second Temple Judaism at the University of Edinburgh, says that the Old Testament is "a collection of authoritative texts of divine origin that went through a human process of writing and editing."
He states that it is not a magical book, nor was it written by God and passed to mankind. Parallel to the solidification of the Hebrew canon, only the Torah first and the Tanakh began to be translated into Greek and expanded, now referred to as the Septuagint or the Greek Old Testament. In Christian Bibles, the New Testament Gospels were derived from oral traditions in the second half of the first century CE. Riches says that: Scholars have attempted to reconstruct something of the history of the oral traditions behind the Gospels, but the results have not been too encouraging; the period of transmission is short: less than 40 years passed between the death of Jesus and the writing of Mark's Gospel. This means that there was little time for oral trad
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e. sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the residuals made in the results of every single equation. The most important application is in data fitting; the best fit in the least-squares sense minimizes the sum of squared residuals. When the problem has substantial uncertainties in the independent variable simple regression and least-squares methods have problems. Least-squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns; the linear least-squares problem occurs in statistical regression analysis. The nonlinear problem is solved by iterative refinement. Polynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent variable and the deviations from the fitted curve.
When the observations come from an exponential family and mild conditions are satisfied, least-squares estimates and maximum-likelihood estimates are identical. The method of least squares can be derived as a method of moments estimator; the following discussion is presented in terms of linear functions but the use of least squares is valid and practical for more general families of functions. By iteratively applying local quadratic approximation to the likelihood, the least-squares method may be used to fit a generalized linear model; the least-squares method is credited to Carl Friedrich Gauss, but it was first published by Adrien-Marie Legendre. The method of least squares grew out of the fields of astronomy and geodesy, as scientists and mathematicians sought to provide solutions to the challenges of navigating the Earth's oceans during the Age of Exploration; the accurate description of the behavior of celestial bodies was the key to enabling ships to sail in open seas, where sailors could no longer rely on land sightings for navigation.
The method was the culmination of several advances that took place during the course of the eighteenth century: The combination of different observations as being the best estimate of the true value. The combination of different observations taken under the same conditions contrary to trying one's best to observe and record a single observation accurately; the approach was known as the method of averages. This approach was notably used by Tobias Mayer while studying the librations of the moon in 1750, by Pierre-Simon Laplace in his work in explaining the differences in motion of Jupiter and Saturn in 1788; the combination of different observations taken under different conditions. The method came to be known as the method of least absolute deviation, it was notably performed by Roger Joseph Boscovich in his work on the shape of the earth in 1757 and by Pierre-Simon Laplace for the same problem in 1799. The development of a criterion that can be evaluated to determine when the solution with the minimum error has been achieved.
Laplace tried to specify a mathematical form of the probability density for the errors and define a method of estimation that minimizes the error of estimation. For this purpose, Laplace used a symmetric two-sided exponential distribution we now call Laplace distribution to model the error distribution, used the sum of absolute deviation as error of estimation, he felt these to be the simplest assumptions he could make, he had hoped to obtain the arithmetic mean as the best estimate. Instead, his estimator was the posterior median; the first clear and concise exposition of the method of least squares was published by Legendre in 1805. The technique is described as an algebraic procedure for fitting linear equations to data and Legendre demonstrates the new method by analyzing the same data as Laplace for the shape of the earth; the value of Legendre's method of least squares was recognized by leading astronomers and geodesists of the time. In 1809 Carl Friedrich Gauss published his method of calculating the orbits of celestial bodies.
In that work he claimed to have been in possession of the method of least squares since 1795. This led to a priority dispute with Legendre. However, to Gauss's credit, he went beyond Legendre and succeeded in connecting the method of least squares with the principles of probability and to the normal distribution, he had managed to complete Laplace's program of specifying a mathematical form of the probability density for the observations, depending on a finite number of unknown parameters, define a method of estimation that minimizes the error of estimation. Gauss showed that the arithmetic mean is indeed the best estimate of the location parameter by changing both the probability density and the method of estimation, he turned the problem around by asking what form the density should have and what method of estimation should be used to get the arithmetic mean as estimate of the location parameter. In this attempt, he invented the normal distribution. An early demonstration of the strength of Gauss's method came when it was used to predict the future location of the newly discovered astero
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics. By extension, use of complex analysis has applications in engineering fields such as nuclear, aerospace and electrical engineering; as a differentiable function of a complex variable is equal to the sum of its Taylor series, complex analysis is concerned with analytic functions of a complex variable. Complex analysis is one of the classical branches in mathematics, with roots in the 18th century and just prior. Important mathematicians associated with complex numbers include Euler, Riemann, Cauchy and many more in the 20th century. Complex analysis, in particular the theory of conformal mappings, has many physical applications and is used throughout analytic number theory. In modern times, it has become popular through a new boost from complex dynamics and the pictures of fractals produced by iterating holomorphic functions.
Another important application of complex analysis is in string theory which studies conformal invariants in quantum field theory. A complex function is a function from complex numbers to complex numbers. In other words, it is a function that has a subset of the complex numbers as a domain and the complex numbers as a codomain. Complex functions are supposed to have a domain that contains a nonempty open subset of the complex plane. For any complex function, the values z from the domain and their images f in the range may be separated into real and imaginary parts: z = x + i y and f = f = u + i v, where x, y, u, v are all real-valued. In other words, a complex function f: C → C may be decomposed into u: R 2 → R and v: R 2 → R, i.e. into two real-valued functions of two real variables. Any complex-valued function f on an arbitrary set X can be considered as an ordered pair of two real-valued functions: or, alternatively, as a vector-valued function from X into R 2; some properties of complex-valued functions are nothing more than the corresponding properties of vector valued functions of two real variables.
Other concepts of complex analysis, such as differentiability are direct generalizations of the similar concepts for real functions, but may have different properties. In particular, every differentiable complex function is analytic, two differentiable functions that are equal in a neighborhood of a point are equal on the intersection of their domain; the latter property is the basis of the principle of analytic continuation which allows extending every real analytic function in a unique way for getting a complex analytic function whose domain is the whole complex plane with a finite number of curve arcs removed. Many basic and special complex functions are defined in this way, including exponential functions, logarithmic functions, trigonometric functions. Complex functions that are differentiable at every point of an open subset Ω of the complex plane are said to be holomorphic on Ω. In the context of complex analysis, the derivative of f at z 0 is defined to be f ′ = lim z → z 0 f − f z − z 0, z ∈ C.
Superficially, this definition is formally analogous to that of the derivative of a real function. However, complex derivatives and differentiable functions behave in different ways compared to their real counterparts. In particular, for this limit to exist, the value of the difference quotient must approach the same complex number, regardless of the manner in which we
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (. Sometimes referred to as the Princeps mathematicorum and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, is ranked among history's most influential mathematicians. Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick, in the Duchy of Brunswick-Wolfenbüttel, to poor, working-class parents, his mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension. Gauss solved this puzzle about his birthdate in the context of finding the date of Easter, deriving methods to compute the date in both past and future years, he was christened and confirmed in a church near the school he attended as a child. Gauss was a child prodigy. In his memorial on Gauss, Wolfgang Sartorius von Waltershausen says that when Gauss was three years old he corrected a math error his father made. Many versions of this story have been retold since that time with various details regarding what the series was – the most frequent being the classical problem of adding all the integers from 1 to 100.
There are many other anecdotes about his precocity while a toddler, he made his first groundbreaking mathematical discoveries while still a teenager. He completed his magnum opus, Disquisitiones Arithmeticae, in 1798, at the age of 21—though it was not published until 1801; this work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day. Gauss's intellectual abilities attracted the attention of the Duke of Brunswick, who sent him to the Collegium Carolinum, which he attended from 1792 to 1795, to the University of Göttingen from 1795 to 1798. While at university, Gauss independently rediscovered several important theorems, his breakthrough occurred in 1796 when he showed that a regular polygon can be constructed by compass and straightedge if the number of its sides is the product of distinct Fermat primes and a power of 2. This was a major discovery in an important field of mathematics. Gauss was so pleased with this result that he requested that a regular heptadecagon be inscribed on his tombstone.
The stonemason declined, stating that the difficult construction would look like a circle. The year 1796 was productive for both Gauss and number theory, he discovered a construction of the heptadecagon on 30 March. He further advanced modular arithmetic simplifying manipulations in number theory. On 8 April he became the first to prove the quadratic reciprocity law; this remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. The prime number theorem, conjectured on 31 May, gives a good understanding of how the prime numbers are distributed among the integers. Gauss discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and jotted down in his diary the note: "ΕΥΡΗΚΑ! num = Δ + Δ' + Δ". On 1 October he published a result on the number of solutions of polynomials with coefficients in finite fields, which 150 years led to the Weil conjectures. Gauss remained mentally active into his old age while suffering from gout and general unhappiness.
For example, at the age of 62, he taught himself Russian. In 1840, Gauss published his influential Dioptrische Untersuchungen, in which he gave the first systematic analysis on the formation of images under a paraxial approximation. Among his results, Gauss showed that under a paraxial approximation an optical system can be characterized by its cardinal points and he derived the Gaussian lens formula. In 1845, he became an associated member of the Royal Institute of the Netherlands. In 1854, Gauss selected the topic for Bernhard Riemann's inaugural lecture "Über die Hypothesen, welche der Geometrie zu Grunde liegen". On the way home from Riemann's lecture, Weber reported that Gauss was full of excitement. On 23 February 1855, Gauss died of a heart attack in Göttingen. Two people gave eulogies at his funeral: Gauss's son-in-law Heinrich Ewald, Wolfgang Sartorius von Waltershausen, Gauss's close friend and biographer. Gauss's brain was preserved and was studied by Rudolf Wagner, who found its mass to be above average, at 1,492 grams, the cerebral area equal to 219,588 square millimeters.
Developed convolutions were found, which in the early 20th century were suggested as the explanation of his genius. Gauss was a Lutheran Protestant, a member of the St. Albans Evangelical Lutheran church in Göttingen. Potential evidence that Gauss believed in God comes from his response after solving a problem that had defeated him: "Finally, two days ago, I succeeded—not on account of my hard efforts, but by th
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics. His work is known for its influence on the philosophy of science, he is best known to the general public for his mass–energy equivalence formula E = mc2, dubbed "the world's most famous equation". He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory. Near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field; this led him to develop his special theory of relativity during his time at the Swiss Patent Office in Bern. However, he realized that the principle of relativity could be extended to gravitational fields, he published a paper on general relativity in 1916 with his theory of gravitation.
He continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He investigated the thermal properties of light which laid the foundation of the photon theory of light. In 1917, he applied the general theory of relativity to model the structure of the universe. Except for one year in Prague, Einstein lived in Switzerland between 1895 and 1914, during which time he renounced his German citizenship in 1896 received his academic diploma from the Swiss federal polytechnic school in Zürich in 1900. After being stateless for more than five years, he acquired Swiss citizenship in 1901, which he kept for the rest of his life. In 1905, he was awarded a PhD by the University of Zurich; the same year, he published four groundbreaking papers during his renowned annus mirabilis which brought him to the notice of the academic world at the age of 26. Einstein taught theoretical physics at Zurich between 1912 and 1914 before he left for Berlin, where he was elected to the Prussian Academy of Sciences.
In 1933, while Einstein was visiting the United States, Adolf Hitler came to power. Because of his Jewish background, Einstein did not return to Germany, he settled in the United States and became an American citizen in 1940. On the eve of World War II, he endorsed a letter to President Franklin D. Roosevelt alerting him to the potential development of "extremely powerful bombs of a new type" and recommending that the US begin similar research; this led to the Manhattan Project. Einstein supported the Allies, but he denounced the idea of using nuclear fission as a weapon, he signed the Russell–Einstein Manifesto with British philosopher Bertrand Russell, which highlighted the danger of nuclear weapons. He was affiliated with the Institute for Advanced Study in Princeton, New Jersey, until his death in 1955. Einstein published more than 150 non-scientific works, his intellectual achievements and originality have made the word "Einstein" synonymous with "genius". Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire, on 14 March 1879.
His parents were Hermann Einstein, a salesman and engineer, Pauline Koch. In 1880, the family moved to Munich, where Einstein's father and his uncle Jakob founded Elektrotechnische Fabrik J. Einstein & Cie, a company that manufactured electrical equipment based on direct current; the Einsteins were non-observant Ashkenazi Jews, Albert attended a Catholic elementary school in Munich, from the age of 5, for three years. At the age of 8, he was transferred to the Luitpold Gymnasium, where he received advanced primary and secondary school education until he left the German Empire seven years later. In 1894, Hermann and Jakob's company lost a bid to supply the city of Munich with electrical lighting because they lacked the capital to convert their equipment from the direct current standard to the more efficient alternating current standard; the loss forced the sale of the Munich factory. In search of business, the Einstein family moved to Italy, first to Milan and a few months to Pavia; when the family moved to Pavia, Einstein 15, stayed in Munich to finish his studies at the Luitpold Gymnasium.
His father intended for him to pursue electrical engineering, but Einstein clashed with authorities and resented the school's regimen and teaching method. He wrote that the spirit of learning and creative thought was lost in strict rote learning. At the end of December 1894, he travelled to Italy to join his family in Pavia, convincing the school to let him go by using a doctor's note. During his time in Italy he wrote a short essay with the title "On the Investigation of the State of the Ether in a Magnetic Field". Einstein always excelled at math and physics from a young age, reaching a mathematical level years ahead of his peers; the twelve year old Einstein taught himself algebra and Euclidean geometry over a single summer. Einstein independently discovered his own original proof of the Pythagorean theorem at age 12. A family tutor Max Talmud says that after he had given the 12 year old Einstein a geometry textbook, after a short time " had worked through the whole book, he thereupon devoted himself to higher mathematics...
Soon the flight of his mathematical genius was so high I could not follow." His passion for geometry and algebra led the twelve year old to become convinced that nature could be understood as a "mathematical structure". Einstein started teaching himself calculus at