Carl Friedrich Gauss
Johann Carl Friedrich Gauss (1777-1855), painted by Christian Albrecht Jensen
Born	30 April 1777(1777-04-30) Braunschweig, Electorate of Brunswick-Lüneburg, Holy Roman Empire
Died	23 February 1855 (aged 77) Göttingen, Kingdom of Hanover
Residence	Kingdom of Hanover
Nationality	German
Fields	Mathematician and physicist
Institutions	University of Göttingen
Alma mater	University of Helmstedt
Doctoral advisor	Johann Friedrich Pfaff
Other academic advisors	Johann Christian Martin Bartels
Doctoral students	Friedrich Bessel Christoph Gudermann Christian Ludwig Gerling Richard Dedekind Johann Encke Johann Listing Bernhard Riemann Christian Peters Moritz Cantor
Other notable students	August Ferdinand Möbius Julius Weisbach L. C. Schnürlein
Known for	See full list
Influenced	Sophie Germain
Notable awards	Copley Medal (1838)
Religious stance	Lutheran
Signature

Johann Carl Friedrich Gauss (IPA: /ˈɡaʊs/, Audio (help·info), German: Gauß, Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. Christian Albrecht Jensen ( June 26, 1792 &mdash July 13, 1870) was a Danish painter born in Bredstedt, Nordfriesland. Events 313 - Roman emperor Licinius unifies the entire Eastern Roman Empire under his rule Year 1777 ( MDCCLXXVII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common Braunschweig, known as Brunswiek in Low German, is a city of 245810 people (as of 31 December 2007 located in Lower Saxony, Germany. The Electorate of Hanover (or more formally the Electorate of Brunswick-Lüneburg; Kurfürstentum Hannover Kurfürstentum Braunschweig-Lüneburg became the ninth Electorate The Holy Roman Empire ( HRE; German Heiliges Römisches Reich (HRR, Latin Sacrum Romanum Imperium (SRI was a union of territories in Events 1455 - Traditional date for the publication of the Gutenberg Bible, the first Western Book printed from Movable Year 1855 ( MDCCCLV) was a Common year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Common year Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany. The Kingdom of Hanover (Königreich Hannover was established in October of 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian The Kingdom of Hanover (Königreich Hannover was established in October of 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. The University of Göttingen ( German: Georg-August-Universität Göttingen) is a University in the city of Göttingen, Germany. Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval The University of Helmstedt, official Latin name Academia Julia ("Julius University" was a University in Helmstedt, Brunswick-Lüneburg A doctorate is an Academic degree that indicates the highest level of academic achievement Johann Friedrich Pfaff (sometimes spelled Friederich) was born in Stuttgart on December 22, 1765, and died in Halle on April Johann Christian Martin Bartels (* 12 August 1769 in Brunswick; d Friedrich Wilhelm Bessel (22 July 1784 &ndash 17 March 1846 was a German Mathematician, Astronomer, and systematizer of the Bessel functions Christoph Gudermann ( March 25, 1798 &ndash September 25, 1852) was born in Vienenburg, Germany. Christian Ludwig Gerling (1788-1864 studied under Carl Friedrich Gauss, obtaining his doctorate in 1812 for a thesis entitled Methodi proiectionis orthographicae Julius Wilhelm Richard Dedekind ( October 6, 1831 &ndash February 12, 1916) was a German mathematician who did important Johann Franz Encke ( 23 September 1791 – 26 August 1865) was a German Astronomer, born in Hamburg. Johann Benedict Listing ( July 25, 1808 &ndash December 24 1882) was a German Mathematician. Moritz Benedikt Cantor ( August 23, 1829 &ndash April 10, 1920) was a German historian of mathematics. August Ferdinand Möbius ( November 17, 1790 &ndash September 26, 1868, (ˈmøbiʊs was a German Mathematician and Julius Ludwig Weisbach (born 10 August 1806 in Mittelschmiedeberg (now Mildenau Erzgebirge, died 24 February 1871, Freiberg L C Schnürlein ( fl Nineteenth century) was a German Mathematician and Educator. Carl Friedrich Gauss (1777 &ndash 1855 is the Eponym of all of the topics listed below This article is about the mathematician Marie-Sophie Germain See also Sophie Germain primes Marie-Sophie Germain ( April 1, 1776 The Copley Medal is a scientific award for distinguished achievement in any field of Science established by the Royal Society of London in 1731 Lutheranism is a major branch of Western Christianity that identifies with the teachings of the sixteenth-century German reformer Martin Luther The German language (de ''Deutsch'') is a West Germanic language and one of the world's major languages. Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. Events 313 - Roman emperor Licinius unifies the entire Eastern Roman Empire under his rule Year 1777 ( MDCCLXXVII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common Events 1455 - Traditional date for the publication of the Gutenberg Bible, the first Western Book printed from Movable Year 1855 ( MDCCCLV) was a Common year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Common year The German people (Deutsche are an Ethnic group, in the sense of sharing a common German culture, descent and speaking the German language as A mathematician is a person whose primary area of study and research is the field of Mathematics. A scientist, in the broadest sense refers to any person that engages in a systematic activity to acquire Knowledge or an individual that engages in such practices Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Analysis has its beginnings in the rigorous formulation of Calculus. Differential geometry is a mathematical discipline that uses the methods of differential and integral Calculus to study problems in Geometry Geodesy (dʒiːˈɒdɪsi also called geodetics, a branch of Earth sciences, is the scientific discipline that deals Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Sometimes known as the princeps mathematicorum^[1] (Latin, usually translated as "the Prince of Mathematicians", although Latin princeps also can simply mean "the foremost") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. ^[2]

Gauss was a child prodigy, of whom there are many anecdotes pertaining to his astounding precocity while a mere toddler, and made his first ground-breaking mathematical discoveries while still a teenager. List of child prodigies|Fictional child prodigies A child prodigy is a one who masters one or more skills or arts at an early age For other uses see Anecdota. For a comparison of anecdote with other kinds of stories see Myth legend fairy tale and fable. He completed Disquisitiones Arithmeticae, his magnum opus, in 1798 at the age of 21, though it would not be published until 1801. The Disquisitiones Arithmeticae is a textbook of Number theory written by German Mathematician Carl Friedrich Gauss in 1798 Magnum opus (sometimes Opus magnum, plural magna opera) from the Latin meaning great work, refers to the best the greatest This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

Early years (1777–1798)

Statue of Gauss in his birthplace of Braunschweig

Gauss was born in Braunschweig, in the Electorate of Brunswick-Lüneburg, now part of Lower Saxony, Germany, as the only son of poor working-class parents. Braunschweig, known as Brunswiek in Low German, is a city of 245810 people (as of 31 December 2007 located in Lower Saxony, Germany. The Electorate of Hanover (or more formally the Electorate of Brunswick-Lüneburg; Kurfürstentum Hannover Kurfürstentum Braunschweig-Lüneburg became the ninth Electorate Lower Saxony ( German: Niedersachsen ch is pronounced before an s --> lies in north-western Germany and is second Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. ^[3] There are several stories of his early genius, all of them open to doubt; according to one, his gifts became very apparent at the age of three when he corrected, in his head, an error his father had made on paper while calculating finances.

Another famous story, and one that has evolved in the telling, has it that in primary school his teacher, J. See also Primary education A primary school (from French école primaire) is an institution where children receive the first stage of Compulsory G. Büttner, tried to occupy pupils by making them add a list of integers. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels. Johann Christian Martin Bartels (* 12 August 1769 in Brunswick; d Gauss' presumed method, which supposes the list of numbers was from 1 to 100, was to realise that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050 (see arithmetic series and summation). In Mathematics, an arithmetic progression or arithmetic sequence is a Sequence of Numbers such that the difference of any two successive members ^[4] However whilst the method works, the incident itself is probably apocryphal; some, such as Joseph Rotman in his book A first course in Abstract Algebra, question whether it ever happened.

As his father wanted him to follow in his footsteps and become a mason, he was not supportive of Gauss's schooling in mathematics and science. Gauss was primarily supported by his mother in this effort and by the Duke of Braunschweig,^[2] who awarded Gauss a fellowship to the Collegium Carolinum (now Technische Universität Braunschweig), which he attended from 1792 to 1795, and subsequently he moved to the University of Göttingen from 1795 to 1798. Charles William Ferdinand Duke of Brunswick-Lüneburg Prince of Brunswick-Wolfenbuttel-Bevern ( Karl Wilhelm Ferdinand Herzog zu Braunschweig-Lüneburg Fürst von Braunschweig-Wolfenbüttel-Bevern The University of Göttingen ( German: Georg-August-Universität Göttingen) is a University in the city of Göttingen, Germany. While in university, Gauss independently rediscovered several important theorems; his breakthrough occurred in 1796 when he was able to show that any regular polygon with a number of sides which is a Fermat prime (and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a power of 2) can be constructed by compass and straightedge. In Geometry a polygon (ˈpɒlɨɡɒn ˈpɒliɡɒn is traditionally a plane figure that is bounded by a closed path or circuit In Mathematics, a Fermat number, named after Pierre de Fermat who first studied them is a positive integer of the form F_{n} = 2^{2^{ Pentagon constructgif|thumb|right|Construction of a regular pentagon]] Compass-and-straightedge or ruler-and-compass construction is the construction of lengths or Angles This was a major discovery in an important field of mathematics; construction problems had occupied mathematicians since the days of the Ancient Greeks, and the discovery ultimately led Gauss to choose mathematics instead of philology as a career. The term ancient Greece refers to the period of Greek history lasting from the Greek Dark Ages ca See Comparative linguistics for the narrower field of "comparative philology" Gauss was so pleased by this result that he requested that a regular heptadecagon be inscribed on his tombstone. Heptadecagon construction The regular heptadecagon is a Constructible polygon, as was shown by Carl Friedrich Gauss in 1796 A headstone, tombstone or gravestone is a marker normally carved from stone, placed over or next to the site of a Burial The stonemason declined, stating that the difficult construction would essentially look like a circle. The craft of stonemasonry has existed since the dawn of Civilization - creating Buildings structures and Sculpture using stone from the earth

The year 1796 was most productive for both Gauss and number theory. He discovered a construction of the heptadecagon on March 30. Heptadecagon construction The regular heptadecagon is a Constructible polygon, as was shown by Carl Friedrich Gauss in 1796 ^[5] He invented modular arithmetic, greatly simplifying manipulations in number theory. In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers He became the first to prove the quadratic reciprocity law on April 8. The law of quadratic reciprocity is a theorem from Modular arithmetic, a branch of Number theory, which shows a remarkable relationship between the solvability Events 217 - Roman Emperor Caracalla is Assassinated (and succeeded by his Praetorian This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. The prime number theorem, conjectured on May 31, gives a good understanding of how the prime numbers are distributed among the integers. Events 1279 BC - Rameses II (The Great (19th dynasty becomes pharaoh of Ancient Egypt. In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on July 10 and then jotted down in his diary the famous words, "Heureka! num = Δ + Δ + Δ. A triangular number is the sum of the n Natural numbers from 1 to n. Events 48 BC - Battle of Dyrrhachium, Julius Caesar barely avoids a catastrophic defeat to Pompey in Macedonia. Eureka ( Greek "I have found it" is an exclamation used as an Interjection to celebrate a discovery " On October 1 he published a result on the number of solutions of polynomials with coefficients in finite fields, which ultimately led to the Weil conjectures 150 years later. Events 331 BC - Alexander the Great defeats Darius III of Persia in the Battle of Gaugamela. In Abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains only finitely many elements In Mathematics, the Weil conjectures, which had become theorems by 1974 were some highly-influential proposals from the late 1940s by André Weil on the

Middle years (1799–1830)

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial over the complex numbers has at least one root. In Mathematics, the Fundamental theorem of algebra states that every non-constant single-variable Polynomial with complex coefficients has at In Mathematics, a polynomial is an expression constructed from Variables (also known as indeterminates and Constants using the operations Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted This article is about the zeros of a function which should not be confused with the value at zero. Mathematicians including Jean le Rond d'Alembert had produced false proofs before him, and Gauss's dissertation contains a critique of d'Alembert's work. Ironically, by today's standard, Gauss's own attempt is not acceptable, owing to implicit use of the Jordan curve theorem. In Topology, the Jordan curve theorem states that every non-self-intersecting loop in the plane divides the plane into an "inside" and an "outside" However, he subsequently produced three other proofs, the last one in 1849 being generally considered rigorous. His attempts clarified the concept of complex numbers considerably along the way.

Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae (Latin, Arithmetical Investigations), which contained a clean presentation of modular arithmetic and the first proof of the law of quadratic reciprocity. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes The Disquisitiones Arithmeticae is a textbook of Number theory written by German Mathematician Carl Friedrich Gauss in 1798 Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers The law of quadratic reciprocity is a theorem from Modular arithmetic, a branch of Number theory, which shows a remarkable relationship between the solvability

Title page of Gauss's Disquisitiones Arithmeticae

In that same year, Italian astronomer Giuseppe Piazzi discovered the dwarf planet Ceres, but could only watch it for a few days. Italy (Italia officially the Italian Republic, (Repubblica Italiana is located on the Italian Peninsula in Southern Europe, and on the two largest Giuseppe Piazzi ( July 7 1746 - July 22 1826) was an Italian Theatine monk Mathematician, and Astronomer A dwarf planet, as defined by the International Astronomical Union (IAU is a Celestial body Orbiting the Sun that is massive enough to be rounded Ceres (ˈsɪəriːz Gauss predicted correctly the position at which it could be found again, and it was rediscovered by Franz Xaver von Zach on December 31, 1801 in Gotha, and one day later by Heinrich Olbers in Bremen. Baron Franz Xaver von Zach ( Franz Xaver Freiherr von Zach) ( June 4, 1754 &ndash September 2, 1832) was a Hungarian astronomer Events 406 – Vandals, Alans and Suebians cross the Rhine, beginning an invasion of Gallia. Year 1801 ( MDCCCI) was a Common year starting on Thursday (see link for calendar of the Gregorian calendar (or a Common year starting on Tuesday Gotha is a town in Thuringia, within the central core of Germany. Bremen (ˈbʁeːmən is a Hanseatic city in northwestern Germany (official name Stadtgemeinde Bremen / City Municipality of Bremen Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have found Ceres again. " Though Gauss had been up to that point supported by the stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support. Thus he sought a position in astronomy, and in 1807 was appointed Professor of Astronomy and Director of the astronomical observatory in Göttingen, a post he held for the remainder of his life. Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany.

The discovery of Ceres by Piazzi on January 1, 1801 led Gauss to his work on a theory of the motion of planetoids disturbed by large planets, eventually published in 1809 under the name Theoria motus corporum coelestium in sectionibus conicis solem ambientum (theory of motion of the celestial bodies moving in conic sections around the sun). New Year See also New Year The Ancient Romans began their consular year on January 1st since 153 BC Year 1801 ( MDCCCI) was a Common year starting on Thursday (see link for calendar of the Gregorian calendar (or a Common year starting on Tuesday Piazzi had only been able to track Ceres for a couple of months, following it for three degrees across the night sky. Then it disappeared temporarily behind the glare of the Sun. Several months later, when Ceres should have reappeared, Piazzi could not locate it: the mathematical tools of the time were not able to extrapolate a position from such a scant amount of data—three degrees represent less than 1% of the total orbit.

Gauss, who was 23 at the time, heard about the problem and tackled it. After three months of intense work, he predicted a position for Ceres in December 1801—- just about a year after its first sighting—and this turned out to be accurate within a half-degree. In the process, he so streamlined the cumbersome mathematics of 18th century orbital prediction that his work—- published a few years later as Theory of Celestial Movement—- remains a cornerstone of astronomical computation. It introduced the Gaussian gravitational constant, and contained an influential treatment of the method of least squares, a procedure used in all sciences to this day to minimize the impact of measurement error. Carl Friedrich Gauss expressed the Gravitational constant in units of the Solar system rather than SI units The method of least squares is used to solve Overdetermined systems Least squares is often applied in statistical contexts particularly Regression analysis. Observational error is the difference between a measured value of quantity and its true value Gauss was able to prove the method in 1809 under the assumption of normally distributed errors (see Gauss–Markov theorem; see also Gaussian). The normal distribution, also called the Gaussian distribution, is an important family of Continuous probability distributions applicable in many fields This article is not about Gauss–Markov processes In Statistics, the Gauss–Markov theorem, named after Carl Friedrich Carl Friedrich Gauss (1777 &ndash 1855 is the Eponym of all of the topics listed below The method had been described earlier by Adrien-Marie Legendre in 1805, but Gauss claimed that he had been using it since 1795. Adrien-Marie Legendre ( September 18 1752 – January 10 1833) was a French Mathematician.

Gauss' portrait published in Astronomische Nachrichten 1828

Gauss was a prodigious mental calculator. Mental calculators are people with a prodigious ability in some area of Mental calculation, such as multiplying large numbers or factoring large numbers Reputedly, when asked how he had been able to predict the trajectory of Ceres with such accuracy he replied, "I used logarithms. In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce " The questioner then wanted to know how he had been able to look up so many numbers from the tables so quickly. "Look them up?" Gauss responded. "Who needs to look them up? I just calculate them in my head!"

In 1818 Gauss, putting his calculation skills to practical use, carried out a geodesic survey of the state of Hanover, linking up with previous Danish surveys. Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space Position of points and the distances and angles between The Kingdom of Hanover (Königreich Hannover was established in October of 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian The Kingdom of Denmark ( ˈd̥ænmɑɡ̊ (archaic ˈd̥anmɑːɡ̊ commonly known as Denmark, is a country in the Scandinavian region of northern Europe To aid in the survey, Gauss invented the heliotrope, an instrument that uses a mirror to reflect sunlight over great distances, to measure positions. The heliotrope is an instrument that uses a Mirror to reflect Sunlight over great distances to mark the positions of participants in a land survey.

Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it. In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory. Research on these geometries led to, among other things, Einstein's theory of general relativity, which describes the universe as non-Euclidean. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical His friend Farkas Wolfgang Bolyai with whom Gauss had sworn "brotherhood and the banner of truth" as a student had tried in vain for many years to prove the parallel postulate from Euclid's other axioms of geometry. Farkas Bolyai ( February 9, 1775 - November 20, 1856, also known as Wolfgang Bolyai in Germany was a Hungarian mathematician Bolyai's son, János Bolyai, discovered non-Euclidean geometry in 1829; his work was published in 1832. János Bolyai ( December 15, 1802 – January 27, 1860) was a Hungarian Mathematician, known for his work in Non-Euclidean After seeing it, Gauss wrote to Farkas Bolyai: "To praise it would amount to praising myself. For the entire content of the work. . . coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years. " This unproved statement put a strain on his relationship with János Bolyai (who thought that Gauss was "stealing" his idea), but it is now generally taken at face value. Letters by Gauss years before 1829 reveal him obscurely discussing the problem of parallel lines. Waldo Dunnington, a life-long student of Gauss, successfully proves in Gauss, Titan of Science that Gauss was in fact in full possession of non-Euclidian geometry long before it was published by János, but that he refused to publish any of it because of his fear of controversy. Guy Waldo Dunnington ( January 15, 1906 &ndashApril 1974 was a life-long student of Carl Friedrich Gauss, a famous German mathematician

Four Gaussian distributions in statistics

The survey of Hanover fueled Gauss's interest in differential geometry, a field of mathematics dealing with curves and surfaces. The normal distribution, also called the Gaussian distribution, is an important family of Continuous probability distributions applicable in many fields Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Differential geometry is a mathematical discipline that uses the methods of differential and integral Calculus to study problems in Geometry In Mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object In Mathematics, specifically in Topology, a surface is a Two-dimensional Manifold. This led in 1828 to an important theorem, the Theorema Egregium (remarkable theorem in Latin), establishing an important property of the notion of curvature. Gauss's Theorema Egregium (Latin "Remarkable Theorem" is a foundational result in Differential geometry proved by Carl Friedrich Gauss that concerns the Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. In Mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface. In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called Distance is a numerical description of how far apart objects are That is, curvature does not depend on how the surface might be embedded in 3-dimensional space. In Mathematics, an embedding (or imbedding) is one instance of some Mathematical structure contained within another instance such as a group

Later years and death (1831–1855)

Grave of Gauss at Albanifriedhof

In 1831 Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber, leading to new knowledge in magnetism (including finding a representation for the unit of magnetism in terms of mass, length and time) and the discovery of Kirchhoff's circuit laws in electricity. Albanifriedhof is a Cemetery in Göttingen, Germany just outside the city wall to the southeast Wilhelm Eduard Weber ( October 24, 1804 &ndash June 23, 1891) was a German Physicist. In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. For other laws named after Gustav Kirchhoff, see Kirchhoff's laws. They constructed the first electromagnetic telegraph in 1833, which connected the observatory with the institute for physics in Göttingen. The electrical telegraph is a telegraph that uses electric signals The electromagnetic telegraph is a device for human-to-human transmission Gauss ordered a magnetic observatory to be built in the garden of the observatory, and with Weber founded the magnetischer Verein (magnetic club in German), which supported measurements of earth's magnetic field in many regions of the world. An observatory is a location used for observing terrestrial and/or celestial events The German language (de ''Deutsch'') is a West Germanic language and one of the world's major languages. He developed a method of measuring the horizontal intensity of the magnetic field which has been in use well into the second half of the 20th century and worked out the mathematical theory for separating the inner (core and crust) and outer (magnetospheric) sources of Earth's magnetic field. The planetary core consists of the innermost layer(s of a Planet. In Geology, a crust is the outermost solid shell of a planet or moon A magnetosphere' is a highly magnetized region around and possessed by an Astronomical object.

Gauss died in Göttingen, Hanover (now part of Lower Saxony, Germany) in 1855 and is interred in the cemetery Albanifriedhof there. The Kingdom of Hanover (Königreich Hannover was established in October of 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian Lower Saxony ( German: Niedersachsen ch is pronounced before an s --> lies in north-western Germany and is second Albanifriedhof is a Cemetery in Göttingen, Germany just outside the city wall to the southeast Two individuals gave eulogies at his funeral, Gauss's son-in-law Heinrich Ewald and Wolfgang Sartorius von Waltershausen, who was Gauss's close friend and biographer. Georg Heinrich August Ewald ( November 16, 1803 - May 4, 1875) was a German Orientalist and theologian. His brain was preserved and was studied by Rudolf Wagner who found its weight to be 1,492 grams and the cerebral area equal to 219,588 square centimeters (236. Rudolf Wagner ( June 30, 1805 - May 13, 1864) was a German Anatomist and Physiologist and the co-discoverer of 363 square feet). Highly developed convolutions were also found, which in the early 20th century was suggested as the explanation of his genius. ^[6]

Family

Gauss's personal life was overshadowed by the early death of his first wife, Johanna Osthoff, in 1809, soon followed by the death of one child, Louis. Gauss plunged into a depression from which he never fully recovered. Major depressive disorder, also known as major depression, unipolar depression, unipolar disorder, clinical depression, or simply depression He married again, to Johanna's best friend named Friederica Wilhelmine Waldeck but commonly known as Minna. This second marriage does not seem to have been very happy as it was plagued by Minna's continuous illness. When his second wife died in 1831 after a long illness,^[7] one of his daughters, Therese, took over the household and cared for Gauss until the end of his life. His mother lived in his house from 1817 until her death in 1839. ^[2]

Gauss had six children. With Johanna (1780–1809), his children were Joseph (1806–1873), Wilhelmina (1808–1846) and Louis (1809–1810). Of all of Gauss's children, Wilhelmina was said to have come closest to his talent, but she died young. With Minna Waldeck he also had three children: Eugene (1811–1896), Wilhelm (1813–1879) and Therese (1816–1864). Eugene emigrated to the United States about 1832 after a falling out with his father, eventually settling in St. Charles, Missouri, where he became a well-respected member of the community. The United States of America —commonly referred to as the St Charles ( French: "Saint-Charles" Spanish: "San Carlos" is a city in and the county seat of St Missouri ( or) is a state in the Midwestern region of the United States bordered by Iowa, Illinois, Kentucky, Tennessee Wilhelm also settled in Missouri, starting as a farmer and later becoming wealthy in the shoe business in St. Louis. A farmer is a person who raises living organisms for food or raw materials Therese kept house for Gauss until his death, after which she married.

Gauss eventually had conflicts with his sons, two of whom migrated to the United States. He did not want any of his sons to enter mathematics or science for "fear of sullying the family name". His conflict with Eugene was particularly bitter. Gauss wanted Eugene to become a lawyer, but Eugene wanted to study languages. A lawyer, according to Black's Law Dictionary, is "a person learned in the law as an attorney, Counsel or Solicitor; a person They had an argument over a party Eugene held, which Gauss refused to pay for. The son left in anger and emigrated to the United States, where he was quite successful. It took many years for Eugene's success to counteract his reputation among Gauss's friends and colleagues. See also the letter from Robert Gauss to Felix Klein on September 3, 1912. Events 36 BC - In the Battle of Naulochus, Marcus Vipsanius Agrippa, Admiral of Octavian, defeats Sextus Pompeius Year 1912 ( MCMXII) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Leap year starting

Personality

Gauss was an ardent perfectionist and a hard worker. Perfectionism, in Psychology, is a belief that perfection can and should be attained According to Isaac Asimov, Gauss was once interrupted in the middle of a problem and told that his wife was dying. Isaac Asimov (c January 2 1920 &ndash April 6 1992 ˈaɪzək ˈæzɪmʌv originally Исаак Озимов but now transcribed into Russian as, was a Russian He is purported to have said, "Tell her to wait a moment till I'm done. "^[8] This anecdote is briefly discussed in Waldo Dunnington's Gauss, Titan of Science where it is suggested that it is an apocryphal story.

He was never a prolific writer, refusing to publish works which he did not consider complete and above criticism. This was in keeping with his personal motto pauca sed matura (few, but ripe). A study of his personal diaries reveals that he had in fact discovered several important mathematical concepts years or decades before they were published by his contemporaries. Mathematical historian Eric Temple Bell estimated that had Gauss made known all of his discoveries, mathematics would have been advanced by 50 years. Eric Temple Bell ( February 7 ^[9]

A criticism of Gauss is that he did not support the younger mathematicians who followed him. He rarely, if ever, collaborated with other mathematicians and was considered aloof and austere by many. Though he did take in a few students, Gauss was known to dislike teaching. It is said that he attended only a single scientific conference, which was in Berlin in 1828. Berlin is the capital city and one of sixteen states of Germany. However, several of his students became influential mathematicians, among them Richard Dedekind, Bernhard Riemann, and Friedrich Bessel. Julius Wilhelm Richard Dedekind ( October 6, 1831 &ndash February 12, 1916) was a German mathematician who did important Friedrich Wilhelm Bessel (22 July 1784 &ndash 17 March 1846 was a German Mathematician, Astronomer, and systematizer of the Bessel functions Before she died, Sophie Germain was recommended by Gauss to receive her honorary degree. This article is about the mathematician Marie-Sophie Germain See also Sophie Germain primes Marie-Sophie Germain ( April 1, 1776

Gauss usually declined to present the intuition behind his often very elegant proofs—-he preferred them to appear "out of thin air" and erased all traces of how he discovered them. This is fully, however briefly, explained by Gauss himself in his "Disquisitiones Arithmeticae", where he states that all analysis (i. e. the paths one travelled to reach the solution of a problem) must be suppressed for sake of brevity.

Gauss was deeply religious and conservative. He supported monarchy and opposed Napoleon, whom he saw as an outgrowth of revolution. Napoleon Bonaparte (15 August 1769 – 5 May 1821 was a French military and political leader who had a significant impact on the History of Europe. A revolution (from the Latin revolutio, "a turnaround" is a fundamental change in power or organizational structures that takes place in a relatively

Commemorations

The CGS unit for magnetic induction was named gauss in his honour. The centimetre-gram-second system ( CGS) is a system of physical units. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of The gauss, abbreviated as G is the Cgs unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic

From 1989 until the end of 2001, his portrait and a normal distribution curve as well as some prominent buildings of Göttingen were featured on the German ten-mark banknote. Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany. The other side of the note features the heliotrope and a triangulation approach for Hanover. The heliotrope is an instrument that uses a Mirror to reflect Sunlight over great distances to mark the positions of participants in a land survey. In Trigonometry and Geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either The Kingdom of Hanover (Königreich Hannover was established in October of 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian Germany has issued three stamps honouring Gauss, as well. A righteous stamp (no. 725), was issued in 1955 on the hundredth anniversary of his death; two other stamps, no. 1246 and 1811, were issued in 1977, the 200th anniversary of his birth.

In 2007, his bust was introduced to the Walhalla temple. A bust is a sculpted or cast representation of the upper part of the human figure depicting a person's head and Neck, as well as a variable portion of The Walhalla Hall of Fame and Honor is a neo-classical Hall of fame located on the Danube River 10 km east of Regensburg, in Bavaria ^[10]

Places, vessels and events named in honour of Gauss:

• Gauss crater on the Moon^[11]
• Asteroid 1001 Gaussia. Gauss is a large lunar crater, named after Carl Friedrich Gauss, that is located near the northeastern limb of the Moon 's near side Asteroids, sometimes called Minor planets or planetoids', are bodies—primarily of the inner Solar System —that are smaller than planets but
• The ship Gauss, used in the Gauss expedition to the Antarctic. Gauss was a ship used for the Gauss expedition to Antarctica (1901-1903 led by Arctic veteran and geology professor Erich von Drygalski. The Gauss Expedition (1901 – 1903 was the first German expedition to Antarctica led by Arctic veteran and geology professor Erich von Drygalski in the ship
• Gaussberg, an extinct volcano discovered by the above mentioned expedition
• Gauss Tower, an observation tower
• In Canadian junior high schools, an annual national mathematics competition administered by the Centre for Education in Mathematics and Computing is named in honour of Gauss. Gaussberg (or Mount Gauss) is an extinct volcanic cone 370 metres high The Gauss Tower is a reinforced Concrete Observation tower on the summit of the High Hagens in Dransfeld, Germany. The Centre for Education in Mathematics and Computing (CEMC founded in 1995 and hosted at the University of Waterloo, administers Mathematics and
• In University of California, Santa Cruz, in Crown College, a dormitory building is named after Gauss. Crown College is one of the Residential colleges that makes up the University of California Santa Cruz, USA.
• The Gauss Haus, an NMR center at the University of Utah. The University of Utah (referred to locally as ' The U' or ' the U of U') is a publicly funded Research university in Salt Lake
• The Carl-Friedrich-Gauß School for Mathematics, Computer Science, Business Administration, Economics, and Social Sciences of University of Braunschweig

See also

• List of topics named after Carl Friedrich Gauss

References

Notes

Writings

• 1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse ("New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors [i. A dissertation (also called thesis or disquisition) is a document that presents the author's Research and findings and is submitted in support of candidature In Mathematics, the Fundamental theorem of algebra states that every non-constant single-variable Polynomial with complex coefficients has at e. polynomials] of the first or second degree")
• 1801: Disquisitiones Arithmeticae, online at [1]
• 1809: Theoria Motus Corporum Coelestium in sectionibus conicis solem ambientium (Theorie der Bewegung der Himmelskörper, die die Sonne in Kegelschnitten umkreisen), online at [2] English translation by C. H. Davis, reprinted 1963, Dover, New York.
• 1821, 1823 und 1826: Theoria combinationis observationum erroribus minimis obnoxiae. Drei Abhandlungen betreffend die Wahrscheinlichkeitsrechnung als Grundlage des Gauß'schen Fehlerfortpflanzungsgesetzes. English translation by G. W. Stewart, 1987, Society for Industrial Mathematics.
• 1827: Disquisitiones generales circa superficies curvas (Allgemeine Untersuchung über gekrümmte Flächen), Commentationes Societatis Regiae Scientiarum Gottingesis Recentiores. Volumen VI, S. 99-146
• 1843/44: Untersuchungen über Gegenstände der Höheren Geodäsie. Erste Abhandlung, Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen. Zweiter Band, S. 3-46
• 1846/47: Untersuchungen über Gegenstände der Höheren Geodäsie. Zweite Abhandlung, Abhandlungen der Königlichen Gesellschaft der Wissenschaften in Göttingen. Dritter Band, S. 3-44
• Mathematisches Tagebuch 1796–1814, Ostwaldts Klassiker, Harri Deutsch Verlag 2005, mit Anmerkungen von Neumamn, ISBN 978-3-8171-3402-1 (es gibt auch engl. Übers. mit Anmerkungen von Jeremy Gray, Expositiones Math. 1984)

Die Gesammelten Werke von Gauß are online here: [3]. This includes German translations of Latin texts and commentaries by various authorities

Further reading

• Carl Friedrich Gauss. Retrieved on June, 2005.
• Carl Friedrich Gauss on PlanetMath
• Dunnington, G. PlanetMath is a free, collaborative online Mathematics Encyclopedia. Waldo. (June 2003). Carl Friedrich Gauss: Titan of Science. The Mathematical Association of America. ISBN 0-88385-547-X.  
• Gauss, Carl Friedrich (1965). Disquisitiones Arithmeticae, tr. The Disquisitiones Arithmeticae is a textbook of Number theory written by German Mathematician Carl Friedrich Gauss in 1798 Arthur A. Clarke, Yale University Press. ISBN 0-300-09473-6.  
• Hall, Tord (1970). Carl Friedrich Gauss: A Biography. Cambridge, MA: MIT Press. ISBN 0-262-08040-0.  
• Gauss and His Children. Retrieved on June, 2005.
• Simmons, J. (1996). The Giant Book of Scientists: The 100 Greatest Minds of All Time. Sydney: The Book Company.  

External links

• Gauss biography
• O'Connor, John J. & Robertson, Edmund F. , “Carl Friedrich Gauss”, MacTutor History of Mathematics archive 
• Carl Friedrich Gauss at the Mathematics Genealogy Project
• Carl Friedrich Gauss, Biography at Fermat's Last Theorem Blog. The MacTutor History of Mathematics archive is an award-winning website maintained by John J The Mathematics Genealogy Project is a web-based Database that gives an Academic genealogy based on Dissertation supervision relations
• Gauss: mathematician of the millennium, by Jürgen Schmidhuber
• Digitized English Translation of Waltershausen's Gauss biography, Gauss zum Gedächtnis, 1862, translated by Gauss' great-granddaughter
• Gauss, general information, submit your site about Gauss. Jürgen Schmidhuber (born 1963 in Munich) is a Computer scientist and Artist known for his work on Machine learning, universal
• Obituary: MNRAS 16 (1856) 80
• A discussion of childhood problem and the sources
• Complete works
• Carl Friedrich Gauss on the 10 Deutsch Mark banknote.

Further reading

• Kehlmann, Daniel (2005). Die Vermessung der Welt. Measuring the World was written in German by Daniel Kehlmann as Die Vermessung der Welt. Rowohlt. ISBN 3-498-03528-2.