A (very) Brief History of Carl Friedrich Gauss

[Music] carl friedrich gauss is one of the most important mathematicians to exist in the 19th century he is sometimes referred to as the greatest mathematician since antiquity or princeps mathematic quorum which means the foremost of mathematicians a glimpse into what is notable for includes his contributions to the theory of magnetism proving the fundamental theorem of algebra deriving the function representation of the normal distribution and being PhD advisor to richard dedekind and bernhard riemann who would themselves go on to be very influential mathematicians Gauss was born a Johann Carl Friedrich Gauss on April 30th 1777 in the Duchy of Brunswick and butyl now part of Lower Saxony Germany his parents were poor working-class citizens and with his mother being illiterate Gauss's date of birth was never recorded she only knew he was born on a Wednesday eight days before the feast of Ascension which occurs thirty-nine days after Easter the Gauss derived methods to compute the date of Easter NAT a year I was able to then figure out his birthday Gauss was known to be a child prodigy there's many variations of the story but the way it usually goes is that when Gauss first got to Elementary School in 1784 the class was asked to find the sum of the integers from 1 to 100 soon after the question was presented Gauss provided the solution having recognized that 100 times 100 and 1/2 would yield the results with the support of his elementary school teacher Gauss went on to attend senior secondary school in 1788 where he studied language he drew quite a bit of attention for his intellectual abilities including from the Duke of Brunswick the Duke provided him funding to attend university thus allowing Gauss to attend the Collegium Carroll enum from 1792 to 1795 and the University of göttingen from 1795 to 1798 1796 was apparently quite the year for Gauss he advanced modular arithmetic which greatly simplified manipulations in number theory he was the first to prove the quadratic reciprocity law which allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic he discovered every positive integer is representable as a sum of at most three triangular numbers and he showed that a regular polygon can be constructed by a compass and straightedge if the number of its side is the product of distinct vermont primes and a power of two construction problems that occupied mathematicians since the ancient Greeks so this construction discovery firmly turned ghosts towards a career in mathematics instead of studying language in 1798 Gauss left the University of göttingen without a degree but he did complete his writing of a fundamental work a number theory officially being published in 1801 titled disk whisset Onis arithmetic a or arithmetic 'l investigations in english this was a pivotal work as a consolidated number theory as a discipline and shaped the field as we know it today after leaving the University of Gert Segen gauss returned to brunswick in 1799 finally receiving his degree the Duke agreed to continue Gauss's funding but requested that Gauss submit a doctoral dissertation to the University of helm stead Gauss knew a professor there named Johann Friedrich faff which made it easier to get his dissertation through and ultimately get his PhD the work that Gauss submitted provided the first proper proof of the fundamental theorem of algebra formulated over the real line as well as arguments against people's previous attempts of proving the results Gauss actually proved the fundamental theorem of algebra four times in his lifetime the first proof in 1799 was topological in nature and doesn't hold up to the rigor of today's standards the second proof was published in 1816 and was influenced by the approach that was originally taken by Euler without assuming the existence of roots this proof is both complete and correct rigorous enough for today's standards the third proof was published later in 1816 sharing the topological spirit of the first proof his fourth and final proof was provided in 18-49 fifty years after his first proof the approach taken was similar to the first proof simply extending the theorem to work for complex numbers things seem to be going quite well for Gauss after returning to Brunswick and he got married to Johanna ah stuff on October 9th 1805 sadly the Duke of Brunswick died on November 10th 1806 about two months after Gauss and his wife had their first child Joseph Gauss ended up getting an offer to work as the director of the astronomical observatory at the university of goethe ghen in 1807 it seemed this was the most appropriate move to make especially after the Duke aside from the Dukes death more tragedy would strike cows upon his move to go diggin on April 14th 1808 Gauss's father died this was about a month and a half after Gauss and his wife had their second child Phil held Mina on October 11 1809 Johanna died just two days after their four year anniversary and a month after giving birth to their third and final child Louie and on March 1st 1810 Louie died considering these terrible events especially the death of johanna gauss attained a depression that he be afflicted with for the remainder of his life but he didn't let this affect his work publishing his second book in 1809 this was a major two-volume work on the motion of celestial bodies titled theory of the motion of the heavenly bodies surrounding the Sun and conic sections volume one discusses differential equations conic sections and elliptic orbits volume two showed how to estimate and then refine the estimation of a planet's orbit focusing heavily on astronomy until 1817 Gauss still found time to work on other things such as general investigations of curved surfaces which was a rigorous treatment of series and introduced the hyper geometric function and determination of the accuracy of observations which was a discussion of statistical estimators in 1818 Gauss was asked to carry out a geodesic survey of the state of Han over to link up with the existing Danish grid this led Gauss to become heavily focused on the study of geodesy which is the branch of mathematics dealing with the and area of the earth or large portions of it throughout the 1820s his work on the Danish Grid project led him to creating the heliotrope which worked by reflecting the sun's rays using a design of mirrors and a small telescope alas the measurements ended up missing the mark leaving Gauss to wonder what kind of mathematician he really was regardless of the Geo desi hiccups gauss still pursued mathematical physics in 1832 gauss began working with Vilhelm weber on the theory of terrestrial magnetism the work Weber and Gauss did together led to the discovery of kerkoff's laws and to the building of a primitive Telegraph that could send messages a distance just shy of one mile by 1840 Gauss had written three papers on terrestrial magnetism all of which dealt with the current theories at the time as well as absolute measure of magnetic force and an empirical definition of terrestrial magnetism Gauss became kind of as hoary us for letting mathematical results ripen it's claimed that if he had published all of the results that he'd let ripen mathematics could have been 50 years ahead of what it currently is a prime example of this ripening which goes never actually published work for is non Euclidean geometry his wandering of the existence of non-euclidean geometry began in the early 1800s he primarily corresponded with Farkas boli on this matter but expressed that he developed a non Euclidean system for himself to tinker with and a letter written to Terenas in November of 1824 in 1831 boy a son Janos had published work on non Euclidean geometry but Gauss's response was essentially that he derived this years earlier being occupied with these thoughts for thirty to thirty-five years Gauss with later expressed something similar in a letter to Schumacher in 1846 regarding a work published by Lobachevsky in 1840 so even though gauss probably didn't mean it to sound the way it did he was essentially giving off the vibe that the results weren't that impressive since already discovered them years ago and just never published them returning to use his personal life Gauss got married to his previous wife's best friend Mina valdek on August 4th 1810 this was about five months after the death of his son Louie and given how depressed Gauss was over the death of Johanna let alone all the other events that had unfolded up to that point it is speculated this marriage was largely for convenience despite having a marriage with Mina for about 21 years Gauss had three children with Mina Eugen born in 1811 Vilhelm born in 1813 and Theresa born in 1816 Gauss wasn't very supportive of his children pursuing mathematics for fear they could never live up to his quality of work and thus tarnished the Gauss name this presumably led Eugene and vilhelm to immigrate to United States eugene emigrating to Missouri in 1832 and vilhelm the following suit in 1837 they both independently became very wealthy entrepreneurs so this move seemed to be quite successful in the year following Teresa's birth Gauss's mother moved in as she was too ill to take care of herself Mina and her family had been trying to persuade Gauss they should move to Berlin as Gauss got an offer from the University of Berlin to work there Gauss wasn't too keen on the change and with his mother moving in this seemed to be the nail in the coffin for any ideas for moving to Berlin Gauss's mother lived with him and his family until she died in 1839 after Mina died on September 12 1831 and Teresa becoming the caretaker of the household she tended to her grandmother and then ultimately her father as is quite clear Gauss made incredible contributions to mathematics and mathematical physics but he was also able to make incredible contributions to his pockets from 1845 to about 1850 1851 Gauss worked on updating the widows fund for the University of Girton the experience he gained from this led him to make investments in bonds issued by private companies which turned out to be incredibly successful after this series of investments Gauss began to focus almost primarily on mathematical physics and he went on to do this until his death on February 23rd 1855 fortunate enough to pass in his sleep well there you have it a very brief history and one of the most important mathematicians if not the most important of the 19th century thanks for watching and long live Gauss [Music]

Channel: moderndaymath

Views: 99,115

Keywords: gauss, fundamental theorem of algebra, math history, number theory, complex numbers, mathematics, magnetism, geodesy, geodesic, gauß, physics

Id: Pqh9CK7wBZo

Length: 12min 32sec (752 seconds)

Published: Mon May 27 2019