A (very) Brief History of Bernhard Riemann

bernhard riemann was a german mathematician in the 19th century his PhD advisor was carl friedrich gauss amongst his many contributions he's notable for the Riemann integral as well as being the first person to rigorously defined the integral the analytic continuation of euler's zeta function Romani and geometry which was fundamental in Einstein's general theory of relativity romanian services which made a strong link between topology and complex function theory and the Riemann hypothesis which is probably the greatest unsolved injection in number theory riemann was born to friedrich bernhard riemann and charlotte Abel on September 17 1826 under the name Georg Friedrich Bernhard Riemann they lived in quick Bourne a village located in the gentleman municipality in Lower Saxony Germany father Eamonn was a Lutheran pastor and very poor so the family lived rather harshly often malnourished due to poor diet the threat of tuberculosis was always staring the family in the face in fact Charlotte died when Herman was 20 years old and basically all of Herman's siblings one brother and four sisters died at young ages only sister Ida lived till at least middle age Ramon's parents believed the most important thing they could give their children was a strong education aside from a few classes in the local school Herman was primarily homeschooled by his father age 10 his father hired a local teacher who we know under the name Schulz to teach Riemann arithmetic and geometry Ramon quickly outgrew Schulz actually beginning to teach the teacher some mathematics at age 13 Riemann was sent to live with his maternal grandmother in the city of Han / city was about 90 miles from quick born which made trips back to quick born very difficult he was terribly homesick during his time there and the fact that he was incredibly timid and had a fear of public speaking only than this during his time at his grandmother's Ramon attended the tercio dis Lyceum's Ganassi owned a school for students expected to attend University he was behind his classmates and most subjects but he worked very hard and still managed to get good marks at age fifteen Riemann's grandmother died which forced him to move he ended up in lüneburg attending the johan IAM Ganassi um which was 45 miles from quick born making it much easier for him to go home and see his family Ramon was quite frail so the trips were rough but his homesickness was too profound for him to care at the school Ramon attended a teacher named hare schmuck who's noticed Ramon strong mathematical abilities he ended up lending Ramon college-level mathematical texts including works from Euler and usual it is rumoured that he read a usual news 900 page number theory work understood in full detail in a six-day period at age 19 after father Ramon was able to save enough money to send him off Ramon began attending the University of göttingen he began attending in the spring of 1846 majoring in theology Ramon was a devout Lutheran and wanted to follow in his father's footsteps his deep interest in mathematics led him to attend mathematical lectures most influential being from carl friedrich gauss apparently after a bit of getting to know riemann gauss recommended that he give up his theological studies to pursue mathematics after Eamon asked his father if that would be okay he switched over to mathematics and philosophy had his father said no the progress of mathematics could have been greatly slowed down as Ramon would have never gone against his father's will after about a year ago Negin Ramon transferred to the University of Berlin to learn from mathematicians who were on the front lines of mathematics at the time he ended up being taught by people like Carl Jacobi you Jean Derek Lee and go told Eisenstein Eisenstein was only three years older than Ramon so they actually became good friends but sadly Eisenstein did not live very long dying in 1852 despite the close friendship Eisenstein and Ramon had the most influence was from dduk lead diva Klee has very intuitive explanations very logical analysis from additional questions and avoided long computations as much as he could Ramon ended up adopting the style almost wholly in the spring of 18-49 Ramon decided to go back to Kernighan to work on his PhD under ghosts he also studied philosophy and theoretical physics which would become lifelong interests of his he was fascinated by vilhelm vapors physics lectures and actually became an assistant him for 18 months in December 1851 at age 25 Ramon finally obtained his PhD in mathematics he could have obtained it sooner but like Gauss he was a perfectionist thus he published far less than he probably could have during his career Gauss who was notorious for ridiculously high standards praised riemann for the work describing him as having a glorious fertile originality Riemann's thesis was on the theory of complex functions which studied what we now refer to as Riemann surfaces it introduced topological methods in a complex function theory and built on cochise foundations of complex analysis as well as tweezers ideas of branch points of analytic functions for those curious a branch point as a point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range a one to many relationship riemann thesis was incredibly original examining geometric properties of analytic functions conformal mappings and connectivity of surfaces this work also introduced an early version of the data key principle which is the assumption that the minimizer of a certain energy functional is a solution to Poisson equation rahman of course learn this from lectures he attended Wallenberg but the principal did not actually originate from Dida key people like Gauss and George Green had leveraged this methodology beforehand due to how Riemann had presented the Didache key principal Carl buyer Straus pointed out the issues with its use in his paper this made people doubt Riemann's methods though virus shares did firmly believe in ramond results the path to trying to patch up this issue by other mathematicians was actually quite fruitful people like Alfred clebsch and Max neither were able to uncover important algebraic ideas even with non successful patching David Hilbert was the one to finally provide a correct form of DDX peace principle which finally closed that rigor gap / Gauss's recommendation Riemann was appointed a post at the University of Jernigan to become a lecturer he had to work on a habitation which is a post doctoral thesis it took him two and a half years to complete and was on the represent ability of functions by way of trigonometric series for the post doctoral defense Rahman had to give a lecture on the work he did on June 10th 1854 Riemann gave his lecture entitled on the hypothesis underlying geometry this lecture introduced the world to Romani in geometry the first part of the lecture posed the problem of how to define n-dimensional space leading to the definition of Romani in space the second part of the lecture posed deep questions about the relationship of geometry to reality what is the dimension of real space what geometry describes real space needless to say the lecture is too far ahead of its time of those that attended only Gauss appreciated the depth of Riemann's thinking ramones insights weren't fully understood until about 60 years later when in 1915 Einstein introduced the general theory of relativity [Music] after this lecture riemann was finally able to teach at the university of Jernigan initially he wasn't too keen on teaching gears of how shy he was but he slowly grew out of this and began to love it in 1857 Riemann was appointed to professor at the University of Jernigan and was put on a regular salary he also published a paper titled theory of abelian functions this is a result of work carried out over several years he gave a lecture on some of the material somewhere between 1855 and 1856 to three people one of which was dedicated Dedekind is notable because he ended up publishing material from Raymond's lectures after he died this paper continued where Riemann's original dissertation left off like expanding on the theory of Riemann surfaces and their topological properties examining multi valued functions a single valued over a special type of Riemann surface and solving general inversion problems Riemann's paper was so good it actually got Beier stress to pull his own paper on the same subject matter out of publication Riemann had introduced a lot of new things that were richer than what Beier shares had attempted to publish he must be noted that neither Riemann nor virus Rose had any proofs in their Balian papers the first proof of any of the theorems contained didn't show up until 1883 in a short paper published by a Henri Poincare and Emil Picard in 1859 dduk Lee died at that time he had held Gauss's chair of mathematics at the University of Guernica so in July 30th 1859 it was only fitting that Rahman be appointed to the chair he was also elected to the Berlin Academy of Sciences with recommendation from Ernst Coomer Karl Vilhelm Borchardt and vyr Strauss any new elect had to show their most recent research and ramon shows his paper on the number of primes less than a given magnitude this paper explored properties of the zeta function riemann expanded euler's original function of the complex plane allowing for all values except for zero and one to be used as inputs this is of course made possible using the functional representation of the zeta function besides introducing this functional form riemann also proposed the infamous Riemann hypothesis which states that all non-trivial roots of the zeta function have real part one half as mentioned it still has not been proven or disproven stumping mathematicians to this very day there were actually no proofs in the paper provided by Rima Jacques had the mouth and Charles Jean devadip whose scene ended up proving many of the results later on in June 1862 riemann married elise koch a friend of his sister Ida and they had a daughter later that year very soon after having their daughter the family made their way down to Italy Riemann had a very bad cold that turned into tuberculosis so they thought that the warmer climate of Italy would help him get better given the poor circumstances riemann grew up in he was pretty much always in poor health thus it's believed that his getting tuberculosis shouldn't solely be attributed to his cold and rather attributed to years with a bad immune system from this point forward there was a lot of back-and-forth travelling between Italy and Kernighan in the winter of 1862 to 1863 riemann traveled down to sicily with his family and then they traveled through italy a bit before returning to Kernighan in June 1863 alas Riemann's health plummeted soon after arriving back and about a year later they made their way back to Italy living in northern Italy from August 1864 to October 1865 they then made another trek back to Kernighan for the winter of 1865 to 1866 the return was even more short-lived in the last as Gert and getting got caught in a clash between the armies of Hanover and Prussia Ramon and his family made their final trek down to Silesia Italy where Ramon would die on the shores of Lake Maggiore On June 16th 1866 finally succumbing to tuberculosis well there you have it a very brief history of bernhard riemann i've personally spent a lot of time playing around with the riemann zeta function so riemann maybe my favorite mathematician from the 19th century but as i keep researching well we'll see if that changes I hope you guys enjoyed the video and I will catch you next time [Music] you

Channel: moderndaymath

Views: 29,551

Keywords: riemann, riemann hypothesis, riemannian geometry, riemann surface, germany, poor, tuberculosis, mathematics, complex analysis, riemann integral, integration, math history, hanover

Id: YYGfqpivvQI

Length: 13min 17sec (797 seconds)

Published: Mon Feb 24 2020