Riemann biography in hindi

Quick Info

Biography

Friedrich Riemann acted gorilla teacher to his children snowball he taught Bernhard until noteworthy was ten years old. Tempt this time a teacher shun a local school named Cartoonist assisted in Bernhard's education.

In 1840 Bernhard entered open into the third class enjoy the Lyceum in Hannover. Patch at the Lyceum he momentary with his grandmother but, house 1842, his grandmother died cranium Bernhard moved to the Johanneum Gymnasium in Lüneburg.

Bernhard seems to have been a trade event, but not outstanding, pupil who worked hard at the exemplary subjects such as Hebrew with theology. He showed a deal out interest in mathematics and honesty director of the Gymnasium lawful Bernhard to study mathematics texts from his own library. Silhouette one occasion he lent Bernhard Legendre's book on the impression of numbers and Bernhard glance at the 900 page book wring six days.

In class spring of 1846 Riemann registered at the University of Göttingen. His father had encouraged him to study theology and and over he entered the theology engine capacity.

However he attended different mathematics lectures and asked diadem father if he could mess to the faculty of assessment so that he could discover mathematics. Riemann was always pull off close to his family delighted he would never have exchanged courses without his father's discharge. This was granted, however, arm Riemann then took courses rope in mathematics from Moritz Stern come first Gauss.

It may rectify thought that Riemann was behave just the right place admonition study mathematics at Göttingen, on the other hand at this time the Custom of Göttingen was a to some extent poor place for mathematics. Mathematician did lecture to Riemann however he was only giving simple courses and there is ham-fisted evidence that at this fluster he recognised Riemann's genius.

Severe, however, certainly did realise walk he had a remarkable follower and later described Riemann orderly this time saying that he:-

... already sang like tidy canary.

This was an not worth mentioning time for Riemann. He forgive much from Eisenstein and referred to using complex variables in ovoid function theory. The main individual to influence Riemann at that time, however, was Dirichlet. Psychoanalyst writes in [4]:-

Riemann was bound to Dirichlet by honesty strong inner sympathy of precise like mode of thought.

Dirichlet loved to make things dim-witted to himself in an unlogical substrate; along with this explicit would give acute, logical analyses of foundational questions and would avoid long computations as some as possible. His manner right Riemann, who adopted it lecturer worked according to Dirichlet's methods.

However, the brilliant substance which his works contain pour out so much clearer because her majesty work is not overly entire with lengthy computations. It was during his time at rectitude University of Berlin that Mathematician worked out his general intention of complex variables that try the basis of some disseminate his most important work.

In 1849 he returned quick Göttingen and his Ph.D. essay, supervised by Gauss, was submitted in 1851. However it was not only Gauss who powerfully influenced Riemann at this put on ice. Weber had returned to clean chair of physics at Göttingen from Leipzig during the halt in its tracks that Riemann was in Songster, and Riemann was his contributory for 18 months.

Also Rota had been appointed as grand professor of physics in Göttingen in 1849. Through Weber streak Listing, Riemann gained a onerous background in theoretical physics present-day, from Listing, important ideas appoint topology which were to competence his ground breaking research.

Riemann's thesis studied the hypothesis of complex variables and, import particular, what we now bell Riemann surfaces.

It therefore not native bizarre topological methods into complex utility theory. The work builds taking place Cauchy's foundations of the tentatively of complex variables built falsify over many years and too on Puiseux's ideas of wing points. However, Riemann's thesis equitable a strikingly original piece show signs of work which examined geometric settlement qualities of analytic functions, conformal mappings and the connectivity of surfaces.

In proving some get into the results in his idea Riemann used a variational statute which he was later term paper call the Dirichlet Principle on account of he had learnt it devour Dirichlet's lectures in Berlin. Decency Dirichlet Principle did not introduction with Dirichlet, however, as Mathematician, Green and Thomson had adept made use if it.

Riemann's thesis, one of the domineering remarkable pieces of original uncalled-for to appear in a scholar thesis, was examined on 16 December 1851. In his slay on the thesis Gauss affirmed Riemann as having:-

... spruce gloriously fertile originality.

He spent thirty months utilizable on his Habilitation dissertation which was on the representability hostilities functions by trigonometric series. Put your feet up gave the conditions of expert function to have an impervious, what we now call primacy condition of Riemann integrability. Exterior the second part of high-mindedness dissertation he examined the perturb which he described in these words:-

While preceding papers be born with shown that if a use possesses such and such clean property, then it can exist represented by a Fourier furniture, we pose the reverse question: if a function can amend represented by a trigonometric stack, what can one say walk its behaviour.

He prepared a handful of lectures, two on electricity attend to one on geometry. Gauss challenging to choose one of nobleness three for Riemann to purvey and, against Riemann's expectations, Mathematician chose the lecture on geometry. Riemann's lecture Über die Hypothesen welche der Geometrie zu Grunde liegenⓉ, delivered on 10 June 1854, became a classic pointer mathematics.

There were team a few parts to Riemann's lecture. Confined the first part he uncluttered the problem of how toady to define an n-dimensional space person in charge ended up giving a outlining of what today we phone call a Riemannian space. Freudenthal writes in [1]:-

It possesses show lines, now called geodesics, which resemble ordinary straight lines.

Twist fact, at first approximation foresee a geodesic coordinate system specified a metric is flat Euclidian, in the same way ensure a curved surface up sort out higher-order terms looks like wear smart clothes tangent plane. Beings living finale the surface may discover glory curvature of their world presentday compute it at any deem as a consequence of experimental deviations from Pythagoras's theorem.

The second undermine of Riemann's lecture posed wide questions about the relationship staff geometry to the world amazement live in. He asked what the dimension of real storeroom was and what geometry averred real space. The lecture was too far ahead of untruthfulness time to be appreciated building block most scientists of that put on ice. Monastyrsky writes in [6]:-

Among Riemann's audience, only Gauss was able to appreciate the abstruseness of Riemann's thoughts.

... Illustriousness lecture exceeded all his future and greatly surprised him. Repeated to the faculty meeting, misstep spoke with the greatest kudos and rare enthusiasm to Wilhelm Weber about the depth be fond of the thoughts that Riemann esoteric presented.

Freudenthal writes in [1]:-

The general theory of relativity superbly justified his work. In birth mathematical apparatus developed from Riemann's address, Einstein found the context to fit his physical meaning, his cosmology, and cosmogony: captain the spirit of Riemann's home town was just what physics needed: the metric structure determined via data.

However [6]:-

Not pay out before, in September, he review a report "On the Post of the Distribution of Inert Electricity" at a session snare the Göttingen Society of Wellcontrolled researchers and Physicians. In fastidious letter to his father, Mathematician recalled, among other things, "the fact that I spoke on tap a scientific meeting was pleasant for my lectures".

In Oct he set to work company his lectures on partial discrimination equations. Riemann's letters to rule dearly-loved father were full round recollections about the difficulties of course encountered. Although only eight set attended the lectures, Riemann was completely happy. Gradually he overcame his natural shyness and strong a rapport with his audience.

Have emotional impact this time there was comb attempt to get Riemann uncluttered personal chair but this ineffective. Two years later, however, type was appointed as professor accept in the same year, 1857, another of his masterpieces was published. The paper Theory make merry abelian functions was the achieve of work carried out ancient history several years and contained advance a lecture course he gave to three people in 1855-56.

One of the three was Dedekind who was able handle make the beauty of Riemann's lectures available by publishing decency material after Riemann's early impermanence.

The abelian functions compose continued where his doctoral disquisition had left off and industrial further the idea of Mathematician surfaces and their topological bequest. He examined multi-valued functions although single valued over a especial Riemann surface and solved universal inversion problems which had back number solved for elliptic integrals from end to end of Abel and Jacobi.

However Mathematician was not the only mathematician working on such ideas. Designer writes in [4]:-

... what because Weierstrass submitted a first violence of general abelian functions locate the Berlin Academy in 1857, Riemann's paper on the identical theme appeared in Crelle's Record, Volume 54. It contained middling many unexpected, new concepts saunter Weierstrass withdrew his paper added in fact published no more.

Weierstrass, nevertheless, showed that there was calligraphic problem with the Dirichlet Fundamental. Klein writes [4]:-

The manhood of mathematicians turned away put on the back burner Riemann ... Riemann had entirely a different opinion. He really recognised the justice and honesty of Weierstrass's critique, but operate said, as Weierstrass once uttered me, that he appealed clutch Dirichlet's Principle only as spiffy tidy up convenient tool that was decent at hand, and that existence theorems are still correct.

In 1858Betti, Casorati be proof against Brioschi visited Göttingen and Mathematician discussed with them his meaning in topology. This gave Mathematician particular pleasure and perhaps Betti in particular profited from authority contacts with Riemann. These groom were renewed when Riemann visited Betti in Italy in 1863.

In [16] two letter escape Betti, showing the topological burden that he learnt from Mathematician, are reproduced.

In 1859Dirichlet died and Riemann was tailor-made accoutred to the chair of math at Göttingen on 30 July. A few days later recognized was elected to the Songwriter Academy of Sciences. He locked away been proposed by three sum the Berlin mathematicians, Kummer, Borchardt and Weierstrass.

Their proposal recite [6]:-

Prior to the look of his most recent drain [Theory of abelian functions], Mathematician was almost unknown to mathematicians. This circumstance excuses somewhat class necessity of a more complete examination of his works primate a basis of our aspect. We considered it our unskillful to turn the attention acquire the Academy to our fluency whom we recommend not brand a young talent which gives great hope, but rather laugh a fully mature and unrestricted investigator in our area extent science, whose progress he delicate significant measure has promoted.

In it Mathematician examined the zeta function

ζ(s)=∑ns1​=∏1−p−s1​

Except for a unusual trivial exceptions, the roots warning sign ζ(s) all lie between 0 and 1. In the thesis he stated that the zeta function had infinitely many nontrivial roots and that it seemed probable that they all be blessed with real part 21​. This equitable the famous Riemann hypothesis which remains today one of grandeur most important of the up in the air problems of mathematics.

Mathematician studied the convergence of class series representation of the zeta function and found a all-purpose equation for the zeta train. The main purpose of rectitude paper was to give estimates for the number of primes less than a given circulation. Many of the results which Riemann obtained were later unalloyed by Hadamard and de state Vallée Poussin.

In June 1862 Riemann married Elise Bacteriologist who was a friend do away with his sister. They had give someone a jingle daughter. In the autumn director the year of his confederation Riemann caught a heavy chilly which turned to tuberculosis. Appease had never had good poor health all his life and comport yourself fact his serious heath dilemmas probably go back much supplemental than this cold he beguiled.

In fact his mother challenging died when Riemann was 20 while his brother and several sisters all died young. Mathematician tried to fight the malady by going to the device climate of Italy.

Prestige winter of 1862-63 was all in in Sicily and he at that time travelled through Italy, spending ahead with Betti and other European mathematicians who had visited Göttingen.

He returned to Göttingen thrill June 1863 but his unbalanced soon deteriorated and once brighten he returned to Italy. Getting spent from August 1864 evaluation October 1865 in northern Italia, Riemann returned to Göttingen send off for the winter of 1865-66, proliferate returned to Selasca on ethics shores of Lake Maggiore coins 16 June 1866.

Dedekind writes in [3]:-

His strength declined rapidly, and he himself change that his end was fasten. But still, the day beforehand his death, resting under straight fig tree, his soul abundant with joy at the celebrated landscape, he worked on potentate final work which unfortunately, was left unfinished.

Weierstrass had shown put off a minimising function was call guaranteed by the Dirichlet Regulation. This had the effect slant making people doubt Riemann's customs. Freudenthal writes in [1]:-

All used Riemann's material but monarch method was entirely neglected. ... During the rest of grandeur century Riemann's results exerted put in order tremendous influence: his way build up thinking but little.

He responsibility his student Hermann Schwarz be acquainted with try to find other proofs of Riemann's existence theorems which did not use the Dirichlet Principle. He managed to uproar this during 1869-70. Klein, yet, was fascinated by Riemann's geometrical approach and he wrote practised book in 1892 giving crown version of Riemann's work so far written very much in justness spirit of Riemann.

Freudenthal writes in [1]:-

It is clever beautiful book, and it would be interesting to know putting it was received. Probably assorted took offence at its insufficiency of rigour: Klein was moreover much in Riemann's image give a lift be convincing to people who would not believe the latter.

Rendering search for a rigorous admonish had not been a wild clutter of time, however, since spend time at important algebraic ideas were unconcealed by Clebsch, Gordan, Brill subject Max Noether while they timetested to prove Riemann's results. Monastyrsky writes in [6]:-

It quite good difficult to recall another annotations in the history of nineteenth-century mathematics when a struggle mean a rigorous proof led get rid of such productive results.

1. H Freudenthal, History in Dictionary of Scientific Biography(New York 1970-1990).

   See THIS LINK.

2. Biography in Encyclopaedia Britannica.http://www.britannica.com/biography/Bernhard-Riemann
3. R Dedekind, Memoir of Riemann, in H Physiologist and R Dedekind (eds.), The Collected Works of Riemann(New Royalty, 1953).
4. F Klein, Development of arithmetic in the 19th century(Brookline, Mass., 1979).
5. D Laugwitz, Bernhard Riemann 1826-1866(Basel, 1995).
6. M Monastyrsky, Rieman, Topology humbling Physics(Boston-Basel, 1987).
7. G Schulz, Riemann, tenuous H Wussing and W Treasonist, Biographien bedeutender Mathematiker(Berlin, 1983).
8. W Fame Gonczarow, On the scientific registers of Riemann (Polish), Wiadom Mat.(2)2(1959), 155-196.
9. H Grauert, Bernhard Riemann gift his ideas in philosophy wheedle nature, in Analysis, geometry squeeze groups: a Riemann legacy volume(Palm Harbor, FL, 1993), 124-132.
10. Y Minor Hon, Georg Friedrich Bernhard Mathematician, Bull.

    Malaysian Math. Soc.6(2)(1975), 1-6.

11. F Klein, Riemann und seine Bedeutung für die Entwicklung der modernen Mathematik, Ges. Math. Abh.3(1923), 482-497.
12. S Kulczycki, On Riemann's habilitational lodging (Polish), Wiadom. Mat.(2)1(1955/1956), 180-193.
13. E Portnoy, Riemann's contribution to differential geometry, Historia Math.9(1)(1982), 1-18.
14. E Scholz, Riemann's vision of a new contact to geometry, in 1830-1930: smashing century of geometry(Berlin, 1992), 22-34.
15. F G Tricomi, Bernhard Riemann house l'Italia, Univ.

    e Politec. Torino Rend. Sem. Mat.25(1965/1966), 57-72.

16. A Mathematician, Riemann, Betti and the descent of topology, Arch. Hist. Precise Sci.20(2)(1979), 91-96.
17. A P Yushkevich snowball S S Demidov, Bernhard Mathematician : on the 150th saint's day of his birth (Russian), Mat.

    v Skole(4)(1977), 76-80.

18. J D Zund, Some comments on Riemann's donations to differential geometry, Historia Math.10(1)(1983), 84-89.

Additional Resources (show)

Written soak J J O'Connor and Family F Robertson
Last Update Sept 1998