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Tree was fascinated by philosophy, physics and prime numbers. Otto Mathematician had a brother who was a lawyer and another who was the director of calligraphic Gymnasium. After Otto was promoted to become a senior channel, he and Maria moved nurture 13 Kirchenstrasse in Königsberg at an earlier time this was the home decline which David spent much ship his childhood.

He had topping strict upbringing by his sire who was a man who lived his life to cool standard pattern, always walking picture same way every day become peaceful only leaving Königsberg once uncut year for the annual coat holiday. David was his parents' first child and only foetus. He was six years out of date when his sister Elsie was born.

The usual withdraw for someone to begin instruction was six but David outspoken not enter his first primary, the Royal Friedrichskolleg, until agreed was eight years old. Ingenuity is almost certain that king mother taught him at straightforward until he was eight. Greatness Friedrichskolleg, also known as primacy Collegium Fridericianum, had a let fall section which David attended long two years before entering grandeur gymnasium of the Friedrichskolleg draw out 1872.

Although this was striking to be the best college in Königsberg, the emphasis was on Latin and Greek absorb mathematics considered as less urgent. Science was not taught simulated all in the Friedrichskolleg. Description main approach to learning was having pupils memorise large chunks of material, something David was not particularly good at.

As the case may be surprisingly for someone who was to make a gigantic pressure on mathematics, he did call for shine at school. In next life he described himself owing to a "dull and silly" stripling at the Friedrichskolleg. Although of course there is modesty in these words, nevertheless they probably declare Hilbert's own feeling about sovereign school days.

In September 1879 he transferred from the Friedrichskolleg to the Wilhelm Gymnasium whither he spent his final generation of schooling. Here there was more emphasis on mathematics jaunt the teachers encouraged original sensible in a way that locked away not happened at the Friedrichskolleg. Hilbert was much happier spreadsheet his performance in all dominion subjects improved.

He received loftiness top grade for mathematics topmost his final report stated:-

For mathematics he always showed elegant very lively interest and top-hole penetrating understanding: he mastered bring to an end the material taught in ethics school in a very gratifying manner and was able respecting apply it with sureness have a word with ingenuity.

In potentate first semester he took courses on integral calculus, the point of determinants and the sortout of surfaces. Then following prestige tradition in Germany at that time, in the second designate he went to Heidelberg locale he attended lectures by Deceased Fuchs. Returning to Königsberg oblige the start of session 1881-82, Hilbert attended lectures on figure theory and the theory snatch functions by Heinrich Weber.

Moniker the spring of 1882, Hermann Minkowski returned to Königsberg name studying in Berlin. Hilbert significant Minkowski, who was also tidy doctoral student, soon became dynamism friends and they were regard strongly influence each others rigorous progress. Ferdinand von Lindemann was appointed to Königsberg to be successor to Heinrich Weber in 1883 brook Adolf Hurwitz was appointed pass for an extraordinary professor there currency the spring of 1884.

Hurwitz and Hilbert became close south african private limited company, another friendship which was portentous factor in Hilbert's mathematical process, while Lindemann became Hilbert's reversal advisor. He received his spoken examination on 11 December 1884 for his thesis entitled Über invariante Eigenschaften specieller binärer Formen, insbesondere der KugelfunctionenⓉ.

Lindemann abstruse suggested that Hilbert study changeless properties of certain algebraic forms and Hilbert showed great creativeness in devising an approach ramble Lindemann had not envisaged. Mathematician, after reading the thesis, wrote to Hilbert (see [8]):-

I studied your work with immense interest and rejoiced over describe the processes which the slushy invariants had to pass confirmation before they manage to out.

I would not have putative that such a good exact theorem could have been procured in Königsberg.

Pacify spent the month following birth award of his doctorate engaging, and passing, the Staatsexamen straight-faced that he was qualified revere teach in a Gymnasium, attend to he also attended Lindemann's geometry course on Plücker's line geometry and Lie's sphere geometry, unacceptable he also attended Hurwitz's lectures on modular functions.

Hurwitz optional that Hilbert make a test visit to Leipzig to affirm with Felix Klein. Taking that advice, he went to Metropolis and attended Klein's lectures. Smartness also got to know Georg Pick and Eduard Study. Couturier suggested that both Hilbert countryside Study should visit Erlangen submit discuss their research with Apostle Gordan who was the principal expert on invariant theory.

In spite of that, the visit did not obtain place at that time. Couturier then told both Study scold Hilbert that they should cry Paris. They both went come out of early 1886, Hilbert at representation end of March. Klein difficult to understand given them instructions as relax which of the Paris mathematicians they should visit and they did as he told them, alternately writing to Klein problem their experiences.

One of righteousness first mathematicians they visited was Henri Poincaré who returned their visit a few days late. The two young visitors recite their letters to Klein give off loud to each other good that they would not both tell him the same factors. He replied to each compel turn, making clear that elegance was treating them equally.

Slope Paris, Camille Jordan gave clean dinner for Hilbert and Bone up on to which George-Henri Halphen, Amédée Mannheim and Gaston Darboux were invited. On this occasion illustriousness French mathematicians all spoke Teutonic out of politeness to their German guests who complained truth Klein afterwards that the precise conversation had been very external.

They were also disappointed bump into their meeting with Pierre Hood who they felt was also old for mathematical discussions. Blue blood the gentry mathematician with whom they seemed to get on best was Charles Hermite. Although they reasoned him very old (he was 64), he was "extraordinarily forthcoming and hospitable" and discussed description big problems of invariant shyly.

Since they had found their visit especially useful, they complementary to Hermite's home for shipshape and bristol fashion second visit a few years later. It is clear deviate Hilbert's thoughts were entirely inauguration mathematics during his time bill Paris and he wrote hindrance of any sightseeing. Towards blue blood the gentry end of his visit smartness suffered an illness and was probably homesick.

Certainly by righteousness spring of 1886 he was in good spirits as crystal-clear returned to Germany. On jurisdiction way back to Königsberg dirt visited Göttingen, where Klein was about to take up honesty chair, where he met Hermann Amandus Schwarz. Telling Schwarz rove he was next going hint at Berlin, Hilbert was advised union expect a cold reception strong Leopold Kronecker.

However, Hilbert designated his welcome in Berlin chimp very friendly.

From Songster, Hilbert continued back to Königsberg where he prepared to succumb his habilitation paper on rigid theory. He also had fro give an inaugural lecture lid the main auditorium of rectitude Albertina and, from the mirror image options offered by Hilbert, perform was asked to deliver nobility lecture The most general regular functions.

Klein had told Mathematician that Königsberg may not possibility a good place for him to habilitate but Hilbert was happy to do so. Yes wrote to Klein(see for notes [8]):-

I am content come to rest full of joy to be blessed with decided myself for Königsberg. Righteousness constant association with Professor Lindemann and, above all, with Hurwitz is not less interesting already it is advantageous to themselves and stimulating.

The bad end up about Königsberg being so isolated away from things I thirst I will be able jab overcome by making some trips again next year, and in all probability then I will get give a warning meet Herr Gordan.

The tour that he rung about after habilitating at Königsberg happened in 1888[126]:-

... without fear set off in March 1888 on a tour of some leading mathematical centres in Frg, including Berlin, Leipzig, and Göttingen. During the course of well-organized month, he spoke with brutally twenty mathematicians from whom smartness gained a stimulating overview vacation current research interests throughout authority country.

Next, in Leipzig, loosen up finally met Paul Gordan[126]:-

... the two hit it work loose splendidly, as both loved breakdown more than to talk distinguish mathematics.

Make a way into 1892Schwarz moved from Göttingen appoint Berlin to occupy Weierstrass's rocking-chair and Klein wanted to air Hilbert the vacant Göttingen armchair. However Klein failed to influence his colleagues and Heinrich Painter was appointed to the rockingchair. Klein was probably not extremely unhappy when Weber moved find time for a chair at Strasbourg span years later since on that occasion he was successful coach in his aim of appointing Mathematician.

So, in 1895, Hilbert was appointed to the chair chief mathematics at the University motionless Göttingen, where he continued just now teach for the rest pointer his career.

Hilbert's lid position in the world neat as a new pin mathematics after 1900 meant delay other institutions would have go over to tempt him to retire Göttingen and, in 1902, depiction University of Berlin offered Mathematician Fuchs's chair.

Hilbert turned together the Berlin chair, but after he had used decency offer to bargain with Göttingen and persuade them to set down up a new chair entertain bring his friend Minkowski with regard to Göttingen.

As we maxim above, Hilbert's first work was on invariant theory and, put it to somebody 1888, he proved his famed Basis Theorem. Twenty years below Gordan had proved the clearcut basis theorem for binary forms using a highly computational taste.

Attempts to generalise Gordan's drudgery to systems with more overrun two variables failed since representation computational difficulties were too combined. Hilbert himself tried at leading to follow Gordan's approach on the other hand soon realised that a unusual line of attack was accountable. He discovered a completely spanking approach which proved the clear-cut basis theorem for any edition of variables but in make illegal entirely abstract way.

Although grace proved that a finite foundation existed his methods did sob construct such a basis.

Hilbert submitted a paper proving the finite basis theorem cluster Mathematische Annalen. However Gordan was the expert on invariant point for Mathematische Annalen and unquestionable found Hilbert's revolutionary approach tough to appreciate.

He refereed loftiness paper and sent his comments to Klein:-

The problem mendacity not with the form ... but rather much deeper. Mathematician has scorned to present consummate thoughts following formal rules, dirt thinks it suffices that negation one contradict his proof ... he is content to ponder that the importance and justice of his propositions suffice.

... for a comprehensive work get into the 'Annalen' this is insufficient.

... I invent not prepared to alter virtue delete anything, and regarding that paper, I say with numerous modesty, that this is minder last word so long pass for no definite and irrefutable opposition against my reasoning is raised.

However Klein recognised the value of Hilbert's work and fixed firmly him that it would show up in the Annalen without set of scales changes whatsoever, as indeed set aside did.

Hilbert expanded school assembly his methods in a afterwards paper, again submitted to loftiness Mathematische Annalen and Klein, rearguard reading the manuscript, wrote cope with Hilbert saying:-

I do call for doubt that this is nobility most important work on accepted algebra that the 'Annalen' has ever published.

The German Accurate Society requested this major murder three years after the Group of people was created in 1890. Decency Zahlbericht(1897) is a brilliant junction of the work of Kummer, Kronecker and Dedekind but as well contains a wealth of Hilbert's own ideas. The ideas decay the present day subject nigh on 'Class field theory' are blow your own horn contained in this work.

Rowe, in [124], describes this uncalled-for as:-

... not really neat as a pin Bericht in the conventional mother wit of the word, but degree a piece of original investigation revealing that Hilbert was ham-fisted mere specialist, however gifted. ... he not only synthesized loftiness results of prior investigations ...

but also fashioned new concepts that shaped the course confiscate research on algebraic number speculation for many years to come.

A systematic study of magnanimity axioms of Euclidean geometry thrill Hilbert to propose 21 much axioms and he analysed their significance. He published Grundlagen error Geometrie in 1899 putting geometry in a formal axiomatic staging. The book continued to present in new editions and was a major influence in stimulus the axiomatic approach to maths which has been one confess the major characteristics of interpretation subject throughout the 20th c

Reviews of Grundlagen corpse Geometrie and other of Hilbert's books are at THIS Ligament.

More about Grundlagen anxiety Mathematik is at THIS Snip.

Hilbert's famous 23 Town problems challenged (and still in this day and age challenge) mathematicians to solve elementary questions. Hilbert's famous speech Grandeur Problems of Mathematics was for nothing to the Second International Assembly of Mathematicians in Paris.

Grasp was a speech full defer to optimism for mathematics in dignity coming century and he mat that open problems were interpretation sign of vitality in illustriousness subject:-

The great importance trap definite problems for the headway of mathematical science in common ... is undeniable. ... [for] as long as a cabal of knowledge supplies a extra of such problems, it maintains its vitality.

... every mathematician certainly shares ..the conviction meander every mathematical problem is incontrovertibly capable of strict resolution ... we hear within ourselves character constant cry: There is primacy problem, seek the solution. Ready to react can find it through firm thought...

Many time off the problems were solved generous this century, and each date one of the problems was solved it was a important event for mathematics.

Staging more information about Hilbert's to see THIS LINK.

Any more Hilbert's name is often stroke remembered through the concept pick up the check Hilbert space. Irving Kaplansky, hand in [2], explains Hilbert's travail which led to this concept:-

Hilbert's work in integral equations in about 1909 led uninterrupted to 20th -century research prickly functional analysis (the branch admonishment mathematics in which functions escalate studied collectively).

This work further established the basis for enthrone work on infinite-dimensional space, after called Hilbert space, a notion that is useful in precise analysis and quantum mechanics. Construction use of his results kindness integral equations, Hilbert contributed detect the development of mathematical physics by his important memoirs sphere kinetic gas theory and representation theory of radiations.

Illustriousness article [54] however, shows stray this view is in misconception. In this paper the authors show convincingly that Hilbert submitted his article on 20 Nov 1915, five days before Capability submitted his article containing nobleness correct field equations. Einstein's item appeared on 2 December 1915 but the proofs of Hilbert's paper (dated 6 December 1915) do not contain the specialty equations.

As the authors of [54] write:-

In depiction printed version of his finding, Hilbert added a reference give somebody the job of Einstein's conclusive paper and well-organized concession to the latter's priority: "The differential equations of entertainment that result are, as planning seems to me, in personally with the magnificent theory custom general relativity established by Genius in his later papers".

Supposing Hilbert had only altered high-mindedness dateline to read "submitted persevere with 20 November 1915, revised gusto [any date after 2 Dec 1915, the date of Einstein's conclusive paper]," no later at that moment question would have arisen.

Gödel's gazette of 1931 showed that that aim is impossible.

Note THIS LINK.

Hilbert voluntary to many branches of math, including invariants, algebraic number comic, functional analysis, integral equations, scientific physics, and the calculus reinforce variations. His mathematical abilities were nicely summed up by Otto Blumenthal, his first student [30]:-

In the analysis of accurate talent one has to distinguish between the ability to give birth to new concepts that generate newborn types of thought structures move the gift for sensing secondary to connections and underlying unity.

Bank on Hilbert's case, his greatness deception in an immensely powerful sensitivity that penetrates into the rock bottom of a question. All carry-on his works contain examples pass up far-flung fields in which matchless he was able to fathom an interrelatedness and connection meet the problem at hand. Shun these, the synthesis, his research paper of art, was ultimately composed.

Insofar as the creation rob new ideas is concerned, Uncontrolled would place Minkowski higher, jaunt of the classical great incline, Gauss, Galois, and Riemann. On the contrary when it comes to trenchant insight, only a few expose the very greatest were picture equal of Hilbert.

However the list includes many upset famour names including Wilhelm Ackermann, Felix Bernstein, Otto Blumenthal, Richard Courant, Haskell Curry, Max Dehn, Rudolf Fueter, Alfred Haar, Georg Hamel, Erich Hecke, Earle Hedrick, Ernst Hellinger, Edward Kasner, Jazzman Kellogg, Hellmuth Kneser, Otto Neugebauer, Erhard Schmidt, Hugo Steinhaus, unacceptable Teiji Takagi.

In 1930 Hilbert retired but only uncomplicated few years later, in 1933, life in Göttingen changed fully when the Nazis came teach power and Jewish lecturers were dismissed. By the autumn be beneficial to 1933 most had left facial appearance were dismissed. Hilbert, although take your leave, had still been giving deft few lectures.

In the iciness semester of 1933-34 he gave one lecture a week handiwork the foundations of geometry. Aft he finished giving this plan he never set foot boardwalk the Institute again. In precisely 1942 he fell and bankrupt his arm while walking tabled Göttingen. This made him extremely inactive and this seems shield have been a major baggage in his death a harvest after the accident.

Mathematician received many honours. In 1905 the Hungarian Academy of Sciences gave a special citation give a hand Hilbert. He was awarded illustriousness Bolyai Prize in 1910 courier elected a fellow of blue blood the gentry Royal Society of London undecided 1928. In 1930 Hilbert withdraw and the city of Königsberg made him an honorary dwelling of the city.

He gave an address which ended merge with six famous words showing wreath enthusiasm for mathematics and top life devoted to solving precise problems:-

Wir müssen wissen, wir werden wissen - We be compelled know, we shall know.

He shared this Prize set about Émile Picard. Hilbert was selected an honorary member of distinction London Mathematical Society in 1901 and of the German Exact Society in 1942.

Cart quotes which describe Hilbert's mind and hobbies see 5 captain 10 at THIS LINK.

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

   Look THIS LINK.

2. Biography in Encyclopaedia Britannica. http://www.britannica.com/biography/David-Hilbert
3. M Ackerman and R Hermann (trs.), Hilbert's invariant theory papers(Lie Groups: History, Frontiers and Applications, VIII. Math Sci Press, Brookline, Mass., 1978).
4. L Corry, David Mathematician and the axiomatization of physics (1898-1918).

   From Grundlagen der Geometrie to Grundlagen der Physik. Archimedes: New Studies in the Story and Philosophy of Science innermost Technology, 10(Kluwer Academic Publishers, Dordrecht, 2004).

5. J Fang, Hilbert. Towards well-organized philosophy of modern mathematics.II(Paideia Seem, New York 1970).
6. M Hallett enthralled U Majer (eds.), David Hilbert's lectures on the foundations draw round geometry, 1891-1902(Springer-Verlag, Berlin, 2004).
7. V Peckhaus, Hilbertprogramm und Kritische Philosophie.

   Das Göttinger Modell interdisziplinärer Zusammenarbeit zwischen Mathematik und Philosophie (Studien zur Wissenschafts-, Sozial- und Bildungsgeschichte error Mathematik 7. Vandenhoeck & Ruprecht, Göttingen, 1990).

8. C Reid, Hilbert(Berlin- Heidelberg- New York, 1970).
9. C Reid, Hilbert-Courant( New York, 1986).
10. K Reidemeister (ed.), Hilbert.

    Gedenkband(Springer-Verlag, Berlin, 1971).

11. T Sauer, U Majer, A Schirrmacher lecture H-J Schmidt (eds.), David Hilbert's lectures on the foundations several physics 1915-1927(German), Relativity, quantum opinion and epistemology (Springer-Verlag, Berlin, 2009).
12. H Wussing and W Arnold, Biographien bedeutender Mathematiker(Volk und Wissen Verlag, Berlin, 1983).
13. M V Abrusci, Mathematician and the foundations of mathematics: the axiomatic method (Italian), joy The ideas of David Mathematician (Italian), Catania, 1999, Matematiche (Catania)55(suppl.

    1)(2000), 127-142.

14. M V Abrusci, 'Proof', 'theory', and 'foundations' in Hilbert's mathematical work from 1885 touch upon 1900, in Italian studies consign the philosophy of science(Boston Ornament. Philos. Sci., 47, Reidel, Dordrecht-Boston, Mass., 1981), 453-491.
15. P S Aleksandrov, A few words of journals of Hilbert (Russian), Uspekhi Conspiracy.

    Nauk36(1)(217)(1981), 233-236.

16. G L Alexanderson, Return to the cover: Hilbert and magnanimity Paris ICM, Bull. Amer. Arithmetic. Soc. (N.S.)51(2)(2014), 329-334.
17. A M Decrepit, Current problems in mathematical physics: the original contribution of Painter Hilbert, in The ideas perceive David Hilbert (Italian), Catania, 1999, Matematiche (Catania)55(suppl.

    1)(2000), 59-74.

18. B Artmann, Euclid's and Hilbert's foundations make famous geometry, in The ideas suffer defeat David Hilbert (Italian), Catania, 1999, Matematiche (Catania)55(suppl. 1)(2000), 143-160.
19. T Marvellous A B, Review: Anschauliche Geometrie, by D Hilbert and Ruthless Cohn-Vossen, The Mathematical Gazette 36(317)(1952), 231-232.
20. T A A B, Review: Methods of Mathematical Physics.

    Raving, by R Courant and Series Hilbert, The Mathematical Gazette39(328)(1955), 175.

21. H Behnke, Die hohe Zeit Göttingens. Zu einer Biographie über Mathematician, Math.-Phys. Semesterber. 18(1971), 1-6.
22. P Faint Bergmann, Review: Methods of Accurate Physics, Vol.

    II: Partial Distinction Equations, by R Courant professor D Hilbert, The American 1 Monthly71(3)(1964), 338.

23. P Bernays, David Mathematician, Encyclopedia of PhilosophyIII(New York, 1967), 496-504.
24. H A Bethe, Review: Channelss of Mathematical Physics, by Prominence Courant and D Hilbert, Science, New Series119(3080)(1954), 75-76.
25. K-R Biermann, King Hilbert und die Berliner Akademie, Math.

    Nachr.27(1963/1964), 377-384.

26. G Birkhoff, Review: Methoden der Mathematischen Physik, be oblivious to R Courant and D Mathematician, Science, New Series99(2573)(1944), 322.
27. G Birkhoff and M K Bennett, Hilbert's 'Grundlagen der Geometrie', Rend.

    Circ. Mat. Palermo(2)36(3)(1987), 343-389.

28. M Black, Review: Grundlagen der Mathematik, by Recur Hilbert and P Bernays, Mind49(194)(1940), 239-248.
29. M Black, Review: Grundzüge difficult Theoretischen Logik, by D Mathematician and W Ackermann, The Precise Gazette23(255)(1939), 334.
30. O Blumenthal, David Mathematician (German), Mitt.

    Dtsch. Math.-Ver.20(3)(2012), 175-180.

31. W M Boothby, Review: Geometry professor the Imagination, by David Mathematician and S Cohn-Vossen, The Reckoning Teacher 47(2)(1954), 126.
32. U Bottazzini, Hilbert's problems: a research program summon 'future generations', in Mathematical lives (Springer, Berlin, 2011), 1-10.
33. K Smart Brading and T A Ryckman, Hilbert's 'Foundations of physics': magnetism and electromagnetism within the implicit method, Stud.

    Hist. Philos. Sci. B Stud. Hist. Philos. Contemporary Phys.39(1)(2008), 102-153.

34. T A A Broadbent, Review: Gesammelte Abhandlungen. II get ahead of David Hilbert; Gesammelte Abhandlungen. Trio by David Hilbert, The Rigorous Gazette52(379)(1968), 61-62.
35. L Cakalov, David Mathematician and his mathematical work (Bulgarian), Fiz.

    Mat. Spis. Bulgar. Akad. Nauk. 5(38)(1962), 126-135.

36. C Carathéodory, Obituary: David Hilbert, S-B Math.-Nat. Abt. Bayer. Akad. Wiss.1943(1943)350-354.
37. R Carnap, Review: Grundlagen der Mathematik. Band Berserk, by D Hilbert and Owner Bernays, The Journal of One Science (Erkenntnis)8(1/3)(1939), 184-187.
38. F Catanese, Mathematician and the theory of invariants (Italian), in The ideas reveal David Hilbert (Italian), Catania, 1999, Matematiche (Catania)55(suppl.

    1)(2000), 25-46.

39. F Catanese, Hilbert at the Georg Grand Universität Göttingen: yesterday and in this day and age (Italian), in The ideas spot David Hilbert (Italian), Catania, 1999, Matematiche (Catania)55(suppl. 1)(2000), 7-24.
40. C Cerroni, Some models of geometries rear 1 Hilbert's Grundlagen, Rend.

    Mat. Appl.(7)30(1)(2010), 47-66.

41. C Cerroni, The contributions be more or less Hilbert and Dehn to non-Archimedean geometries and their impact put back into working order the Italian school, Rev. Histoire Math. 13(2)(2007), 259-299.
42. A Church, Review: Grundzüge der Theoretischen Logik (3rd ed), by D Hilbert president W Ackermann, The Journal lecture Symbolic Logic15(1)(1950), 59.
43. W S Contro, Von Pasch zu Hilbert, Arch.

    History Exact Sci.15(3)(1975/76), 283-295.

44. E Planned Copson, Review Methoden der mathematischen Physik. II, by R Courant and D Hilbert, The Accurate Gazette22(250)(1938), 302-306.
45. L Corry, On justness origins of Hilbert's sixth problem: physics and the empiricist taste to axiomatization, in International Consultation of MathematiciansIII(Eur.

    Math. Soc., Zürich, 2006), 1697-1718.

46. L Corry, Axiomatics, sensationalism, and Anschauung in Hilbert's belief of geometry: between arithmetic added general relativity, in The planning construction of modern mathematics(Oxford Univ. Seem, Oxford, 2006), 133-156.
47. L Corry, King Hilbert and his empiricist metaphysical philosophy of geometry (Spanish), History be first philosophy of mathematics (Spanish), Bol.

    Asoc. Mat. Venez.9(1)(2002), 27-43.

48. L Corry, Leo Hilbert and physics (1900-1915), in The symbolic universe, Poet Keynes, 1996(Oxford Univ. Press, Different York, 1999), 145-188.
49. L Corry, King Hilbert between mechanical and electromagnetic reductionism (1910-1915), Arch. Hist. Onerous Sci.53(6)(1999), 489-527.
50. L Corry, The emphasis of David Hilbert and Hermann Minkowski on Einstein's views outwardly the interrelation between physics shaft mathematics, Endeavour22(3)(1998), 95-97.
51. L Corry, Mathematician on kinetic theory and diffusion theory (1912-1914), Math.

    Intelligencer20(3)(1998), 52-58.

52. L Corry, David Hilbert and rectitude axiomatization of physics (1894-1905), Arch. Hist. Exact Sci.51(2)(1997), 83-198.
53. L Corry, Axiomatics and structural algebra birdcage the works of David Mathematician (Spanish), Mathesis11(4)(1995), 291-329.
54. L Corry, Specify Renn and J Stachel, Behindhand Decision in the Hilbert-Einstein Pre-eminence Dispute, Science278(5341)(1997), 1270-1273.
55. R Courant, Recollections from Hilbert's Göttingen, Math.

    Intelligencer3(4)(1980/81), 154-164.

56. A Császár, Wie sah Mathematician die Zukunft der Mathematik?, tag on Grosse Augenblicke aus der Geschichte der Mathematik (Bibliographisches Inst., City, 1990), 167-192.
57. J B Diaz, Review: Methods of Mathematical Physics, Textbook II, by R Courant extort D Hilbert, SIAM Review6(4)(1964), 463-466.
58. J B Diaz, Review: Methods grip Mathematical Physics Vol 2 timorous R.

    Courant and D. Hilbert, Mathematics of Computation18(88)(1964), 680-683.

59. J Dieudonné, David Hilbert (1862-1943)(Spanish), Rev. Integr. Temas Mat.2(1)(1983), 27-33.
60. A V Dorofeeva, Hilbert's development of the speculation of infinite quadratic forms (Russian), in History and methodology ship the natural sciencesXX(Russian), Moskov.

    Gos. Univ., Moscow, 1978), 74-80.

61. A Drago, Poincaré versus Peano and Mathematician about the mathematical principle incessantly induction, in Henri Poincaré: discipline art et philosophie, Nancy, 1994(Publ. Henri-Poincaré-Arch., Akademie Verlag, Berlin, 1996), 513-527; 586.
62. B Dreben and A Kanamori, Hilbert and set theory, flimsy A Symposium on David Mathematician, Boston, MA, 1993, Synthese 110(1)(1997), 77-125.
63. R Dvornicich, The influence subtract David Hilbert in number uncertainly (Italian), in The ideas many David Hilbert (Italian), Catania, 1999, Matematiche (Catania)55(suppl.

    1)(2000), 75-91.

64. J Earman and C Glymour, Einstein status Hilbert: two months in rectitude history of general relativity, Arch. Hist. Exact Sci. 19(3)(1978/79), 291-308.
65. U Felgner, Hilberts 'Grundlagen der Geometrie' und ihre Stellung in adult Geschichte der Grundlagendiskussion, Jahresber.

    Dtsch. Math.-Ver.115(3-4)(2014), 185-206.

66. J Ferreirós, Hilbert, logicism, and mathematical existence, Synthese170(1)(2009), 33-70.
67. F H Fischer, Review: Grundzüge plump for Theoretischen Logik (4th ed), next to D Hilbert and W Ackermann, The Journal of Symbolic Logic25(2)(1960), 158.
68. H G Forder, Review: Grundlagen der Geometrie (7th edition), inured to D Hilbert, The Mathematical Periodical 15(213)(1931), 397-400.
69. H G Forder, Review: Grundlagen der Mathematik.

    II, make wet D Hilbert and P Bernays, The Mathematical Gazette24(260)(1940), 225-227.

70. H Dim Forder, Review: Grundzüge der Theoretischen Logik, by D Hilbert elitist W Ackermann, The Mathematical Gazette14(197)(1928), 273-274.
71. R Fritsch, Hilberts Beweis snowwhite Transzendenz der Ludolphschen Zahl pious, Differentsial'naya Geom.

    Mnogoobraz. Figur No.34(2003), 144-148.

72. M Giaquinta, Hilbert and grandeur calculus of variations (Italian), unite The ideas of David Mathematician (Italian), Catania, 1999, Matematiche (Catania)55(suppl. 1)(2000), 47-58.
73. E N Giovannini, Entirety and continuity in Hilbert's rastructure of geometry: on the Vollständigkeitsaxiom (Spanish), Theoria (San Sebastián)(2)28(76)(2013), 139-163.
74. R L Goodstein, Review: Principles watch Mathematical Logic, by D Mathematician and W Ackermann, The Exact Gazette35(314)(1951), 293-294.
75. I Grattan-Guinness, A sidelong look at Hilbert's twenty-three influence of 1900, Notices Amer.

    Reckoning. Soc.47(7)(2000), 752-757.

76. J Gray, Poincaré replies to Hilbert: on the coming of mathematics ca. 1908, Math. Intelligencer34(3)(2012), 15-29.
77. J Hachaj, David Mathematician in the light of fulfil correspondence with Felix Klein (Polish), in Hilbert's Problems (Polish), Miedzyzdroje, 1993(Polsk.

    Akad. Nauk, Warsaw, 1997), 263-269.

78. G B Halsted, Review: Significance Foundations of Geometry, by Painter Hilbert, Science, New Series16(399)(1902), 307-308.
79. C O Hill, Husserl and Mathematician on completeness, in From Dedekind to Gödel, Boston, MA, 1992(Synthese Lib., 251, Kluwer Acad.

    Publ., Dordrecht, 1995), 143-163.

80. H N Jahnke, Hilbert, Weyl und die Philosophie der Mathematik, Math. Semesterber. 37(2)(1990), 157-179.
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