61. [HM] Conference: "Hilbert's Problems Today" By Julio Gonzalez Cabillon HM Conference hilbert s problems today by Julio Gonzalez Cabillon.reply to this message post a message on a new topic Back to historia http://mathforum.org/epigone/historia/maxprangstimp

[HM] Conference: "Hilbert's problems today" by Julio Gonzalez Cabillon reply to this message post a message on a new topic Back to historia Subject: [HM] Conference: "Hilbert's problems today" Author: jgc@adinet.com.uy Date: Fri, 12 Jan 2001 15:27:11 -0300 HILBERT'S PROBLEMS TODAY 5th - 7th, April, 2001 Pisa, Italy The conference "Hilbert's problems today", organized by the Dipartimento di Matematica of the Universita' di Pisa, in collaboration with the Dipartimento di Matematica Applicata and the Dipartimento di Filosofia, will be held from Thursday, April 5th, to Saturday, April 7th 2001, in Pisa, Italy. The meeting will focus around a group of problems, selected from those considered by Hilbert in his celebrated address at the International Congress of Mathematics in Paris in 1900, and spanning on the areas of Logic, Geometry, Number theory, and Analysis. Further information at http://www.dm.unipi.it/hilbertoday/ The Math Forum

62. The Honor's Class: Hilbert's Problems And Their Solvers Benjamin H Yandell The Honor s Class hilbert s problems and Their Solvers Benjamin HYandell. Author or Artist Benjamin H Yandell. Title The Honor s http://www.hockadilly.co.uk/Benjamin-H-Yandell-The-Honors-Class-Hilber-213-282-7

The Honor's Class: Hilbert's Problems and Their Solvers Benjamin H Yandell Author or Artist : Benjamin H Yandell Title: The Honor's Class: Hilbert's Problems and Their Solvers Yandell Benjamin H Benjamin H. Yandell Subject: 20th century Category: Science Nature Mathematics Education Teaching Aids Format: Hardcover Winning Ways for Your Mathematical Plays, Volume 2... Elwyn Berlekamp John H. Conway Richard K. Guy-Winning Ways for Your Mathematical Plays, Volume 3... Winning Ways for Your Mathematical Plays, Volume 4... Henrik Wann Jensen-Realistic Image Synthesis Using Photon Mapping... ... Deirdre Manifold-Fatima and the Great Conspiracy...

63. Hilbert's Problems hilbert s problems. A set of (originally) unsolved problems in mathematicsproposed by hilbert. Of References. hilbert s problems. Anasov http://icl.pku.edu.cn/yujs/MathWorld/math/h/h282.htm

Hilbert's Problems A set of (originally) unsolved problems in mathematics proposed by Hilbert Of the 23 total, ten were presented at the Second International Congress in Paris in 1900. These problems were designed to serve as examples for the kinds of problems whose solutions would lead to the furthering of disciplines in mathematics. 1a. Is there a transfinite number between that of a Denumerable Set and the numbers of the Continuum ? This question was answered by and Cohen to the effect that the answer depends on the particular version of Set Theory assumed. 1b. Can the Continuum of numbers be considered a Well-Ordered Set ? This question is related to Zermelo's Axiom of Choice . In 1963, the Axiom of Choice was demonstrated to be independent of all other Axioms in Set Theory , so there appears to be no universally valid solution to this question either. 2. Can it be proven that the Axioms of logic are consistent? indicated that the answer is ``no,'' in the sense that any formal system interesting enough to formulate its own consistency can prove its own consistency Iff it is inconsistent.

64. The Honors Class: Hilbert's Problems And Their Solvers By Benjamin Yandell (Hard Buy The Honors Class hilbert s problems and Their Solvers by BenjaminYandell (Hardcover) from home at our online store. Click http://www.mathbook.com/bio/h/David_Hilbert/The_Honors_Class_Hilbert_s_Problems_

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65. CVGMT: Hilbert's Problems Today 9.30 10.30 Carlo Cellucci hilbert on mathematical problems and problemsolving; 16.30 - 17.30 Michele Abrusci hilbert s Second Problem. http://cvgmt.sns.it/news/20010405/

Home People News Add News ... Help Hilbert's Problems Today Meeting Announcement 5 Apr 2001 - 7 Apr 2001 Reference: fibonacci.dm.unipi.it/hilbertoday PRELIMINARY PROGRAM Thursday, April 5th, Aula Magna Storica, University of Pisa. 15.00 - 15.30 Address of the Rector. 15.30 - 16.30 Gregory Moore: Hilbert's First Problem: The Contributions of Hausdorff and Sierpinski to the Continuum Problem, 1900-1940, and the Heritage of Their Work Today 17.00 - 18.00 Umberto Bottazzini: Foundations of Geometry and Mathematical Problems. Friday, April 6th. 9.30 - 10.30 Mario Miranda:Hilbert 20th problem on the existence of solutions of the boundary value problem 11.00 - 12.00 Louis Nirenberg: Hilbert's 19th problem: on regularity of solutions of problems in the calculus of variations 15.00 - 16.00 Corrado de Concini:Hilbert's 15th problem: Schubert calculus 16.30 - 17.30 Oleg Viro: The sixteenth problem: what was the problem and has it been solved? 18.00 - 19.00, Michel Waldschmidt: Some open Diophantine Problems 20. Social Dinner.

66. Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks The 10th of these 23 hilbert s problems was the following 10. Note.During his lecture hilbert mentioned only 10 of 23 problems. http://www.ltn.lv/~podnieks/gt4.html

Hilbert tenth problem, Diophantine equation, Hilbert, tenth problem, Matiyasevich, Robinson, Julia, 10th, problem, Davis, Martin, Diophantine, equation Back to title page Left Adjust your browser window Right 4. Hilbert's Tenth Problem Statement of the problem: 10. Determining the solvability of a Diophantine equation. Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could determine by a finite number of operations whether the equation is solvable in rational integers. (See the original statement in German at http://logic.pdmi.ras.ru/Hilbert10/stat/stat.html 4.1. History of the Problem. Story of the Solution Linear Diophantine equations Problems that can be solved by finding solutions of algebraic equations in the domain of integer numbers are known since the very beginning of mathematics. Some of these equations do not have solutions at all. For example, the equation 2x-2y=1 cannot have solutions in the domain of integer numbers since its left-hand side is always an even number. Some other equations have a finite set of solutions. For example, the equation 3x=6 has only one solution x=2. And finally, some equations have an infinite set of integer solutions. For example, let us solve the equation 7x-17y=1:

67. Hilbert hilbert s problems included the continuum hypothesis, the well ordering of the reals,Goldbach s conjecture, the transcendence of powers of algebraic numbers http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hilbert.html

David Hilbert Born: Died: Click the picture above to see eight larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index David Hilbert attended the gymnasium Lindemann for his doctorate which he received in 1885 for a thesis entitled One of Hilbert's friends there was Minkowski In 1884 Hurwitz In 1892 Schwarz Weierstrass 's chair and Klein Klein failed to persuade his colleagues and Heinrich Weber was appointed to the chair. Klein Fuchs Minkowski Hilbert's first work was on invariant theory and, in 1888, he proved his famous Basis Theorem. Twenty years earlier Gordan had proved the finite basis theorem for binary forms using a highly computational approach. Attempts to generalise Gordan 's work to systems with more than two variables failed since the computational difficulties were too great. Hilbert himself tried at first to follow Gordan 's approach but soon realised that a new line of attack was necessary. He discovered a completely new approach which proved the finite basis theorem for any number of variables but in an entirely abstract way. Although he proved that a finite basis existed his methods did not construct such a basis. Hilbert submitted a paper proving the finite basis theorem to Mathematische Annalen.

68. A. K. Peters, Ltd. -|- Book The Honors Class hilbert s problems and Their Solvers. Ben Yandell.This eminently readable book focuses on the people of mathematics http://www.akpeters.com/book.asp?BID=160

69. A Riemann - Hilbert Problem For An Energy Dependent Schrödinger Operator Inverse problems 12 (December 1996) 10031025. A Riemann - Hilbertproblem for an energy dependent Schrödinger operator. David H http://www.iop.org/EJ/abstract/0266-5611/12/6/014

@import url(http://ej.iop.org/style/nu/EJ.css); Electronic Journals quick guide Journals sitemap: IOP home page IOP online services EJs HOME JOURNAL HOME   - Editorial information   - Scope   - Editorial board   - Submit an article   - Pricing and ordering   - Request sample copy EJS EXTRA   - IOP Select   - IOP Physics Reviews   - BEC Matters! SEARCH   - Content finder   - Default searches AUTHORS   - Submit an article   - Status enquiry   - Get LaTeX class file   - Classification schemes   - Scope   - Editorial board REFEREES   - Submit referee report   - Become a referee   - Update personal details   - Classification schemes   - Scope   - Editorial board LIBRARIANS   - Register your institution   - Pricing and ordering   - Library branding   - How to link to IOP journals   - Librarian help USER OPTIONS   - Create account   - Lost password Login Create account Alerts Contact us ... Table of contents Inverse Problems (December 1996) 1003-1025 David H Sattinger and Jacek Szmigielski University of Minnesota, Minneapolis, Minnesota 55455, USA and the University of Saskatchewan, Saskatoon, Saskatchewan, Canada

70. [The Summaries Here Of Hilbert S Problems Are Necessarily Brief The summaries here of hilbert s problems are necessarily In 1900 hilbert gave 23problems before the 1990 International Congress of Mathematics at Paris. http://www.math.niu.edu/~rusin/known-math/95/hilb.list

[The summaries here of Hilbert's problems are necessarily brief and sometimes a bit wide of the mark; see some corrections below djr] ============================================================================== From: Aleph Software Consulting > for all x boundary conditions can be set ============================================================================== From: kevin2003@delphi.com (Kevin Brown) Newsgroups: sci.math Subject: Re: Hilbert's problems Date: 7 Jan 1995 20:49:19 GMT MV = M.J.Vasko MV> Here is a brief list of 22 of David Hilbert's 23 problems,... MV> The basic list was extracted from "The Harper Collins Dictionary MV> of Mathematics", ... MV> [1-20 deleted] MV> 21. Oddly enough, this problem is missing. If anyone can supply its MV> definition, please do. According to the "Encyclopedic Dictionary of Mathematics" (ed by Kiyosi Ito) the Hilbert's 21st problem was "To show that there always exists a linear differential equation of the Fuchsian class with given singular points and monodromic group. Solved by H. Rohrl and others (1957)." ============================================================================== Date: Mon, 07 Jun 1999 18:01:46 -0500 From: Tamara MIller

71. Encyclopedia4U - Hilbert's Problems - Encyclopedia Article hilbert s problems. This article is licensed under the GNU Free DocumentationLicense. It uses material from the Wikipedia article hilbert s problems . http://www.encyclopedia4u.com/h/hilbert-s-problems.html

ENCYCLOPEDIA U com Lists of articles by category ... Encyclopedia Home Page SEARCH : Hilbert's problems Hilbert's problems are a list of 23 problems in mathematics put forth by David Hilbert in the Paris conference of the International Congress of Mathematicians in 1900. The problems were all unsolved at the time, and several of them turned out to be very influential for twentieth-century mathematics. Hilbert's 23 problems are: Problem 1 solved The continuum hypothesis Problem 2 solved Are the axioms of arithmetic consistent? Problem 3 solved Can two tetrahedra be proved to have equal volume (under certain assumptions)? Problem 4 too vague Construct all metrics where lines are geodesics Problem 5 solved Are continuous groups automatically differential groups Problem 6 open Axiomatize all of physics Problem 7 partially solved Is a b transcendental , for algebraic a irrational b Problem 8 open The Riemann hypothesis and Goldbach's conjecture Problem 9 solved Find most general law of reciprocity in any algebraic number field Problem 10 solved Determination of the solvability of a diophantine equation Problem 11 solved Quadratic forms with algebraic numerical coefficients Problem 12 solved Algebraic number field extensions Problem 13 solved Solve all 7-th degree equations using functions of two arguments Problem 14 solved Proof of the finiteness of certain complete systems of functions Problem 15 solved Rigorous foundation of Schubert's enumerative calculus Problem 16 open Topology of algebraic curves and surfaces Problem 17 solved Expression of definite rational function as quotient of sums of squares

72. Hilbert's Tenth Problem: A History Of Mathematical Discovery hilbert (1862 1943). In our Museum we will not analyze in detail all 23 hilbert sproblems. The 10th of these 23 hilbert s problems was the following 10. http://www.goldenmuseum.com/1612Hilbert_engl.html

Hilbert's Tenth Problem: a History of Mathematical Discovery (Diophantus, Fermat, Hilbert, Julia Robinson, Nikolay Vorob'ev, Yuri Matiyasevich) About Hilbert's address and his 23 mathematical problems In the summer of 1900 mathematicians met on the Second International Congress in Paris. David Hilbert (1862-1943), the famous German mathematician, Professor of the Goettingen University, was invited to deliver one of the main lectures. As the greatest World mathematician he became famous by his works in algebra and number theory, and shortly before the Congress resolutely, he has rebuilt an axiomatics of the Euclidean geometry in the fundamental work "Foundations of Geometry" (1899). After long doubts Hilbert chose an unusual form of the lecture. In the speech "Mathematical Problems" he decided to formulate those mathematical problems, which, in his opinion, should determine development of mathematics in the upcoming century. Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics. In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century. Some are broad, such as the axiomatization of physics (problem 6) and might never be considered completed. Others, such as problem 3, were much more specific and solved quickly. Some were resolved contrary to Hilbert's expectations, as the continuum hypothesis (problem 1).

73. Hiro345: Hilbert's Problems Cactus ». 2003?11?29?. hilbert s problems. hilbert s problems.. Posted http://www.sssg.org/blog/koyama/archives/000635.html

Hilbert's Problems Hilbert's Problems The income from AdSense serves as an activity fund of SSS(G). URL: Yes No Comment: Search SSS(G) www.sssg.org SSS(G) mail SSS(G) BBS SSS(G) Wiki ... 惠報処理学会Webサービス

74. BletchleyPark.net took place at the International Congress of Mathematicians in Paris in 1900,when mathematician David hilbert addressed several mathematical problems. http://www.bletchleypark.net/computation/hilberts.html

Hilbert's Problem. Introduction Before the 20 th century the concept of an algorithm was vague. The spark that began the journey into precisely defining algorithms took place at the International Congress of Mathematicians in Paris in 1900, when mathematician David Hilbert addressed several mathematical problems. The tenth mathematical problem consisted of coming up with a process or algorithm for determining whether or not an integral root can be found for any polynomial, i.e. integer value(s) for its variable(s) such that the polynomial evaluates to zero. Unfortunately, currently no algorithm can solve this problem. Thirty-six years after the fact, Alonzo Church and Alan Turing made the connection from the informal notion of an algorithm to a precise definition, called the Church-Turing Thesis . By 1970, Yuri Matijasevic finally demonstrated that no algorithm exists for computing integral roots of a polynomial. The Tenth Problem. We want to know if R is decidable. Of course, we know that the answer is no. However, we can show that R is Turing recognizable. Let R A Turing Machine TM will successively evaluate p with values 0, 1, -1, 2, -2, ..., etc. Then when polynomial p = 0, TM accepts. If there is no acceptance then TM will run indefinitely. Although, TM can actually decide R

75. Read This: The Honors Class Read This! The MAA Online book review column. The Honors Class hilbert s Problemsand their Solvers by Benjamin H. Yandell. Reviewed by Herbert E. Kasube. http://www.maa.org/reviews/honorsclass.html

Search MAA Online MAA Home Read This! The MAA Online book review column The Honors Class: Hilbert's Problems and their Solvers by Benjamin H. Yandell Reviewed by Herbert E. Kasube At the dawn of the twentieth century, David Hilbert challenged the mathematicians of the world with twenty-three problems. These problems encompassed a wide breadth of mathematics and stimulated mathematicians for decades to come. Yandell's book is a (relatively) leisurely stroll through the people and the mathematics associated with these problems. I say "relatively" here because while a deep mathematical background is not necessary to enjoy this book, some mathematical sophistication will add to the reader's appreciation. We can find other descriptions of Hilbert's 1900 lecture and subsequent paper that listed these problems. For example, the two volumes entitled Mathematical developments arising from Hilbert problems ] contains papers from a 1974 symposium sponsored by the American Mathematical Society. This presents the mathematics behind the problems quite thoroughly, but it is not meant to be casual reading. Jeremy Gray's recent text The Hilbert Challenge ] would also be a nice companion to this volume. To learn more about Davis Hilbert himself, the best reference is Contance Reid's classic biography entitled simply

76. Off The Kuff: Hilbert Problem Solved? In 1900, the great mathematician David hilbert listed 23 outstanding problemsin mathematics and challenged his colleagues to solve them. http://www.offthekuff.com/mt/archives/002665.html

Off the Kuff Knowledge Is Good Contact me: kuff - at - offthekuff.com Main November 26, 2003 Hilbert problem solved? In 1900, the great mathematician David Hilbert listed 23 outstanding problems in mathematics and challenged his colleagues to solve them. Three of those problems remain unsolved today, but according to this report , one of them may have been conquered. Elin Oxenhielm, a 22-year-old mathematics student at Stockholm University, may have solved part of one of the science's great problems. Next week an article will be published revealing her solution for part of Hilbert's 16th problem, Swedish news agency TT reports. The set of 23 problems was put forward by Prussian mathematician David Hilbert in 1900 as challenges for the 20th century. Three remain unsolved, numbers 6,8 and 16. Oxenhielm's solution pertains to a special version of the second part of problem 16, the 'boundary cycles for polynomial differential equations'. The mathematical journal Nonlinear Analysis, published by Elsevier, has examined and endorsed Oxenhielm's solution and will publish it in their next issue. Oxenhielm believes her method can be used to unlock the mystery of the entire 16th problem, newspaper Expressen reports.

77. VIVOS VOCO: Äàâèä Ãèëüáåðò, "Ìàòåìàòè÷åñêèå ïðîáà D. hilbert, Gesammelte Abhandlungen ? dieuberzeugung, dass ein jedes bestimmte mathematische Problem einer strengen http://vivovoco.nns.ru/VV/PAPERS/NATURE/GILBERT_R.HTM

íà II Ìåæäóíàðîäíîì Êîíãðåññå ìàòåìàòèêîâ Ñáîðíèê, ïðåäëàãàåìûé âíèìàíèþ ÷èòàòåëÿ, ñîäåðæèò âïåðâûå ïåðåâåäåííûé íà ðóññêèé ÿçûê òåêñò èçâåñòíîãî äîêëàäà èëüáåðòà "Ìàòåìàòè÷åñêèå ïðîáëåìû", ïðîèçíåñåííîãî íà II Ìåæäóíàðîäíîì Êîíãðåññå ìàòåìàòèêîâ, ïðîõîäèâøåì â Ïàðèæå ñ 6 ïî 12 àâãóñòà 1900 ã. îí è ïðåäëîæèë ìàòåìàòèêàì â ñâîåì äîêëàäå. Ñ òåõ ïîð ïðîøëî óæå äâå òðåòè âåêà. Ïðîáëåìû èëüáåðòà â òå÷åíèå âñåãî ýòîãî ñðîêà íå òåðÿëè àêòóàëüíîñòè, ê èõ ðåøåíèþ áûëè ïðèëîæåíû óñèëèÿ òàëàíòëèâåéøèõ ìàòåìàòèêîâ. Ðàçâèòèå èäåé, ñâÿçàííûõ ñ ñîäåðæàíèåì óêàçàííûõ ïðîáëåì, ñîñòàâèëî çíà÷èòåëüíóþ ÷àñòü ìàòåìàòèêè XX â. Ïåðåâîä îñíîâíîé ÷àñòè äîêëàäà (èñêëþ÷àÿ òåêñò 15-é è 23-é ïðîáëåì è çàêëþ÷åíèÿ) îñóùåñòâëåí Ì. . Øåñòîïàë ñ òåêñòà, ïîìåùåííîãî â Gottinger Nachrichten (1900, 253-297), è ïðîñìîòðåí È. Í. Áðîíøòåéíîì è È. Ì. ßãëîìîì, êîòîðûå âíåñëè â íåãî ðÿä ðåäàêöèîííûõ ïîïðàâîê è èçìåíåíèé. Òåêñò 15-é è 23-é ïðîáëåì, à òàêæå çàêëþ÷èòåëüíîé ÷àñòè äîêëàäà ïåðåâåäåí À. Â. Äîðîôååâîé.  ïåðåâîä âíåñåíû äîïîëíåíèÿ, ñäåëàííûå èëüáåðòîì äëÿ èçäàíèÿ äîêëàäà, ïîìåùåííîãî â òðåòüåì òîìå åãî Ñîáðàíèÿ ñî÷èíåíèé (Gesammelte Abhandlungen, Berlin, Springer, 1932-1935), - â òåêñòå îíè çàêëþ÷åíû â êâàäðàòíûå ñêîáêè. Ïåðåâîä áûë ñâåðåí ñ àíãëèéñêèì ïåðåâîäîì (Bull. Amer. Math. Soc. 8, ¹ 10 (1902), 403-479), òàêæå ñ ïåðåâîäîì, îñóùåñòâëåííûì â êàáèíåòå èñòîðèè ìàòåìàòèêè è ìåõàíèêè ÌÓ À. Â. Äîðîôååâîé è Ì. Â. ×èðèêîâûì *. Èçâåñòíóþ òðóäíîñòü ñîñòàâëÿë ïåðåâîä íåêîòîðûõ ñòàðûõ ìàòåìàòè÷åñêèõ òåðìèíîâ.  íåêîòîðûõ ñëó÷àÿõ ðÿäîì ñ ïåðåâîäîì â êðóãëûõ ñêîáêàõ ïîìåùåí íåìåöêèé òåðìèí, à â îäíîì ñëó÷àå òåðìèí (Polarenprocess) îñòàâëåí áåç ïåðåâîäà. Ïåðåâîä÷èêè íåìàëî ïîòðóäèëèñü íàä òåì, ÷òîáû äîíåñòè äî ðóññêîãî ÷èòàòåëÿ ñâîåîáðàçíûé, ìåñòàìè äàæå ïàòåòè÷åñêèé ÿçûê ãèëüáåðòîâñêîãî äîêëàäà. Àâòîðû êîììåíòàðèåâ ê ïðîáëåìàì ëþáåçíî ñîãëàñèëèñü ïðîñìîòðåòü ïåðåâîäû ñîîòâåòñòâóþùèõ ïðîáëåì è âíåñëè ðÿä ñóùåñòâåííûõ èñïðàâëåíèé.

78. About "On The Riemann-Hilbert-Problem" On the Riemannhilbert-Problem. http://mathforum.org/library/view/16378.html

On the Riemann-Hilbert-Problem Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.gang.umass.edu/~kilian/mathesis/mathesis.html Author: Martin Kilian Description: A thesis, first investigating the relation between the factorisation of scalar functions and the theory of singular integral equations as far as they are relevant to boundary value problems for holomorphic functions, then exploring the formula of Sokhotski-Plemelj; the Riemann-problem; Factorisation of matrix valued functions; Diagonalisation; Spectral theory of polynomial matrices; Rational matrices; The partial indices; The Matrix-Riemann-problem; Linear differential equations; and The Dressing method. With a bibliography. Levels: College Research Languages: English Math Topics: Several Complex Vars./Analytic Spaces Differential Equations Home The Math Library ... Contact Us http://mathforum.org/

79. Seminar: 16th HILBERT PROBLEM AND RELATED QUESTIONS 16th hilbert PROBLEM AND RELATED QUESTIONS. Abstract. The current state of researchregarding the second part of hilbert s 16th problem will be discussed. http://www.mat.dtu.dk/events/uk?id=25

80. Hilbert's Problems - Wikipedia, The Free Encyclopedia PDF Eigenfunctions and Eigenvalues for a Scalar Riemann–hilbert http://en.wikipedia.org/wiki/Hilbert's_problems

Hilbert's problems From Wikipedia, the free encyclopedia. Hilbert's problems are a list of 23 problems in mathematics put forth by David Hilbert in the Paris conference of the International Congress of Mathematicians in 1900. The problems were all unsolved at the time, and several of them turned out to be very influential for twentieth-century mathematics. Hilbert's 23 problems are: Problem 1 solved The continuum hypothesis Problem 2 solved Are the axioms of arithmetic consistent Problem 3 solved Can two tetrahedra be proved to have equal volume (under certain assumptions)? Problem 4 too vague Construct all metrics where lines are geodesics Problem 5 solved Are continuous groups automatically differential groups Problem 6 non-mathematical Axiomatize all of physics Problem 7 solved Is a b transcendental , for algebraic a irrational algebraic b Problem 8 open The Riemann hypothesis and Goldbach's conjecture Problem 9 solved Find most general law of reciprocity in any algebraic number field Problem 10 solved Determination of the solvability of a diophantine equation Problem 11 solved Quadratic forms with algebraic numerical coefficients Problem 12 solved Algebraic number field extensions Problem 13 solved Solve all 7-th degree equations using functions of two arguments Problem 14 solved Proof of the finiteness of certain complete systems of functions Problem 15 solved Rigorous foundation of Schubert's enumerative calculus Problem 16 open Topology of algebraic curves and surfaces Problem 17 solved Expression of definite rational function as quotient of sums of squares

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