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# Topic: Hilberts program

###### In the News (Tue 23 Jul 19)

 Hilbert's Program (Stanford Encyclopedia of Philosophy) Hilbert never gave a general account of which operations and methods of proof are acceptable from the finitist standpoint, but only examples of operations and methods of inference in contentual finitary number theory which he accepted as finitary. Although Hilbert's first proposals focused exclusively on consistency, there is a noticeable development in Hilbert's thinking in the direction of a general reductivist project of a sort quite common in the philosophy of science at the time (as was pointed out by Giaquinto 1983). Hilbert's proof theoretic program can then be seen to be a search for a proof theoretic reduction of all of mathematics to finitary mathematics; in a relativized program one looks for reductions of theories weaker than all of classical mathematics to theories often stronger than finitary mathematics. plato.stanford.edu /entries/hilbert-program   (7524 words)

 David Hilbert - Wikipedia, the free encyclopedia Hilbert's basis theorem solved the principal problem in nineteenth century invariant theory by showing that any form of a given number of variables and of a given degree has a finite, yet complete system of independent rational integral invariants and covariants. Hilbert helped provide the basis for the theory of automata which was later built upon by computer scientist Alan Turing. In 1920 he proposed explicitly a research project (in metamathematics, as it was then termed) that became known as Hilbert's program. en.wikipedia.org /wiki/David_Hilbert   (873 words)

 Hilbert's Program Summary - Hilbert's Program Information Hilbert's program, as his initiative as come to be called, was a call to the mathematics community to formalize the basic tenets of the science. Hilbert viewed the new century with great optimism for the study of mathematics, feeling that the 23 unsolved problems demonstrated both the vitality of the field and the opportunity for growth and innovation within it. Hilbert further stated that many problems of mathematics were born of the intertwined relationship between pure reason and the reality of observation and intuition. www.bookrags.com /sciences/mathematics/hilberts-program-wom.html   (717 words)

 Wash U Graduate Program : Graduate Course Offerings Linear and quadratic programming, decision theory, dynamic programming, network analysis. Along with a course in numerical analysis, useful in preparing for the third examination of the Society of Actuaries. The unifying theme is that of finding Hilbert space analogs (quantum groups, operator modules, Lipschitz algebras, etc.) of classical constructions (topological groups, Banach bundles, metric spaces, etc). www.math.wustl.edu /academics/graduate/courses.html   (2228 words)

 From Frege To Godel: von Heijenoort   (Site not responding. Last check: 2007-10-25) Hilbert popularized his program to found mathematics on a logic which can be shown consistent by finitistic methods. Hilbert had already provided axioms for geometry and for the real numbers and shown that the consistency of geometry can be reduced to that of the real-number system. Hilbert and Bernays [1939] carried out the details of Godel's second incompleteness theorem for two number theory systems Z_mu and Z. Godel [1934] made precise the notion of general recursive functions as functions uniquely determined by equations among terms involving known (recursive) functions and the unknown function (following a suggestion by Herbrand). www.andrew.cmu.edu /user/cebrown/notes/vonHeijenoort.html   (8419 words)

 Boston.com / Business / Conseco barred from freezing ex-CEO assets Hilbert and more than 150 former Conseco executives, directors and key employees took loans in the late 1990s to buy Conseco stock in a company-sponsored program of a type now prohibited. Hilbert argues Conseco's shift to new board management and ownership during its Sept. 10 emergence from bankruptcy triggered a "change of control" clause shielding him from repayment obligations. Hilbert and others were unable to repay the loans when Conseco shares tumbled after reaching a high of \$58 in 1998. www.boston.com /business/articles/2003/11/12/conseco_barred_from_freezing_ex_ceo_assets?mode=PF   (586 words)

 Some observations about Hilbert   (Site not responding. Last check: 2007-10-25) Hilbert was invited to give a special address to the Second International Congress of Mathematicians at Paris in 1900. Hilbert was adamently opposed to the position of an earlier mathematician named Kronecker who had insisted that only constructive mathematics was appropriate. Hilbert granted that mathematics could be more rigorous, but insisted we could do this by using a formal axiomatic method. www.oswego.edu /~delancey/309_DIR/LLT_LECTURES/Hilbert.html   (1525 words)

 M. E. Szabo: The Collected Works of Gerhard Gentzen   (Site not responding. Last check: 2007-10-25) After developing and examining the 'natural calculus' Gentzen conjectured that proofs should have a "normal form" in which "all concepts required for the proof would in some sense appear in the conclusion of the proof." This is the subformula property. This necessitated a reconsideration of the notion of the consistency proofs called for by Hilbert's program in light of Godel's second incompleteness theorem. Hilbert agrees with Kant in the sense that the symbols used in mathematics are objects of "immediate experience." This corresponds to Hilberts finitist view of formalist mathematics (which Gentzen helped develop). www.andrew.cmu.edu /user/cebrown/notes/szabo.html   (3057 words)

 Understanding the Ideas of Gregory Chaitin: A Serious Problem with Reality   (Site not responding. Last check: 2007-10-25) According to Hilbert, a systematic search for meaningful statements in mathematics or well formed formulae and their proof in mathematics is a pursuit that is both possible and realistic. Thirty-one years after Hilbert’s speech in Paris Russell and Whitehead are found desperately working on the fourth volume of Principia Mathematica.   With a crash Hilbert’s program is wrecked by a stunting upset theorem developed by Kurt Gödel.  This result would shake the very foundations of mathematics. Hilbert’s program would require a result in the decision problem, information.  In other words, if you put the algorithm to the test and you ran through all the well formed formulae, a decision on a statement’s  provability necessarily results. www.mcorbeil.com /papers/chaitin_web.htm   (2514 words)

 Hilberts' moving sale is anything but ordinary The Hilberts are moving from the 23,000-square-foot Le Chateau Renaissance, sitting on 40 acres and appraised for \$25 million, to a 14,000-square-foot home in the Carmel gated community of Laurelwood. Stephen Hilbert offered to vacate the mansion to win a stay of a judge's ruling that would require him to pay \$72 million to Conseco, the insurance company he co-founded and led until 2000. Hilbert has argued that the debt was nullified for several reasons, including that the ownership of Conseco has changed and that the loan programs, which are now forbidden by law, were illegal. www2.indystar.com /articles/0/212702-1510-126.html   (762 words)

 Peek inside Hilbert home Hilbert gazes down upon his guests from a domed mural fantasy two floors up. In conceiving the brick-and-stone "Le Chateau Renaissance," Hilbert was inspired partly by a 1987 trip to Blenheim Palace in England. Hilbert has appealed the ruling and says he is confident he will win. www2.indystar.com /articles/6/221407-1056-126.html   (777 words)

 SF News - Sept. 24, 1998 - Working professionals earn master's on the job   (Site not responding. Last check: 2007-10-25) The Hilberts are among more than 200 graduates, all professionals working in a variety of fields in six regions of the province, who have earned MEds through the faculty of education's off-campus master of education program over the past five years. Her job is to help increase the number of women in trades programs, which have seen a rise from under three per cent to 11 per cent since she began. The program was created specifically to meet the needs of First Nations teachers and other professionals in the area. www.sfu.ca /mediapr/sfnews/1998/sept24/hilberts.html   (667 words)

 HCMC - Timeline He was a leader in the development of community mental health programs in Hennepin County, worked at the national level to develop nomenclature for psychiatric illnesses, and was a strong advocate for the medically indigent. The Bloodless Medicine and Surgery Program is established at HCMC for adult patients who wish to avoid blood transfusions for religious reasons or to avoid the risk of blood borne diseases. The program is the culmination of longtime efforts by former Emergency Medicine Chief Ernest Ruiz, who is selected to head the program during its expansion period. www.hcmc.org /medcenter/timeline.htm   (8955 words)

 Betsy Hilbert Tributes Betsy Hilbert was, for me, the essence of CEA: she balanced a cheerful and amiable disposition with real scholarly astuteness. Betsy Hilbert was an incomparable friend and valued colleague of mine for over twenty years. Betsy Hilbert was a writer, teacher, humanist, CEA stalwart, and dear friend to many of us. www.as.ysu.edu /~english/cea/hilbert_tributes.html   (1085 words)

 JANE DULANEY HILBERT COLLECTION   (Site not responding. Last check: 2007-10-25) Jane Hilbert is a charter member of the Tennessee chapter of the Ninety-Nines, Inc., the international organization for women pilots. The Jane Dulaney Hilbert Collection consists of photographic images which focus on aviation in the Tri-Cities, 1937-60; the 1958 visit to the Tri-Cities of Vice-President Richard M. Nixon; and the 1970 visit to the area by President Nixon. Hilbert, Louis: APA 1045, 1046, 1050; JDH 7, 12. cass.etsu.edu /ARCHIVES/AFINDAID/a112.html   (1090 words)

 Hilbert’s Problems (PRIME) Because of Hilbert’s prestige, these problems were tackled by mathematicians assiduously, and many of them solved. This “decidability” problem is kin to the larger problem pursued by the logicist program of decidability of theories in general. The particular case of Diophantine equations was finally dealt with in a direct way by Matijasevich in 1970, who showed that no such method exists. www.mathacademy.com /pr/prime/articles/hilbert_prob/index.asp   (627 words)

 Journal of TeeJay (2309) I just spent 45 minutes in gdb trying to figure out why my C++ program was repeatedly segfaulting, after adding breakpoints, stepping through, and adding lots of cout statements printing all the values I finally discovered that where I expected calls to the getCoordinateFromPoint(int point) method I was geting \$BIG_NEGATIVE_NUM rather than 1 to 4. Even using strict wouldn't have caught that, in C and C++ I must remember to initialise all values to 0 when declaring them unless I want to pass around random junk when I use the wrong variable, easier to trace that than segfaults. Anyway, just before getting off the train I managed to run a test program using the class and killed my machine twice in a row because the code went into a fast infinate loop. use.perl.org /~TeeJay/journal/19192   (383 words)

 Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks 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. The idea that problems like Hilbert's, maybe, have negative solutions could appear only in 1930s, when the notion of algorithm ("process, which could determine by a finite number of operations...") was formalized. Thus, in 1961 the unsolvability of (modified) Hilbert's 10th problem for exponential Diophantine equations was proved. www.ltn.lv /~podnieks/gt4.html   (4241 words)

 [No title] One of the major deficiencies of the CC-40 is that when a Solid State Cartridge program is operated from the keyboard the results are brought to the display in a form that does not permit additional calculations on the result without reentering the value. where the program completes the sum of the products in sequence and in essence throws away digits beyond the fourth digit to the right of the decimal point because of the larger magnitude of the first product. Thanks for your hard work to get and post those interesting results, but may I suggest once again that using Hilbert matrices for such tests is actually a less than good idea and the three matrices I offered would actually be much better suited to the task. www.hpmuseum.org /cgi-sys/cgiwrap/hpmuseum/archv015.cgi?read=74206   (2454 words)

 1899-1930: FROM HILBERT TO BROUWER (PHIL 296) D. Hilbert, ``On the foundations of logic and arithmetic,'' 1904. D. Hilbert, ``On the new grounding of mathematics,'' 1922. D. Hilbert, ``Problems of the grounding of mathematics,'' 1928, English translation in [PM]. www.msu.edu /user/aantonel/Hilb-Brou-Syl.html   (655 words)

 News - September 28/98 - Working grads earn graduate degrees 'at home'   (Site not responding. Last check: 2007-10-25) Steve and Carolyn Hilbert are both working professionals who've lived in the Cariboo - in a log cabin on 10 acres - for nearly 30 years. This year's graduates account for 10-per cent of the fall graduating class and represent the largest cohort to complete the highly successful program, which offers degrees in curriculum and instruction, and administrative leadership. For high school teacher and vice-principal Sally Thicke, completing the program in her own 'backyard' - the Sunshine Coast - provided a rare chance to upgrade her skills and continue her education without interfering with her job. www.sfu.ca /mediapr/Releases/News/1998/Convocation_Oct98/Working.html   (538 words)

 [No title] Set theoretic and constructivist foundations for analysis are described; Hilberts program is analyzed in detail. Topics may include: the emergence of Hilbert's program, and proof theoryÕs more general reductive goals; deductive systems, cut-elimination, and normalization; the ordinal analysis of arithmetic; functional interpretation and the extraction of computational information from proofs; and subsystems of second order arithmetic. For example, in the context of Hilbert's program, fragments of first and second-order arithmetic are investigated. www.contrib.andrew.cmu.edu /~kk3n/curriculum/logiccds.html   (1392 words)

 Historic Algebra Problems highly rated algebra help, highschool algebra test questions, hilberts basis theorem lecture notes, high school math tutor portland oregon, high school plato pathways algebra 2 changing grades, high school second year algebra, high school sophmore teacher edition textbooks, high school tutor in mission viejo, higher algebra problems techniques, Take a look at the demo and see how incredibly helpful this program is. Are you finally ready to finish your homework and be prepared for class? Now go take on your homework with this program at your side and you'll be out and about having fun before you know. www.algebra-answer.com /algebra-helper/historic-algebra-problems.html   (577 words)

 Re: Explicit versus implicit subtyping mechanisms Programming > Languages Misc > Re: Explicit ve... But I am suggesting this....I am suggesting that common sense tells us that Q is bigger that Z, but formalism tells us not. Common sense tells us Hilberts program is doable, formalism tell us not. www.talkaboutprogramming.com /group/comp.lang.misc/messages/46806.html   (2390 words)

 Rip Off Report:HILBERTS BODYWORKS auto repair ripoff fraud   (Site not responding. Last check: 2007-10-25) Has changed his name many times-Once with a serious employee injury moves the company to a family member and when it gets to the supreme court lies that he is just an employee poor and what not then sticks then x-employee is stuck, hurt and tons of medical bills. He has had his protectors and made his former friends his enemies who just could not face or dare to continue to be a part of his illegal activties-like wink,davis, freddie, anthony,ayer, kerry, george,ramriez, so-forth. Consumers this business owned by Milton Hilbert and his many names goes on TV to help the consumer to recoginze 20 ways mind you to detect fraud. www.ripoffreport.com /reports/ripoff4448.htm   (2143 words)

 [No title] His work in programming languages focuses primarily on the role of type structure in language design, and on the use of operational semantics as the basis for the definition and implementation of programming languages. Professor Reynolds is interested in the design of programming languages and languages for program specification, mathematical tools for defining the semantics of such languages, and methods for proving that programs satisfy their specifications. Prerequisites: 80-210 or 80-211 and a programming course www.cs.cmu.edu /afs/cs.cmu.edu/project/pal/www/brochure.html   (9950 words)

 Kurt Grelling Biography HILBERTs efforts to axiomatize mathematics were shaken, as were the entire foundations of mathematics, by the announcement in 1903 of Bertrand RUSSELLs antinomy or paradox. BORN was HILBERTs assistant when GRELLING arrived and later a professor of physics at Göttingen and much later (in 1954) a Nobel Laureate in Physics. Assisted by Paul BERNAYS, HILBERT revised the logical calculus of the Principia Mathematica (1910-1913) of Alfred North WHITEHEAD (1881-1947) and RUSSELL, and distinguished between mathematics proper and meta-mathematics (literally, about mathematics), the latter confined to finite means and concerned with proof theory (Beweistheorie). www.enabling.org /ia/gestalt/kgbio.html   (18087 words)

 Powell's Books - Cooking with Grease: Stirring the Pots in American Politics by Donna Brazile My mother did domestic work for the Hilberts, starting out at about fifty dollars a week and topping off near the end of twenty years of service at maybe one hundred dollars, without any Social Security or other benefits. Hilbert's children thought my momma was their momma because, in fact, she raised them. My mother signed up her three little girls to be part of the program and dropped us off, said hello to her old friends and caught the bus to Mrs. www.powells.com /biblio?show=0743253981&page=excerpt   (10073 words)

 [No title] When I looked at his program I concluded that it was a special purpose program which will calculate the determinant of a Hilbert matrix but has no obvious capability to calculate the determinant of a general matrix. The Hilbert matrix entries are floating-point, and the determinant is calculated with floating-point arithmetic. For a Hilbert matrix of order n, divide the determinant of this "integerized" matrix by the LCM of the denominators of the original Hilbert matrix, raised to the power n, and that will be the determinant of the original Hilbert matrix. www.hpmuseum.org /cgi-sys/cgiwrap/hpmuseum/archv015.cgi?read=72045   (6942 words)

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