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Topic: Automated Mathematician

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	The Automath Archive - About Automath Article
		Automatic theorem provers may occasionally do amazing things, but they have their limitations.
		For communication between mathematicians this idea is irrelevant: in a mathematical discussion between a believer and a non-believer none of the two notices their different backgrounds.
		But all mathematicians agree that the results of intuitive thinking have to be justified by rigorous reasoning, even though there may be different opinions about the level of formality.
	www.win.tue.nl /automath/aboutautomath-article.htm (6793 words)

	AI Magazine: Automated Deduction Looking Ahead. @ HighBeam Research (Site not responding. Last check: 2007-11-06)
		Automated deduction is concerned with the mechanization of the deductive process in the fullest meaning of the concept.
		Some of the goals of the automated deduction field, such as fully mechanizing the proof capability of a mathematician, are still distant, but others, such as verifying computer chip designs, are already doable in part.
		There are advantages to addressing the automatic generation of induction hypotheses (one of the most creative tasks in deductive mathematics) within the verification setting because verification tasks have certain forms that allows specialization of the induction hypothesis methods.
	highbeam.com /library/doc0.asp?DOCID=1G1:54367775&... (15080 words)

	Automated Mathematician -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		The Automated Mathematician is one of the earliest successful (Click link for more info and facts about discovery system) discovery systems developed.
		It was created by (Click link for more info and facts about Doug Lenat) Doug Lenat in (A flexible procedure-oriented programing language that manipulates symbols in the form of lists) Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award.
		This intuition was the basis of AM's successor (Click link for more info and facts about Eurisko) Eurisko, which attempted to generalize the search for mathematical concepts to the search for useful (A commonsense rule (or set of rules) intended to increase the probability of solving some problem) heuristics.
	www.absoluteastronomy.com /encyclopedia/a/au/automated_mathematician.htm (268 words)

	Goldbach's conjecture - Wikipedia, the free encyclopedia
		Doug Lenat's Automated Mathematician rediscovered Goldbach's Conjecture in 1982.
		This is considered one of the earliest demonstrations that artificial intelligences are capable of scientific discovery (but see the discussion at Automated Mathematician).
		Because it is easily understood by laymen, Goldbach's conjecture is a popular target for pseudomathematicians who attempt to prove it, sometimes even disprove it, using only high-school-level mathematics.
	www.wikipedia.org /wiki/Goldbachs_conjecture (1418 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		German astronomer and mathematician Johannes Kepler theorized in 1611 that the most efficient way to stack round things is by mounding them, pyramid shape, much like oranges and apples in the produce aisle.
		Mathematicians are curious people, people with a passion for certainty.
		Mathematicians like elegant answers, too, solutions that are innovative and insightful and practical, with applications beyond the ivory towers of academia.
	www.discover.pitt.edu /pittmag/fall2004/feature3.html (2031 words)

	DMG-FG2: projects
		The aim of this project is to provide tools for the automated generation of analytic calculi (with hypersequent and sequent of relations) for broad classes of logics.
		The interaction between mathematician and computer however depends on the ability of the system to analyze and comprehend proof segments provided by the mathematician.
		The automatization of this investigation will help the working mathematician to enrich his results by additional useful informations at low costs.
	www.dmg.tuwien.ac.at /fg2/index.php?id=40 (1923 words)

	O-ANTS -- An Agent Based Approach to Reasoning
		The approach is motivated by the discrepancy of the flexible problem solving behavior of human mathematicians on the one hand and the control determination of automated reasoning systems on the other hand.
		A recent trend in the automated reasoning community therefore is to integrate specialized external reasoning systems in a central theorem proving environment.
		As a consequence, for instance, proof subgoals that could be automatically solved by an integrated external reasoner within seconds may remain undetected simply because appropriate control knowledge is not available in the core system.
	www.ags.uni-sb.de /~omega/research/agentsTP (988 words)

	Countrybookshop.co.uk - Automated Theory Formation in Pure Mathematics
		The subject of this book, automated theory formation in mathematics, is such a large scale task.
		Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems.
		Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer.
	www.countrybookshop.co.uk /books/index.phtml?whatfor=1852336099 (309 words)

	Larry Wos (Site not responding. Last check: 2007-11-06)
		Larry Wos is a senior mathematician in the Mathematics and Computer Science Division at Argonne National Laboratory; he joined the laboratory in February 1957.
		He has written more than 70 articles on the automation of reasoning, lectured extensively on both topics, and indeed renamed the field of automated theorem proving to "automated reasoning" in recognition that it had grown to include far more than the consideration of proof finding.
		He was founding editor of the Journal of Automated Reasoning and has been president of the Association for Automated Reasoning since its formulation in 1982.
	www.cse.ogi.edu /tphols2000/wos.htm (238 words)

	Sense of Wonder \| Automated Mathematical Conjecture Making
		For example, profound statements may connect previously disjoint parts of mathematics but, for others, the importance of a statement is given by an agreement in the mathematical community to follow a concrete path of research.
		Arguably, the significance of a particular statement in mathematics is a combination of its historical importance; its abstractness and generality; its beauty and some psychological parameters that trigger the alarm in the brain of the mathematician, among others.
		And if computing power is a constraint, grid computing should provide a powerful platform in which mathematicians will be able to test their conjectures, and, why not, find new ones.
	www.cerezo.name /archives/000079.html (498 words)

	Learn more about Goldbach's conjecture in the online encyclopedia. (Site not responding. Last check: 2007-11-06)
		The majority of mathematicians believe the conjecture to be true, mostly based on statistical considerations focusing on the probabilistic distribution of prime numbers: the bigger the even number, the more "likely" it becomes that it can be written as a sum of two primes.
		In 1966, Chen Jing-run showed that every sufficiently large even number can be written as the sum of a prime and a number with at most two prime factors.
		In 1982 Doug Lenat's Automated Mathematician independently rediscovered Goldbach's Conjecture in one of the earliest demonstrations that Artificial Intelligences were capable of scientific discovery.
	www.onlineencyclopedia.org /g/go/goldbach_s_conjecture.html (477 words)

	Professor Alan Bundy - School of Informatics, University of Edinburgh - teaching project proposals
		To obtain automatic proofs of limit theorems from analysis using proof planning, especially rippling with critics.
		To generate new normal forms automatically, for a class of formulae, from a set of axioms and lemmas.
		To explore the application of automatic code generation techniques to the development of embedded systems in the automotive industry.
	homepages.inf.ed.ac.uk /bundy/teaching_projectProposals.html (1575 words)

	CURRICULUM VITAE (Site not responding. Last check: 2007-11-06)
		Automated Reasoning: Essays in Honor of Woody Bledsoe, R.S. Boyer ed., Kluwer Academic Publ., Dordrecht (1991).
		Purpose is to assess the status and research opportunities of the Automated Deduction field for the NSF.
		The state of automated deduction: a report on the Automatic Deduction Workshop 1977, Fifth Int'l.
	www.cs.duke.edu /~dwl/CV (1452 words)

	Graffiti & Automated Mathematical Conjecture-Making
		It was not until the mid-1980s though that a program produced statements of interest to research mathematicians and actually contributed to the advancement of mathematics.
		These two programs as well as other attempts to automate mathematical conjecture-making are surveyed---the success of a conjecture-making program, it is found, correlates strongly whether the program is designed to produce statements that are relevant to answering or advancing our mathematical questions.
		In the case of the second version all that is missing is automated concept formation.
	www.math.uh.edu /~clarson/graffiti.html (1131 words)

	Techniques for Algorithmic Composition of Music (Site not responding. Last check: 2007-11-06)
		However, it is the authors' opinion that the area of automated musical analysis that holds the most exciting potential, for providing quantified stylistic information which can be used in the generation of new works (for example, as a 'culture' in the system described below, in the section entitled 'Techniques for Evolving Computer Musicians').
		Thus, in the framework of genetic programming, what the system produces are simple programs which take a simple jazz melody as their input, and create another simple jazz melody as their output, which is sent to the fitness function to be evaluated.
		In many systems for automated generation of artworks (be it music, line drawings, or what-have-you), the cultural context is implicit in the rules programmed in to the computer.
	alum.hampshire.edu /~adaF92/algocomp/algocomp95.html (4748 words)

	Eurisko, The Computer With A Mind Of Its Own
		Exploring Traveller’s vast "search space," as mathematicians call it, require the ability to learn from experience, developing heuristics–rules of thumb–about which paths are most likely to yield reasonable solutions.
		His early doctoral work was in automatic programming–the attempt to design software that, given a simple description of a task to be computerized, will write an appropriate program.
		Meanwhile, research in automatic programming is providing insight into how an intelligent system–whether natural or artificial–can analyze a problem and solve it by devising a plan.
	www.aliciapatterson.org /APF0704/Johnson/Johnson.html (3192 words)

	Artificial Intelligence: Structures and Strategies for Complex Problem Solving
		In 1614, the Scots mathematician, John Napier, created logarithms, the mathematical transformations that allowed multiplication and the use of exponents to be reduced to addition and multiplication.
		Our preliminary discussion of the possibility of a theory of automated intelligence is in no way intended to overstate the progress made to date or minimize the work that lies ahead.
		Another reason for the continued interest in automatic theorem provers is the realization that such a system does not have to be capable of independently solving extremely complex problems without human assistance.
	www.cs.unm.edu /~luger/ai-final/chapter1.html (14570 words)

	An Overview of Automated Theorem Proving
		Automated Theorem Proving (ATP) deals with the development of computer programs that show that some statement (the conjecture) is a logical consequence of a set of statements (the axioms and hypotheses).
		Fujita, Slaney, and Bennett (the first two being ATP researchers, the last a mathematician) decided many quasi-group problems using a system built at ICOT in Japan.
		PVS is a verification system that has been used in various applications, including diagnosis and scheduling algorithms for fault tolerant architectures, and requirements specification for portions of the space shuttle flight control system.
	www.cs.miami.edu /~tptp/OverviewOfATP.html (1495 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		In 1976 he earned his Stanford doctorate with Automated Mathematician, or AM, a program designed to "discover" new mathematical theorems by building on an initial store of 78 basic concepts from set theory and 243 of Lenat's heuristic rules.
		AM was followed by Eurisko (the present tense of the Greek eureka, and root of the word heuristic), which improved on Automated Mathematician by adding the ability to discover not only new concepts but new heuristics.
		In corporate research departments and university programs alike, artificial-intelligence researchers are finding new ways to automate labor-saving devices, analyze information about our physical world or make sense of the vast reserves of information entombed in libraries and databases.
	condor.depaul.edu /~tmuscare/csc250/notes/aireboots.doc (2754 words)

	Learning of Search Heuristics for Theorem Proving
		An important aspect of an automated theorem prover with respect to its success is its control of its inference rules.
		One of the main differences between a mathematician and most of todays automated theorem provers is the amount of learned (control) knowledge a mathematician has and is able to make good use of.
		Naturally, the control knowledge a theorem prover needs and the use it makes of it is quite different from the mathematician's way, but learning from successful proofs is definitely a good way to improve the control of a prover.
	www.uni-kl.de /AG-AvenhausMadlener/lernen.html (360 words)

	Automated Mathematician - Encyclopedia, History, Geography and Biography
		Automated Mathematician - Encyclopedia, History, Geography and Biography
		This page was last modified 02:23, 13 Apr 2005.
		This encyclopedia, history, geography and biography article about Automated Mathematician contains research on
	www.arikah.net /encyclopedia/Automated_Mathematician (227 words)

	Argonne News 06/19/00
		The award is given by the Conference on Automated Deduction (CADE) Inc. to honor exceptional contributions to the field.
		McCune was cited for his outstanding success in answering the Robbins question, which had challenged mathematicians and logicians for six decades, and for his design of the powerful program Otter, which has become a benchmark for automated deduction programs.
		The award is named for French mathematician Jacques Herbrand (1908-1931) who developed an important theorem in mathematical logic with applications to theorem-proving by computer.
	www.anl.gov /Media_Center/Argonne_News/news00/an000619.html (1492 words)

	Robbins Algebras Are Boolean (Site not responding. Last check: 2007-11-06)
		A paper on this topic appears in the Journal of Automated Reasoning [W. McCune, "Solution of the Robbins Problem", JAR 19(3), 263--276 (1997)].
		This theorem was proved automatically by EQP, a theorem proving program developed at Argonne National Laboratory.
		In 1992 and 1996, respectively, the two Winker conditions were shown automatically to be sufficient (see the EQP preprint).
	www.mcs.anl.gov /home/mccune/ar/robbins (793 words)

	Chaitin, Meta Math! The Quest for Omega
		To speak metaphorically, it appears that God is a mathematician, and that the structure of the world---God's thoughts!---are mathematical, that this is the cloth out of which the world is woven, the wood out of which the world is built...
		Mathematicians don't like to talk about what they don't know, they like to talk about the questions that current technique, current mathematical technology, is capable of handling.
		Leibniz invented the calculus, published it, wrote letter after letter to continental mathematicians to explain it to them, initially received all the credit for this from his contemporaries, and then was astonished to learn that Newton, who had never published a word on the subject, claimed that Leibniz had stolen it all from him.
	ibiwan.com /omega.html (20804 words)

	Aura, Download Aura 3.0 Free (Site not responding. Last check: 2007-11-06)
		It combines the unique power of full automated multivariate statistical analysis in unlimited dimensions with the remarkable ease of use.
		Be you the experienced mathematician or just a novice in forecasting with immediate and very practical goals, Aura® is just for you.
		You can instantly import tremendous amounts of data both from the desktop applications and external databases, analyze them with one mouse click and store to disk with unique speed in native format as well as export results for the further use in many formats.
	www.soft-dir.com /aura-212094.html (256 words)

	Chronology of Artificial Intelligence (Site not responding. Last check: 2007-11-06)
		Brothers, Herbert L. Dreyfus, a philosopher, and Stuart E. Dreyfus, a mathematician, wrote a strongly anti-AI paper, "Alchemy and AI," which was published reluctantly by the RAND Corporation for whom Herbert was consulting.
		Earlier machine learning efforts aimed at enabling computers to automatically optimize appropriate weights for variables they had been told were important to solving a problem.
		Now efforts were directed to automatically deriving those variables themselves—in other words, automatic concept formation.
	crl.ucsd.edu /~elman/Courses/cog202/Papers/ai-history.html (4478 words)

	Useful QED Projects: Dahn
		The fruitful application of most current automated theorem provers requires solid knowledge of their specific logical calculi and methods of proof search.
		Input/Output-Tools for mathematicians It should be possible for mathematicians with little extra knowledge to use and extend QED libraries.
		QED libraries should be made available to the mathematician at his desktop and in libraries.
	www.cs.duke.edu /AutoDedFD/contributions/wkshop/dahn.html (967 words)

	AARNEWS - June 1998
		CADE is the major forum for the presentation of new research in all aspects of automated deduction.
		Thus, the vast combinatorial power of fully automatic theorem provers might be opened for nonexpert users through the interface of interactive specification and verification tools.
		FTP'98 is the second in a series of workshops intended to focus effort on first-order theorem proving as a core theme of automated deduction, and to provide a forum for presentation of very recent work and discussion of research in progress.
	www-unix.mcs.anl.gov /AAR/issuejune98/issuejune98.html (1741 words)

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