61. Blind Conjectures And Informated Refutations Blind conjectures and Informated Refutations. There is no other method thanone which proceeds by conjectures and refutations (as proved by Popper http://www.geocities.com/Athens/5235/node5.html

Next: Genetic Learning Systems Up: Evolutionary Epistemology Previous: Implicit and Explicit Knowledge Blind Conjectures and Informated Refutations The structure of an organism is therefore a kind of knowledge, represented by forms and machineries instead of linguistic expressions. Adapting such machineries and forms to the environment is therefore a kind of learning, as it is observed by Michalski in [ ``[According to Mc Carthy] learning is 'constructing or modifying representations of what is being experienced'. The representation of knowledge may be in the form of symbolic descriptions, algorithms or general formal theories. If one stretches the concept of representation to include physical and physiological imprints, occurring in the nervous system when one is acquiring a skill, the above view of learning seems to cover skill acquisition''. And evolution is certainly a matter of skill improvement. But the observation that organisms embody knowledge about their environment is not the only assumption of Evolutionary Epistemology. The key-point found by Popper is that this knowledge grows up exactly in the same way as the one contained in scientific theories. And that both forms of knowledge share the nature of not-verifiable but only refutable conjectures. Even the logical starting-point of their formation (use of regularities in the data for predicting the behaviour of environment) is the same. In [ ] a clear formulation of such analogy is given by Popper: Scientific knowledge contained in the theories is - as a matter of fact - obtained in the same way. There is no other method than one which proceeds by conjectures and refutations (as proved by Popper himself in [

62. Moonshine Workshop Home Page A Workshop on the Moonshine conjectures and Vertex Algebras. ICMS, Edinburgh; 414 July 2004. http://www.ma.hw.ac.uk/icms/meetings/2004/moonshine/

Moonshine - the First Quarter Century and Beyond. A Workshop on the Moonshine Conjectures and Vertex Algebras 5 to 13 July 2004, Edinburgh Scientific Programme and Participants Workshop Arrangements Workshop Home Page Registration Form Scientific Organising Committee: A. Baker (Glasgow) A. A. Ivanov (Imperial College) J. Lepowsky (Rutgers) J. McKay (Concordia) V. Nikulin (Liverpool) M. Tuite (Galway) Moonshine and related topics have been active research areas since the late 1970s. The aim of this Workshop is to review the impact of this research area on mathematics and theoretical physics and to highlight possible new directions. The lectures will start early in the morning of Monday 5 July and finish in the afternoon of Tuesday 13 July. The first part of the meeting will be expository, including such areas as Borcherds's proof of the Conway-Norton conjecture, Construction of the Monster, Vertex (operator) algebras, Modular Moonshine, BKM algebras and automorphic forms, FLM's constuction and proof of the McKay-Thompson conjecture. Saturday 10 July is Spitalfields Day , a day of talks open to everyone, to be held in the William Robertson Building in George Square. The second part of the meeting will consist of invited talks on current research.

63. Related Conjectures Related conjectures. Related conjectures. A related conjecture from Euler.Noam Elkies gave a counterexample, namely . Subsequently, Roger Frye found http://db.uwaterloo.ca/~alopez-o/math-faq/node25.html

Next: Did Fermat prove this Up: Fermat's Last Theorem Previous: What is the current Related Conjectures A related conjecture from Euler Noam Elkies gave a counterexample, namely . Subsequently, Roger Frye found the absolutely smallest solution by (more or less) brute force: it is . "Several years", Math. Comp. 51 (1988) 825-835. This synopsis is quite brief. A full survey would run too many pages. References Irregular Primes to One Million. Math. Comp., 59 (October 1992) pp. 717-722. Fermat's Last Theorem, A Genetic Introduction to Algebraic Number Theory. H.M. Edwards. Springer Verlag, New York, 1977. Thirteen Lectures on Fermat's Last Theorem. P. Ribenboim. Springer Verlag, New York, 1979. Number Theory Related to Fermat's Last Theorem. Neal Koblitz, editor. Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

64. University Of Pittsburgh: Thomas C. Hales University of Pittsburgh. Kepler conjecture (announced a computeraided proof), other space tiling conjectures, Langlands theory. http://www.math.pitt.edu/~thales/

Thomas C. Hales PhD, Princeton University Mellon Professor Representation theory, motivic integration, discrete geometry, honeycombs and foams. Thackeray 416 hales@pitt.edu I suppose you are two fathoms deep in mathematics, and if you are, then God help you, for so am I, only with this difference, I stick fast in the mud at the bottom and there I shall remain. -Charles Darwin Don't use manual procedures -Andrew Hunt and David Thomas and ... don't rely on social processes for verification -David Dill Math 2810 syllabus Errata to Hulek's EAG homework (Sep 13) License This web site is part of the creative commons Research A list of publications The Kepler Conjecture 2002 code update 2003 update ... 2004 update (What is the densest arrangement of spheres in space?) The Dodecahedral Conjecture (2003 update) The Flyspeck Project (Become involved in the Formal Proof of the Kepler Conjecture.) Flyspeck Blog Flyspeck Google Group Jordan Curve Theorem (tar of the formal proof) The honeycomb conjecture (What is the most economical way to partition the plane into equal areas?) Langlands theory and the Fundamental Lemma Links Google search on the Kepler Conjecture Google search on the Honeycomb Conjecture Google search on Flyspeck Mathematics Home ... Top of Page

65. Perfect Graphs conjectures and open problems, maintained at the AIM. http://www.aimath.org/WWN/perfectgraph/

Perfect Graphs This web page highlights some of the conjectures and open problems concerning Perfect Graphs. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Recognition of Perfect Graphs Polynomial Recognition Algorithm Found Interaction Between Skew-Partitions and 2-joins The Perfect-Graph Robust Algorithm Problem ... A Possible New Problem Skew-Partitions Extending a Skew -Partition Graphs Without Skew-Partitions Graphs Without Star Cutsets Finding Skew-Partitions in Berge Graphs ... beta-perfect graphs Partitionable Graphs Perfect, Partitionable, and Kernel-Solvable Graphs Partitionable graphs and odd holes A Property of Partitionable Graphs Small Transversals in Partitionable Graphs ... The Imperfection Ratio Integer Programming Partitionable Graphs as Cutting Planes for Packing Problems? Feasibility/Membership Problem For the Theta Body Balanced Graphs Balanced circulants ... P4-structure and Its Relatives The individual contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.

66. Hellenic News Of America The conjectures is a collection of 39 bilingual poems (Greek and English). In the “ conjectures” an effort is made to express the author’s inner http://www.hellenicnews.com/readnews.html?newsid=3729&lang=US

67. L-functions And Random Matrix Theory conjectures and open problems concerning Lfunctions, focussing on the areas in which there has been recent progress using results from Random Matrix Theory. Maintained at AIM. http://www.aimath.org/WWN/lrmt/

L-functions and Random Matrix Theory This web page highlights some of the conjectures and open problems concerning L-functions and Random Matrix Theory. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Distribution of zeros of L-functions The GUE hypothesis Correlations of zeros Neighbor spacing ... Statistics of the zeros of the derivative of xi Relationship between symplectic and odd orthogonal The Alternative Hypothesis p-adic L-functions Zeros and primes The distribution of primes ... Fractional moments Mollified mean values Mollifying a Family Long Mollifiers Moments of S(T) The integral of exp(i lambda S(t)) ... GOE and Graphs The individual contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.

68. Winds Of Change.NET: 3 Touchstones, 3 Conjectures Belmont Club s 3 conjectures includes scenarios of intraIslamic wars. These 3 conjectures and related articles about the War on Terror s big picture http://www.windsofchange.net/archives/005478.php

Main September 08, 2004 3 Touchstones, 3 Conjectures by Joe Katzman at September 8, 2004 03:36 AM Some essays are so good that they become touchstones for discussion throughout the blogosphere. Steven Den Beste's straightforward, point form explanation of the Global War on Terror's strategy, aims and rationale is one. American Digest's " The First Terrorist War " clearly explains of the stakes we face - avoiding the Islamic War by winning the Terrorist War - and much else besides (Hat Tip: reader John Simutis for finding it again); this ties nicely into... Wretchard's famous and chilling " 3 Conjectures Conjecture 1: Terrorism has lowered the nuclear threshold Conjecture 2: Attaining WMD s will destroy Islam Conjecture 3: The War on Terror is the 'Golden Hour' the final chance Belmont Club also has an important postscript that sums it all up so very well: "And once the WMD manufacturing process were commoditized and grasped by terrorists, all control over WMD manufacture and use would be lost to governments, even the one that gave it to the terrorist organization in the first place. The Three Conjectures further argued that this kind of power, once set loose, would consume Islam itself. Either the terrorist weapons would provoke a catastrophic response against the Muslim world or they would be used in the internecine struggles of the Islam, making the huge bomb detonated outside the Najaf mosque seem like a firecracker by comparison. The appearance of an Islamic WMD capability would hang like a comet of doom over the whole Muslim world.

69. On The 3x + 1 Problem These pages supply numerical data and propose some conjectures on this innocent looking problem. All numbers up to 29,300 * 10^12 ( ~ 26 * 2^50 ) have been checked for convergence. http://personal.computrain.nl/eric/wondrous/

70. Geometry_Class_Notes.html use knowledge of geometry to make conjectures; distinguish interesting from noninteresting conjectures by asking questions such as Has the conjecture been http://www.math.byu.edu/~lfrancis/readings302/Geometry_Class_Notes.html

Geometry Investigations and Conjectures Table of Contents Why should we teach Geometry using an investigations and conjecturing approach? Quote Patterns of Instruction Some Commonly Accepted Myths About a Conjecturing Approach Questions Teachers Typically Ask Inquiry Skills and Understanding Students Should Develop Why should we teach Geometry using an investigations and conjecturing approach? Quote: "There is something odd about the way we teach mathematics in our schools. We teach it as if we expect that our students will never have occasion to make new mathematics. We do not each language that way. If we did, students would never be required to write an original piece of prose or poetry. We would simply require them to recognize and appreciate the great pieces of language of the past, the literary equivalents of the Pythagorean Theorem and the Law of Cosines." - J. Schwartz and M. Yerushalmy Table of Contents Patterns of Instruction: The use of technology in instruction should further alter both the teaching and the learning of mathematics. Computer software can be used effectively for class demonstrations and independently by students to explore additional examples, perform independent investigations, generate and summarize data as part of a project, or complete assignments. Calculators and computers with appropriate software transform the mathematics classroom into a laboratory much like the environment in many science classes, where students use technology to investigate, conjecture, and verify their findings. In this setting, the teacher encourage experimentation and provides opportunities for students to summarize ideas and establish connections with previously studied topics.

71. The Real Paul Jones » Potter Conjectures Potter conjectures. Filed under. General Amusements literature One Responseto “Potter conjectures”. J Says July 23rd, 2005 at 648 pm http://www.ibiblio.org/pjones/wordpress/?p=650

72. [math/0409509] Prove Or Disprove. 100 Conjectures From The OEIS Presented here are over one hundred conjectures ranging from easy to difficult,from many mathematical fields. I also summarize briefly methods and tools http://arxiv.org/abs/math.CO/0409509/

Mathematics, abstract math.CO/0409509 From: Ralf Stephan [ view email ] Date ( ): Mon, 27 Sep 2004 08:44:30 GMT (11kb) Date (revised ): Mon, 11 Oct 2004 17:13:45 GMT (11kb) Date (revised ): Thu, 14 Oct 2004 17:39:11 GMT (11kb) Date (revised v4): Sat, 27 Nov 2004 15:26:55 GMT (12kb) Prove or Disprove. 100 Conjectures from the OEIS Authors: Ralf Stephan Comments: 12 pages, last corrections Subj-class: Combinatorics; Number Theory MSC-class: Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

73. The Evolution Of Consistent Conjectures Downloadable ! Author(s) Dixon, Huw D. Somma, Ernesto. 2003 Abstract Noabstract is available for this item. http://ideas.repec.org/a/eee/jeborg/v51y2003i4p523-536.html

This file is part of IDEAS , which uses RePEc data Papers Articles Software Books ... Help! The evolution of consistent conjectures Author info Abstract Publisher info Download info ... Statistics Author Info Dixon, Huw D. Somma, Ernesto Additional information is available for the following registered author(s): Huw David Dixon Abstract No abstract is available for this item. Download Info To download: If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help file . Note that these files are not on the IDEAS site. Please be patient as the files may be large. File URL: http://www.sciencedirect.com/science/article/B6V8F-4817D9R-1/2/fe683b1607d3925380e3e9d54823b733 File Format: File Function: Download Restriction: Full text for ScienceDirect subscribers only As the access to this document is restricted, you may want to search for a different version of it: Publisher Info Article provided by Elsevier in its journal Volume (Year): Issue (Month): Pages: Download reference.

74. Evolutionary Stability Of Constant Consistent Conjectures Downloadable ! Author(s) Alex Possajennikov. 2004 Abstract The paper shows thatthere is a close connection between (constant) consistent conjectures in a http://ideas.repec.org/p/wpa/wuwpga/0405009.html

This file is part of IDEAS , which uses RePEc data Papers Articles Software Books ... Help! Evolutionary Stability of Constant Consistent Conjectures Author info Abstract Publisher info Download info ... Statistics Author Info Alex Possajennikov (University of Nottingham) Additional information is available for the following registered author(s): Alex Possajennikov Abstract The paper shows that there is a close connection between (constant) consistent conjectures in a given game and evolutionary stability of conjectures. Evolutionarily stable conjectures are consistent and consistent conjectures are the only interior candidates for evolutionary stability. Download Info To download: If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help file . Note that these files are not on the IDEAS site. Please be patient as the files may be large. File URL: http://econwpa.wustl.edu:80/eps/game/papers/0405/0405009.pdf File Format: application/pdf File Function: Download Restriction: no Publisher Info Paper provided by Economics Working Paper Archive at WUSTL in its series Game Theory and Information with number 0405009.

75. The Sympathetic Vibration » Conjectures Of A Guilty Bystander Posted at 644 pm in conjectures of a guilty bystander . I was thinking thismorning that somebody needs to invent this. Looks like someone already has. http://www.withinwithout.org/category/conjectures-of-a-guilty-bystander/

the sympathetic vibration it's calming my suspicion... with soothing intuition. your train is at my station. Friday, September 9, 2005 Shrinky dink me. Posted at 8:27 am in conjectures of a guilty bystander Every bone in my body wishes that I could just stay in bed today. Like ALL day. National Geographic Article about the hurricane threat to New Orleans Written and published in October 2004 But the next day the storm gathered steam and drew a bead on the city. As the whirling maelstrom approached the coast, more than a million people evacuated to higher ground. Some 200,000 remained, however—the car-less, the homeless, the aged and infirm, and those die-hard New Orleanians who look for any excuse to throw a party. The storm hit Breton Sound with the fury of a nuclear warhead, pushing a deadly storm surge into Lake Pontchartrain. The water crept to the top of the massive berm that holds back the lake and then spilled over. Nearly 80 percent of New Orleans lies below sea level—more than eight feet below in places—so the water poured in. A liquid brown wall washed over the brick ranch homes of Gentilly, over the clapboard houses of the Ninth Ward, over the white-columned porches of the Garden District, until it raced through the bars and strip joints on Bourbon Street like the pale rider of the Apocalypse. As it reached 25 feet (eight meters) over parts of the city, people climbed onto roofs to escape it. Thousands drowned in the murky brew that was soon contaminated by sewage and industrial waste. Thousands more who survived the flood later perished from dehydration and disease as they waited to be rescued. It took two months to pump the city dry, and by then the Big Easy was buried under a blanket of putrid sediment, a million people were homeless, and 50,000 were dead. It was the worst natural disaster in the history of the United States.

76. Making Mathematics: Mathematics Research Teacher Handbook conjectures are unproven claims. Once someone proves a conjecture, As a classactivity, present theorems and conjectures and ask students to first list http://www2.edc.org/makingmath/handbook/Teacher/Conjectures/Conjectures.asp

Home Support for Teachers EXAMPLES, PATTERNS, AND CONJECTURES theorem You can introduce the ideas and activities discussed below as the need for them arises during student investigations. If a student uses a particular technique, highlight that approach for the class. Once a conjecture is posed, ask the class what they need to do to understand it and begin to develop an outline that all can use. Regular opportunities for practice with the different skills (organizing data, writing conjectures, etc.) will lead to greater student sophistication over time. GENERATING AND ORGANIZING EXAMPLES Generating Examples In order to get a better view of the "big" picture of a problem, we try to produce examples in a systematic fashion. We often have to choose examples from an infinite domain. These examples should be representative, in ways that we deem significant, of all of the elements of the domain. For example, a problem involving real numbers might involve positive, negative, whole, rational, and irrational examples. Numbers that are less than one or of great magnitude might also be important. In addition to this broad sampling, we also want to generate examples in a patterned way so that relationships between variables stand out (see Organizing Data below).

77. Learning To Give - Lesson Plan - Cooperative Conjectures Using technology, students will work in a cooperative team to explore the effectsof industrialization on wildlife. http://www.learningtogive.org/lessons/unit147/lesson3.html

var my_width = document.body.clientWidth; var my_column_width = ((my_width-693)/2); document.write (""); var my_width = document.body.clientWidth; var my_column_width = ((my_width-693)/2); document.write (""); Other States LTG -Indiana LTG -Michigan ... Sharing Our World > Cooperative Conjectures Unit Contents Sharing Our World 1. Exploring the Neighborhood - Literature Jigsaw 2. Habitats Past and Present 3. Cooperative Conjectures 4. Stop, Look and Listen 5. Lights, Camera, Action! 6. Splish! Splash! Birdbath Other Versions Printer Friendly Teacher Resources Lesson Plans Bibliographies Briefing Papers Nonprofit Career Information ... LTG See more in our Resource Room Sharing Our World LESSON 3: Cooperative Conjectures View Attachments/Handouts for this Lesson. GRADES: 3-5 Subjects: English Language Arts Philanthropy Science and Social Studies Lesson Duration: Four to Seven Fifty-Minute Class Periods Key Words/Concepts: ELA: Analyze/Interpret; Communicate; Expository Text; Reflection PHIL: Community; Cooperate; Stewardship SCI: Analyze; Data Collection/Organization; Observation; Questioning

78. Integermania - Theorems And Conjectures Warning False conjectures could be bumped off this page by true See Exquitenessof Sets for conjectures about different Intergermania problems. http://staff.jccc.net/swilson/integermania/theorems.htm

Integermania! - Theorems and Conjectures Theorems and conjectures about Integermania can be submitted to Steve Wilson for posting on this page. Warning: False conjectures could be bumped off this page by true conjectures! Definition 1: The exquisiteness of a solution to a Integermania problem is the highest level operation used in its construction, as given by the table of levels of exquisiteness , but the table is not repeated here. Definition 2: The exquisiteness of a set of numbers A at level L is the largest positive integer n L having the property that for every positive integer less than or equal to n L there exists a solution to the Integermania problem using set A with exquisiteness level less than L +1. Notationally, we can write: Exq A L n L , or Exq A n n n L See Exquiteness of Sets for conjectures about different Intergermania problems. Theorem 1: In an Integermania problem with n values and k available binary operations, where each value is used exactly once, and values are combined by using only the available binary operations, there are at most positive integers which can be created. See

79. PhilSci Archive - Practical Certainty And Cosmological Conjectures Practical Certainty and Cosmological conjectures. Maxwell, Nicholas (2005)Practical Certainty and Cosmological conjectures. http://philsci-archive.pitt.edu/archive/00002259/

About Browse Search Register ... Help Practical Certainty and Cosmological Conjectures Maxwell, Nicholas (2005) Practical Certainty and Cosmological Conjectures. Full text available as: Microsoft Word - Requires a viewer, such as Microsoft Word Viewer Abstract Keywords: Certainty, knowledge, induction, scepticism, perception, common sense, conjecture, physics, scientific method, corroboration, confirmation, simplicity, unification, Popper, physicalism, metaphysics, cosmology. Subjects: General Issues Confirmation/Induction General Issues Theory Change ... Theory/Observation ID Code: Deposited By: Maxwell, Nicholas Deposited On: 14 April 2005 Send feedback to: philsci-archive@library.pitt.edu

80. Weil Conjectures -- Facts, Info, And Encyclopedia Article Weil himself, it is said, never seriously tried to prove the conjectures. The conjectures of Weil have therefore taken their place within the general http://www.absoluteastronomy.com/encyclopedia/w/we/weil_conjectures.htm

Weil conjectures [Categories: Homological algebra, Number theory, Algebraic geometry, History of mathematics, Theorems, Conjectures, Theorems, Algebraic topology, Algebraic geometry] In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics , the Weil conjectures , which had become theorems by 1975, were some highly-influential proposals from the late 1940s by (United States mathematician (born in France) (1906-1998)) André Weil on the (Click link for more info and facts about generating function) generating function s (known as (Click link for more info and facts about local zeta-function) local zeta-function s) derived from counting the number of points on algebraic varieties over (Click link for more info and facts about finite field) finite field s. The main burden was that such zeta-functions should be (Click link for more info and facts about rational function) rational function s, should satisfy a form of (Click link for more info and facts about functional equation) functional equation , and should have their zeroes in restricted places. The last two parts were quite consciously modelled on the

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