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The article focuses on the science of history and the works of Buckle and Draper. It mentions that Buckle employed the Inductive method in his effort to discover the Principle governing the character and destiny of nations in which he made a collection of historical and scientific facts. It adds that mathematics has ranked as the only exact Science in the history of science.

The article presents several mathematical questions.

The article presents information on the book "Mathematical Recreations, and Problems of Past and Present Times," by W.W. Rouse Ball. Ball whose sketch of the history of mathematics has been noticed in these columns, now selects a subject in which a flumsy treatment is excusable and almost expected, and as his book is decidedly entertaining, perhaps no fault ought to he found with it. On page 33 he gives an amusing example of a fallacy in geometry. The reasoning is of precisely the same nature as that of Euclid.

The article presents information on various publications. The Smithsonian Institution has undertaken to receive pledges of subscription for the International Catalogue of Scientific Literature resolved on at a conference held last June in London. This catalogue is to begin with the new century, will contain both an author and a subject index and will comprise of subjects like mathematics, mechanics, physics, chemistry, astronomy and meteorology among other things. Early in October, Little, Brown & Co., Boston, will issue a "Study of James Martineau," by W.A. Jackson. Doubleday, Page & Co.'s fall announcements include "The Harriman Expedition to Alaska," illustrated, "Through the First Antarctic Night," by Frederick A. Cook.

This article discusses several books on scientific literature and presents developments in the field of science, as of August 29, 1907. The seventh annual meeting of the International Zoological Congress, held at the Harvard Medical School in August 1907, emphasized the new features, which have come to characterize zoology-physiology and mathematics. Professor H.F. Osborn of Columbia University delivered an address on "Evolution as it Appears to the Paleontologist," in which he enunciated some general laws of great significance. The book "Practical Health," L.E. Whipple, principle of the American School of Metaphysics, seeks to simplify the application of doctrines presented for some years past in several editions of his widely read book "Mental Health."

The fourth International Congress of Mathematicians opened on April 6 in the University of Rome in Rome, Italy, as Senator P. Blaserna, president of the Accademia dei Lincei, the scientific society at whose invitation this congress met at Rome, presided. After the opening exercises, the congress met at the headquarters of the Accademia dei Lincei in the Corsini Palace and chose Blaserna as president. The programme was divided into four sections, namely, arithmetic algebra and analysis; geometry; mechanics; physical mathematics; and Geodesy, with a subsection of applied mathematics; philosophical, historical and didactic subjects.

Presents letters to the editor referencing articles and topics discussed in previous issues. Discussion on writings of English poet and dramatist William Shakespeare; Account of the authority of religious leaders in Turkey and Persia; Demand for teachers of advanced mathematics in the U.S.

Presents letters to the editor on various literary topics. Description of the influence of poet Alighieri Dante on American writers; Comments of readers on some literary paradox in English literature; Limitations of mathematical calculations.

The article focuses on the book "Researchers on the Evolution of the Stellar Systems," vol. 2,"The Capture Theory of Cosmical Evolution," by T.J.J. See. See's work is devoted to the amplest exemplification of what he has called the capture theory of the cosmogony with large part mathematical and highly technical. The theory replace every vestige of the Laplacian nebular hypotheses by one which postulates the gradual formation of stars, suns, planets, satellites by capture of the materials composing them from a resisting medium that in the early history of the universe filled all space.

The annual general meeting of the American Philosophical Society, the oldest scientific society in America, was held this year in Philadelphia, Pennsylvania, from April 22 to April 24. The meeting was opened on Thursday afternoon by the President, Dr. W.W. Keen, who, with Vice-Presidents A.A. Michelson, W.B. Scott and C.L. Doolittle, presided over the various sessions. The session on Thursday afternoon was devoted to mathematics and physics. Prof. A.A. Michelson, of Chicago, described the recent progress made by him in the ruling of diffraction gratings.

This article highlights the importance of the use of universal metric system. When the same signs and symbols express to all the same weights and measurements, this will mean a distinct advance along the road leading to international peace and good feeling. The adhesion to the metric standard should be encouraged when it is considered that as early as May 20, 1790, Thomas Jefferson, as Secretary of State, formulated a decimal system of weights and measures, and embodied the scheme in a report. Therefore, in adopting the metric system, the world would be realizing one of the brilliant ideas of the most original thinker among the founders of the republic.

This article highlights the importance of the metric system in export trade. The subject of weights and measures is of such a vast and far-reaching importance that it does the warp and woof of commercial and industrial life. Since the outbreak of World War I, everybody heard repeated insistence that there is a need to adopt the metric system to succeed in the cultivation of foreign markets. Readers must accept the idea that to succeed in export trade, there is no choice except the use of metric system.

This article critically appraises two books "Le Livre cie I'Aveugle," by G. Pérouze and "La Bibliothéque des Aveugles," by Anidré Dreux. The first of these, "Le Livre de l'Aveugle," deals with the evolution of the blind man's book, from the first attempt of Valentin flatly to the latest product of the Braille press or stereotyping machine. It is a succinct and clear little manual, packed with information. It shows the Braille alphabet, to the inexperienced a mere cryptogram of little dots, but really so simple that a blind child of average intelligence can master it in a few hours. This alphabet, moreover, serves not only for all languages living and dead, hut for musical notation and the expression of mathematical formula.

The article presents information on the Irish mathematician William Rowan Hamilton, who invented the quaternion analysis. Quaternion analysis is acknowledged perhaps the greatest of all discoveries in pure mathematics. Hamilton's life was characterized by great metaphysical as well as mathematical activity. While Hamilton was very fond of poetic composition, he was well aware that his productions did not merit consideration as works of art. They were but the natural expression of an imaginative nature in moments of deep emotion, and played an important role in Hamilton's intellectual development and culture.

The article discusses the correct way of using charts by knowing the value of various averages to form the right reference for comparison and judgment. It states that charts offer tangible facts or figures to base decisions, correct basis of comparison, and total comprehensiveness of the problem. It also offers information on how to make and read charts including the squares, scale of measurement, and items to be measured.

The article presents the author's comments on the theory of relativity given by scientist Albert Einstein. He says that Einstein wrapped up theory in mathematical technicalities such that it is almost impossible for non-mathematicians to make out its import from the accounts of specialists, while popular accounts usually suggest ideas that are not wholly correct. For this, the word relativity is partly to blame. People often imagine that the new theory proves everything to be relative, whereas, on the contrary, it is wholly concerned to exclude what is relative and arrive at a statement of physical laws that shall in no way depend upon the circumstances of the observer.

This article focuses on the book "On the Contented Life," by Edgar A. Singer. This is not an easy book to read. Its title does something less than justice to the serious substance and, the disciplined and subtle manner of mind revealed in its pages. This book is free, on the whole, from technical terms, and consists of scattered essays, but each of these is dialectically closely knit, Professor Singer professes a preference for mathematical language, and though there, is unmistakable ardor in these pages, it is the heat of banked fires.

The article discusses the problems faced by rural teachers in the U.S. Many young people who prepare for teaching go out to one-room schools. Some of these are good rural schools, many of them equal, if not superior, to some city schools. But a far linger number are poor one-room schools or graded schools in small villages, with barren, dirty, unattractive classrooms. Today many of these poor schools stand empty, and the teachers who once taught them are gone. Rural teachers are tired of teaching under the conditions they have had to face in one-room schools. They must teach everything in grade arithmetic from beginning counting to using the theorem of Pythagoras; explain movements of the earth, tides, winds, and planers; interpret tariffs and constitutional procedures; teach children how to draw, paint, model; they must thaw out frozen pipes, shovel snow, keep innumerable records, direct plays, and participate in all community affairs. They did all these things and hundreds more for many years. They waded through snow drifts in getting to and from school. They have lived on farms with no modern conveniences and saw no one but pupils and their householders for weeks at a time. Their average monthly salary was $85.

The article features calculating prodigy Shakuntala Devi and describes her experience of giving worldwide demonstrations of her mathematical ability in 1952. Aside from her hometown India, Devi had the opportunity to demonstrate her skills in Europe and the U.S. She could extract sixth roots of numbers up to 10 digits. The view of the mathematicians on the ability of Shakuntala is cited.

There are members of the profession who say that they can wander around a studio or recording hall, head cocked and one ear stopped, and point to the exact spot where the microphone should be set up. Other engineers have developed complex mathematical formulas for this purpose. The truth is that there are many phases of sound engineering which, scientifically speaking, are about on a par with the use of a divining rod in oil prospecting. Opinions even differ on what "good' sound should sound like. This article will not deal with these broad problems, however but will be restricted to a discussion of certain electrical and mechanical problems attendant upon the reproduction of sound.

The article reports on the enhancement of computers, high-powered mathematics, operations research, and many other new tools in the U.S. It discusses the construction of a Data Processing Center by Sylvania Electric Products Inc. to tie in electronically 30 scattered plants to a central fact-gathering and analyzing room. It details the use of General Electric Co.'s Univac computer at its Louisville major appliance headquarters in Kentucky.

The article profiles several U.S. scientists, who, it says, prove why the country's scientific resources are basically promising and sound. It says that Luis Walter Alvarez has been dubbed the "prize wild-idea man," with some prized ideas include isolation of tritium, discovery of helium 3, and a nuclear reaction method without uranium or million-degree heat. Meanwhile, Richard Phillips Feynman won the 1954 Albert Einstein Award for his Feynman diagrams.

The article offers information on the findings of Opinion Research Corp., a private testing organization, regarding the ability of clerical workers of business concerns in solving a sum correctly.

Presents letters to the editor. Information on the performance of U.S. Air Force students in Mathematics; Opinion on an article of author Margaret Halsey about U.S. politician Richard M. Nixon.

The article focuses on the procedures in making hexaflexagons and tetraflexagon out of paper. Diverting six-sided paper structures that can be flexed to bring different surfaces into view is known as hexaflexagons. Tetraflexagon is a three-faced structure. It suggested that papers must be folded according to the number of sides it requires. Tetraflexagon can also be made with four or more faces. It has been stated that all folds of paper are made to conform with the way the lines were originally creased.

The article provides information about Origami, the Japanese art of folding objects made of paper. It is traditionally an art of folding realistic animals without cutting or decorating from a single of sheet of paper. Many mathematicians became fascinated with paper-folding, in view of its geometrical aspect. An interesting mathematical question is raised by the very act of folding a paper.

Presents several curriculum bulletins. Information about Michigan Department of Public Instruction's "Nuclear Science in the Classroom," bulletin; Detail of Pointe Public School System's "The Kindergarten Book: Information for Teachers," bulletin; Discussion of various approaches in Los Angeles City Schools' "Arithmetic in the Elementary Schools," publication.

The article focuses on the use of the discovery technique in teaching the principles of mathematics by Max Beberman, an Algebra teacher, at the University of Illinois in Illinois. Beberman's strategy is being promoted using his project known as the University of Illinois Committee in School Mathematics. The discovery technique is similar with the education philosophy of Jean Piaget, a Swiss educator.

The article presents several mathematical games related to ellipse. This game is tracing a perfect ellipse. One example is the two thumbtacks that stick in a sheet of paper, putting a loop of string around them and keep the string taut with the point of a pencil. Moving a pencil around the tacks will trace a perfect ellipse. Another method can be demonstrated with a circular cake pan and a cardboard disk having half the diameter of the pan.

The article offers information on the exhibition "A World of Numbers...and Beyond," organized by International Business Machines Corp. (IBM) held at the California Museum of Science and Industry in Los Angeles, California in the last week of March 1961. It informs that the exhibition aimed at showing various abstractions of mathematics and mentions about various exhibits at the event which include a Moebius Band by IBM executive Charles Eames, and a pintball machine-like Probability Board.

Presents information about the balanced progress, revolution in school mathematics. Erudition about three theories that have influenced the mathematics curriculum from time to time; Methods adopted by mathematics educators to teach the present content in the new mould; Theme of the entire 1962 issue of the journal "Educational Leadership;" Efforts put in by the journal to bring to the reader the perceptions of several professional educators.

The article describes an experimental program of mathematics for gifted children. The program started in a small way. It started during the school year 1955-56 when several parents and some teachers expressed a desire for offering gifted children work which would present an intellectual challenge beyond that of the regular classroom. The children were fifth and sixth graders from the elementary school on the campus of Illinois State University in Normal, Illinois. Three subject matter areas were represented: social studies, science, and mathematics. Reason for selection of these areas was none other than willingness and availability on the part of the instructors. Selection for the special group was proposed first by classroom teachers. Their judgment was supported by the results of tests, by achievement records, and by consideration of attitudes. The original plan had been to use only fifth and sixth grade children. Choice of topics is continually being modified as the impact of "modern" mathematics is being felt in the regular classroom. Gifted children can be led to extend their mathematical horizons beyond those ordinarily reached through use of graded text material. The work with gifted children came into being in a small, faltering way, and "felt" its way along. It is now in its seventh year and, even though the program appears to be on a firm basis, changes are continually being made.

The article explores how public support is achieved for modern programs in mathematics in Hawaii. Hawaii has the ninth largest school system in the nation. The fact that Hawaii is geographically isolated from continental United States has its disadvantages certainly, but there are also some psychological advantages. High transportation costs make attendance at mainland conferences, seminars, institutes and other professional meetings difficult. Teacher interest is the focal point in winning public support for modern programs in mathematics. When schools are planning new programs, the matter of articulation from the elementary school to the intermediate school, from the intermediate school to the high school must be worked out. The Honolulu Advertiser and the Honolulu Star Bulletin, both daily papers, have manifested an interest in the schools. The Head of the Mathematics Department at one of the intermediate school sponsored a mathematics fair which she introduced to the parents through a letter. Modern programs in mathematics have won public support in Hawaii through interested teachers, cooperative administrators, informed parents, enthusiastic students, and an enlightened public.

The article offers information on the Marienbad match game in the U.S. It mentions that the game is a variation of one of the most ancient of all two-person mathematical divertissements, and it uses move combinations based on binary numbers. It notes that Harvard mathematician Charles Leonard Bouton called the game Nim, in which the successful player has to memorize the numbers.

The author provides an economic outlook for the second half of 1962. He notes that 85 billion U.S. dollars were lost by 17 million investors due to market decline. The author believes that the market decline will have a significant effect on consumer and corporate spending, adding that one of the mathematically unmeasurable factors determining the economic health is the psychological one. He points out that the losses of many investors are still on paper but the psychological impact on their thinking and planning in terms of spending is real.

The article presents various mathematical board games. The Military Game is an example of a two-player game that combines extreme simplicity with extraordinary strategic subtlety. It was popular in French military circles during and after the Franco-Prussian War of 1870-1871. The topological board game Black is easily played as a pencil-and-paper game on a checkered field.

The article presents a simulation of the computer logic equations using Fortran arithmetic expressions. The simulation involved methods such as writing the equations for the logic for each side of the flip-flop which is an A-C coupled, set-reset device. The logic was implemented using the representative terms A, AN, ONA, and OFA, where A and AN represent the outputs of the flip-flop while ONA and OFA represent the set and reset impulses to A. A and AN are unaltered during an entire pass and at the end of the pass, a subroutine SET is called. A logical presentation of the simulation is presented.

The author comments regarding the method for performing Boolean OR, AND and NOT operations using arithmetic and conditional transfer operations presented by M. Morris Mano. He states that the operations are useful in many cases but they are seriously limited by the OR operation in many ways. He notes that in a Fortran program, not all Boolean functions that contain an OR operation can be placed in the parenthesis of an IF statement. He also reveals that because of the number of necessary conditional transfers, a function which includes all three operations is more difficult to program.

A calendar of events for the Association for Computing Machinery (ACM) from August 1965 to November 1967 is presented. The ACM National Conference will be held in Cleveland, Ohio on August 24-26, 1965. The American Mathematical Society Annual Meeting will be held in Chicago, Illinois on January 24-28, 1966. The Spring Joint Computer Conference will be held in Philadelphia on May 9-11, 1967.

A method which finds simultaneously all the zeros of a polynomial, developed by H. Rutishauser, has been tested on a number of polynomials with real coefficients. This slowly converging method (the Quotient-Difference (Q-D) algorithm) provides starting values for a Newton or a Bairstow algorithm for more rapid convergence. Necessary and sufficient conditions for the existence of the Q-D scheme ore not completely known; however, failure may occur when zeros have equal, or nearly equal magnitudes. Success was achieved, in most of the cases tried, with the failures usually traceable to the equal magnitude difficulty. In some cases, computer roundoff may result in errors which spoil the scheme. Even if the Q-D algorithm does not give all the zeros, it will usually find a majority of them. [ABSTRACT FROM AUTHOR]

A large class of problems leading to digital computer processing can be formulated in terms of the numerical solution of systems of ordinary differential equations. Powerful methods are in existence for the solution of such systems. A good general purpose routine for the solution of such systems furnishes a powerful tool for processing many problems. This is true from the point of view of ease of programming, ease of debugging, and minimization of computer time. A number of examples are discussed in detail. [ABSTRACT FROM AUTHOR]

The article features Cleveland Brown quarterback Frank Beale Ryan. He is known for his knowledge about mathematics including geometric function theory in addition to his knowledge about football. According to Ryan, he never played any sport well as a child due to his lack of speed and coordination. His peer Gino Marchetti commends the improvement in performance and confidence of Ryan.