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Inasmuch as the list of recent books for secondary schools published in the June number of the School Review' contained only one title in mathematics, it may be in order to call the attention of teachers of secondary mathematics to numerous other recent books of importance, and to include therewith also a selected list of older standard books, so as to make up a small working library which may fairly be considered necessary to have within the working radius of the teacher. The following list includes books on algebra, geometry, trigonometry, plane analytics, and elementary calculus as the minimum range within which the secondary teacher can afford to be limited. For the most part the high-school texts in common use are not mentioned, and to the list have been added some volumes of general importance and interest on the history and present development and tendencies of the teaching of mathematics.

(1926). Ninth Summer Meeting of the Association. The American Mathematical Monthly: Vol. 33, No. 1, pp. 1-7.

It may seem unwarranted to speak of romance in connection with a subject commonly supposed to be as dry and prosaic as mathematics. The dictionary defines a romance as a “fictitious and wonderful tale.” The tale which I am about to relate is indeed wonderful but it is not fictitious—it is true and it is the kind of truth that is stranger than fiction. It is the story of the birth and growth of the number concept in the human race—it is the story of the struggle of humanity to learn to count. We speak glibly of “thousands,” and “millions,” and “billions,” but we should not forget that these concepts are the cumulative heritage of many centuries. Even to-day there are backward tribes in some parts of the world who have no number words beyond “one,” “two,” or “three” and who designate all larger groups under the single word “many.”

Among the various characteristics which distinguish man from the lower animals, there are two which stand out in bold relief; namely, the language concept and the number concept. These will be made the basis of study and contrast in the present discussion. It will be found that these two concepts did not develop in the human mind with equal ease or with equal speed, and it will be of more than passing interest to examine some of the reasons for such great disparity and possibly to suggest and support an explanation which has not been dwelt upon by the historians. In a word we shall try to find out some of the reasons why mathematics lagged so far behind literature and art in the early centuries. The case for language is comparatively simple to state, though its interpretation and full understanding may often-times be obscure and difficult. The fact is that every nation or tribe of men, ancient or modern, pagan or civilized, has a language which may be crude or well developed but, at any rate, is adequate for their needs of intercommunication. Witness the North American Indian tribes among whom there were some sixty different language stocks; or the inhabitants of Asiatic India who are said to have developed more than one hundred dialects; or the great group of Indo-European languages of which there are eight main divisions and fifty or more subdivisions spread over a large part of Europe and of Asia. In complete bewilderment one exclaims: truly man is a language producing animal. As a leading example of language development of the highest type, let us look more closely into the case of the Greek language which is one of the eight main divisions of the Indo-European family. The first essential in the development of a written language is an adequate alphabet. Perhaps the earliest attempt at alphabetic structure is to be found in the hieratic writings of the Egyptian priests three to five thousand years ago, as for instance in the Ahmes Papyrus of about 1700 B.C. However, such writings were in the nature of a mystery to the common people and little used except by the priests. But it may be that these early attempts at alphabet making inspired the Phoenicians to strive for mastery along this line. At any rate, by the end of the ninth century B.C. they were in possession of a fairly complete alphabet which was in common use, and from this source the Greeks undoubtedly imported the first draft of their own alphabet. Then began a long period, perhaps two or three hundred years, during which the Greeks gradually modified and perfected their alphabet. For instance, the Phoenicians had too many consonants and not enough vowels, they had too many aspirates but no symbols for a number of sounds used by the Greeks. As a result of this long and careful development, the Greeks

The following preliminary draft of the proposed By-Laws contains a number of legal provisions required in case the Council decides to become incorporated in the State of illinois. The By-Laws could be considerably condensed if these were eliminated.

(1908). Joint Meeting of Mathematicians and Engineers. The American Mathematical Monthly: Vol. 15, No. 2, pp. 30-33.

If the average man in the street were asked to name the benefits derived from sunshine, he would probably say “light and warmth” and there he would stop. But, if we analyze the matter a little more deeply, we will soon realize that sunshine is the one great source of all forms of life and activity on I his old planet of ours. To mention only a few particulars, wood, peat, coke, soft coal, anthracite, kerosene, fuel oil, gas, gasoline, are one and all forms of canoed sunshine in varying degrees of transformation. Hence I cannot stoke my furnace, turn on my oil-burner, step on the gasoline jn my automobile, cook my meals by wood, gas, oil or coal, light my house with kerosene or gas, without drawing upon the sunshine which was stored up for me in the form of carbon long ages ago in the deep recesses of the earth. All the industries of the world, great and small, all transportation by rail, water or air, are made possible only through the products of sunshine. Even the wind which drives my sailboat is only the rushing currents of sun-heated air.

No recent educational movement is more remarkable, in certain ways, than the present deep and widespread interest in improving the teaching of mathematics, which is manifest in the large and constantly increasing number of associations throughout the country organized for this distinct purpose. The movement is remarkable for the spontaneity of its inception and for the rapidity of its growth. Fully a score of organizations of mathematics teachers date their origin since 1900, among the largest of which are: The Association of Mathematics Teachers of New England, the Association of Mathematics Teachers of the Middle States and Maryland, and the Central Association of Science and Mathematics Teachers of the Middle

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