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Correlation of Mathematics and Science

Clarence E. Comstock

1905
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The Elementary School Teacher
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A foreword in regard to the point of view of this paper may be of service. I take it that any interplay between the school courses in different subjects to be of lasting value must spring from underlying relations which serve as essential links binding those subjects into one. This interplay must result in mutual helpfulness, or else it fails of its purpose. Science is not to be lugged into mathematics as an outsider, nor is mathematics to be foisted upon science as an added burden. If it can
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... burden. If it can be found that the one is indispensable to the other, then and only then can there be any reasonableness in the remarks offered in this paper. I trust that you will find the position of the speaker a thousand miles removed from that of the teacher in a grammar school of a decade or two ago, who, holding up a bird before her bright-eyed pupils, asked them to count its eyes, its legs, its toes, its wings, etc.; and then propounded these elucidating questions: "How many eyes and toes does the birdie have? If it had three more toes, how many would it have in all? If you multiply the number of its eyes by the number of its toes, what would the result be?" From the point of view of the scientist, mathematics is a tool of science; from the point of view of the mathematician, science is a field for the application of mathematical truth; from the viewpoint of both, mathematics is a method of science. In fact, it may be called the ultimate method of science; the more perfectly a science is developed, the more mathematical does it become, until it reaches a stage when it is classified as mathematics. Away in the past was it when the sciences of arithmetic and geometry assumed their mathematical names. In comparatively recent years mechanics has reached this same development, and is now classed as mathematics. The various branches of physical science, astronomy, meteorology, and chemistry are rapidly being subjugated by this method of exact investigation; while the biological, mental, and social sciences are still in a very unmathematical state of evolution. The method is of such power and value that it must itself be made the subject of investigation; its inner relations must be scrutinized, and the inevitability of its conclusions established on a firm basis. There has thus arisen the most wonderful and enthralling science of them all-that science which defies definition, for it transcends all limiting bounds; that science which rears unto itself in imagination a palace whose walls and turrets know not the limiting thraldom of time and space; the queen science of them all, abstract mathematics. If this view of the relation of mathematics and science in general be true, then it would seem that there should be a corresponding intimacy between the courses offered in schools and colleges for instruction in these subjects. Of course, there is and always has been a certain degree of interplay between such courses; but the query obtrudes itself: Cannot a more vital and effective relation be maintained? It is easy to see that the study of mathematics is absolutely essential to anything but a very superficial knowledge of the sciences. Physical laws of action, the laws of chemical action, and the laws of the formation of crystals are derived from observed data and verified by the methods of the higher mathematics. It is the very language of science. To read Shakespeare, one needs to know the meaning and the use of words. To read Hilton's Chrystallography, Preston's Theory of Light, or the works of the masters in chemistry, a very considerable acquaintance with mathematics is a prerequisite, if they are not to be sealed books. But it is not to the scientific man alone that mathematics is indispensable; the engineering profession, that vast army of workers in applied science, is equally in need of such knowledge. The minute differentiation of the engineering profession which has in very recent times resulted in the separation of the countless pursuits which require technical education, has opened an ever-This content downloaded from 080.082.

doi:10.1086/453521
fatcat:kvza6yqcerfr7jioeuz5zx3gtm