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Asclepiadaceae by T. MeyerValerianaceae by E. 0. Borsini

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12 SCIENCE-ADVERTISEMENTS VoL. 102, No. 2648

SCIENCE -VOL. 102 FRIDAY, SEPTEMBER 28, 1945 No. 2648

On the Problem of Applied Mathematics: DR. JAMES PASCHKIS, DR. A. CANTAROW, A. E. RAKOFF andH. TAYLOR ....... ...................... ............. 315 E. K. TILLSON. Temperatures in Some DeepWells

in Pennsylvania and West Virginia: PROFESSORObituary: KARL VER STEEG. The Meigen 1800 Names Again:

Florence Bascom: PROFESSOR IDA H. OGILvIE. Re- DR. ALAN STONE. Re-employment of Biologists NowcentDeaths ................................................. in the Army Air Forces: DR. W.

Scientific Events: Scientific Books:Public Lands Containing Radioactive Minerals; Culture Growth: DR. WARREN S. THOMPSON.The Coordinating Committee of the United Na- Cult embrowth:D R R S. THOPO.tions Standards; Placemnent of Veterans by the Chemical Embryology: PROFESSOR ALBERT TYLER.ti'Stnars Plceen of Veean byth Radio: DR. S. REID WARREN, JR. Books Received 336National Roster of Scientific and Specialized Per- Rsonne News from Abroad .. 321

' ~~Science News....14Scientific Notes and News .... 324

Special Articles:Role of Unsaturated Fatty Acids in Changes of ScIENcE: A Weekly Journal, since 1900 the officialAdipose and Dental Tissues in Vitamin E Defi- organ of the American Association for the Advancementciency: DR. HENRIK DAM and DR. HUMBERTO of Science. Published by the American Association forGRANADOS. Arterial Anastomosis in Dogs Employ- the Advancement of Science every Friday at Lancaster,ing Vein Grafts from Chickens and Turkeys: DR. Pennsylvania.ALFRED LEWIN COPLEY and PAUL L. STEFKO. TheEffect of Penicillin in Experimental Rabbit Syph- Editors: JOSEPHINE OWEN CATLL and JAQURSilis: THE LATE PROFESSOR GEORGE W. RAIZISS. CATTELL.Non-toxicity of DDT on Cells in Cultures: DR. Policy Committee: MALCOLM H. SOULE, RooM AnAxaWARREN H. LEWIS and DR. A. GLENN RICHARDS, and WALTER R. MILES.J..32 A................ dverti~sing Mfanager: THEO. J. CHRISTENSEN.

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ON THE PROBLEM OF APPLIED MATHEMATICSBy Dr. JAMES H. TAYLOR

THE GEORGE WASHINGTON UNIVERSITY

ALMOST anything is tremendously complicated.Frazier set out to write a monograph on a certaincult of ancient Greece and ended up with his famouswork of twelve volumes entitled "The Golden Bough."Consider a simple hobby like stamp collecting. Oneis soon involved in a maze of pertinent details suchas kinds of paper, methods of printing, types ofperforations, colors and shades which even the Bureauof Standards might find difficult or impossible todetermine, and finally watermarks, overprints, sur-

charges and forgeries.In comparison with any other well-recognized body

of knowledge, mathematics must be relatively simple.Consider for instance a given mathematics, that is,a branch of mathematics like Euclidean geometry or

projective geometry or real variable. You perhaps

know how any one of these subjects may be set up.After two thousand years of experience the "natural"way appears to be as follows. One lists a set ofundefined elements and relations, and a set of un-

proved propositions involving them; and from theseall other propositions or theorems are to be obtainedby the methods of formal, deductive logic. The un-

proved propositions which are imposed are calledaxioms, postulates or assumptions. For example, inprojective or in Euclidean geometry "point" and"line" are undefined elements; the relation "on" is an

undefined relation. One of the axioms reads as

follows: If A and B are distinct points there is atleast one line on both A and B.

It is important to appreciate that a mathematicsseems to be completely determined once the postu-