On the Study and Difficulties of Mathematics

From the EDITOR'S NOTE. No apology is needed for the publication of the present new edition of The Study and Difficulties of Mathematics, -a characteristic production of one of the most eminent and luminous of English mathematical writers of the present century. De Morgan, though taking higher rank as an original inquirer than either Huxley or Tyndall, was the peer and lineal precursor of these great expositors of science, and he applied to his lifelong task an historical equipment and a psychological insight which have not yet borne their full educational fruit. And nowhere have these distinguished qualities been displayed to greater advantage than in the present work, which was conceived and written with the full natural freedom, and with all the fire, of youthful genius. For the contents and purpose of the book the reader may be referred to the Author's Preface. The work still contains points (notable among them is its insistence on the study of logic), which are insufficiently emphasized, or slurred, by elementary treatises; while the freshness and naturalness of its point of view contrasts strongly with the mechanical character of the common text-books. Elementary instructors and students cannot fail to profit by the general loftiness of its tone and the sound tenor of its instructions. The original treatise, which was published by the Society for the Diffusion of Useful Knowledge and bears the date of 1831, is now practically inaccessible, and is marred by numerous errata and typographical solecisms, from which, it is hoped, the present edition is free. References to the remaining mathematical textbooks of the Society for the Diffusion of Useful Knowledge now out of print have either been omitted or supplemented by the mention of more modern works. The few notes which have been added are mainly bibliographical in character, and refer, for instance, to modern treatises on logic, algebra, the philosophy of mathematics, and pangeometry. For the portrait and autograph signature of De Morgan, which graces the page opposite the title, The Open Court Publishing Company is indebted to the courtesy of Principal David Eugene Smith, of the State Normal School at Brockport, N. Y. THOMAS J. MCCORMACK