Review of Graßmann, Robert, Theory of Number or Arithmetic in Strict Scientific Presentation by Strict Use of Formulas (1891)

The author of this book pursues the objective of treating the whole of pure mathematics [die ganze reine Mathematik] in four sections [Abtheilungen]. One half of the first of these sections is dedicated to arithmetic and is already available. The other half of the first section “A heuristic treatise on number [Zahlenlehre in freier Gedankenentwicklung]” which treats the same discipline is supposed to follow. The author may have opted for such an unusual separation [of the treatment of arithme..

Intuition and Reasoning in Geometry

The way in which geometrical knowledge has been obtained has always attracted the attention of philosophers. The fact that there is a science that concerns things outside our thinking and that proceeds inferentially appeared striking, and gave rise to specific theories of experience and space. Nonetheless, the geometrical method has not yet been sufficiently investigated. Philosophers who investigate the theory of knowledge discuss the question of whether geometry is an empirical science, but..

Adolph Mayer : Nekrolog / gesprochen in der öffentlichen Gesamtsitzung beider Klassen am 14. November 1908 von O. Hölder

Adolf Mayer wurde am 15. Februar 1839 zu Leipzig geboren. Er studierte zuerst in Heidelberg anfänglich Chemie, dann auch Mathematik und Mineralogie, danach in Göttingen, Leipzig, wieder in Heidelberg und in Königsberg. Mit einer Habilitationsschrift über Variationsrechnung erhielt er 1866 in Leipzig die Venia legendi. 1871 wurde er Extraordinarius, 1890 Ordinarius daselbst. Im Jahre 1900 setzte er wegen Krankheit vorübergehend aus, anfangs 1908 mußte er die ihm liebgewordene Tätigkeit ganz einstellen. Er suchte Heilung im Süden, starb aber schon am 11. April 1908 in Gries bei Bozen. Seine Arbeiten gehören den Gebieten der Differentialgleichungen, der Variationsrechnung und der Mechanik an. (Rezension von Felix Müller (1843-1928) im Jahrbuch über die Fortschritte der Mathematik, Band 39. 1908, S. 40

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Bieträge zur potentialtheorie ...

Inaug-diss.--Tübingen.Mode of access: Internet