Arthur Buchheim

Arthur Buchheim (1859-1888) was a British mathematician.

His father Carl Adolf Buchheim was professor of German language at King's College London. After attending the City of London School, Arthur Buchheim obtained an open scholarship at New College, Oxford, where he was the favorite student of Henry John Stephen Smith. He then studied at the University of Leipzig as a student of Felix Klein. Eventually, he became mathematical master at the Manchester Grammar School.[1][2][3]

Buchheim wrote several papers of which some deal with universal algebra. For instance, his work on William Kingdon Clifford's biquaternions and Hermann Grassmann's exterior algebra which he applied to screw theory and non-Euclidean geometry, was cited by Alfred North Whitehead (1898),[4] as well as in Klein's encyclopedia by Élie Cartan (1908)[5] and in more detail by Hermann Rothe (1916).[6] He was also concerned with the matrix theory of Arthur Cayley and James Joseph Sylvester.

Works (selection)
  • Buchheim, A. (1883). "On the theory of screws in elliptic space". Proceedings of the London Mathematical Society. s1-15 (1): 83–98. doi:10.1112/plms/s1-15.1.83.
  • Buchheim, A. (1884). "On the Theory of Matrics". Proceedings of the London Mathematical Society. s1-16 (1): 63–82. doi:10.1112/plms/s1-16.1.63.
  • Buchheim, A. (1885). "A memoir on biquaternions". American Journal of Mathematics. 7 (4): 293–326. doi:10.2307/2369176. JSTOR 2369176.
gollark: ?tag bismuth1
gollark: ?tag blub
gollark: ?tag create blub Graham considers a hypothetical Blub programmer. When the programmer looks down the "power continuum", he considers the lower languages to be less powerful because they miss some feature that a Blub programmer is used to. But when he looks up, he fails to realise that he is looking up: he merely sees "weird languages" with unnecessary features and assumes they are equivalent in power, but with "other hairy stuff thrown in as well". When Graham considers the point of view of a programmer using a language higher than Blub, he describes that programmer as looking down on Blub and noting its "missing" features from the point of view of the higher language.
gollark: ?tag blub Graham considers a hypothetical Blub programmer. When the programmer looks down the "power continuum", he considers the lower languages to be less powerful because they miss some feature that a Blub programmer is used to. But when he looks up, he fails to realise that he is looking up: he merely sees "weird languages" with unnecessary features and assumes they are equivalent in power, but with "other hairy stuff thrown in as well". When Graham considers the point of view of a programmer using a language higher than Blub, he describes that programmer as looking down on Blub and noting its "missing" features from the point of view of the higher language.
gollark: > As long as our hypothetical Blub programmer is looking down the power continuum, he knows he's looking down. Languages less powerful than Blub are obviously less powerful, because they're missing some feature he's used to. But when our hypothetical Blub programmer looks in the other direction, up the power continuum, he doesn't realize he's looking up. What he sees are merely weird languages. He probably considers them about equivalent in power to Blub, but with all this other hairy stuff thrown in as well. Blub is good enough for him, because he thinks in Blub.

References
  1. Sylvester, J. J. (1888). "The Late Arthur Buchheim". Nature. 38 (987): 515–516. doi:10.1038/038515d0.
  2. Tattersall, J. (2006). "Arthur Buchheim: Mathematician of Great Promise". Proc. Can. Soc. Hist. And Phil. Math. 18: 200–207.
  3. Nicholas Higham: Arthur Buchheim
  4. Whitehead, A. (1898). A Treatise on Universal Algebra. Cambridge University Press. pp. 370.
  5. Cartan, É.; Study, E. (1908). "Nombres complexes". Encyclopédie des Sciences Mathématiques Pures et Appliquées. 1 (1): 328–468.
  6. Rothe, H. (1916). "Systeme geometrischer Analyse". Encyclopädie der Mathematischen Wissenschaften. 3.1.1: 1282–1425.
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