Document (#35492)

Author
Basieux, P.
Title
¬Die Architektur der Mathematik : Denken in Strukturen
Imprint
Reinbek : Rowohlt Taschenbuch-Verlag
Year
2000
Pages
187 S
Abstract
Pierre Basieux, Unternehmensberater und gelemter Mathematiker, möchte sein Buch als krönende Zusammenfassung seiner drei Essays "Die Welt als Roulette" (1995), "Abenteuer Mathematik" (1999; siehe Spektrum der Wissenschaft 4/1999, S. 122) und "Die Top Ten der schönsten mathematischen Sätze" (2000) verstanden wissen. Erst kommt das Gebäude und dann das Fundament - das ist nicht gerade, was ein Architekt unter "Architektur der Mathematik" verstehen würde, entspricht aber der historischen Entwicklung. Die Mathematik war gleichsam auf Sand gebaut, bis Georg Cantor (1845-1918) und seine Nachfolger sie mit der axiomatischen Mengenlehre auf eine solidere Grundlage stellten. Nun gibt es nichts mehr, was wegrutsehen könnte, denn das ganze Gebäude der Mathematik mit seinen "mehr als dreitausend unterschiedlich spezialisierten Einzeldisziplinen" ruht auf der leeren Menge! Aus diesem Nichts den ganzen Reichtum mathematischer Strukturen zu konstruieren erfordert einigen Aufwand. Basieux erspart uns zwar die "masochistische Tortur" eines kompromisslosen Formalismus, wie die französische Gruppe Bourbaki ihn betrieb. Aber es gibt eine Fülle von Begriffen zu lernen, deren Sinn und Zweck sich erst aus ihrer späteren Verwendung erschließt. Der Überbau bestimmt eben doch weitgehend die Basis. Auf dem Fundament des Mengenbegriffs stehen drei Säulen, die ihrerseits die Mathematik tragen. Es sind drei Typen von Beziehungen unter den Elementen einer Menge: algebraische, topologische und Ordnungsrelationen. In der Tat kann man von diesem radikal abstrakten Standpunkt Gemeinsamkeiten zwischen weit entfernten Teilgebieten sehen, die anderenfalls in der Detailfülle untergehen würden. Das Buch vertritt eine sehr spezielle Sichtweise auf die Mathematik, die vom Leser erhebliche Denkarbeit verlangt. Basieux ist es gelungen, dieses spröde Thema in dem begrenzten Rahmen eines Taschenbuchs schmackhaft aufzubereiten
Footnote
Rez. in: Spektrum der Wissenschaft. 2001, H.1, S.108 (C. Pöppe)
Field
Mathematik

Similar documents (content)

  1. Heintz, B.: ¬Die Innenwelt der Mathematik : Zur Kultur und Praxis einer beweisenden Disziplin (2000) 0.22 
    0.21908045 = sum of:
  0.21908045 = product of:
    0.91283524 = sum of:
      0.022010224 = weight(abstract_txt:mehr in 1736) [ClassicSimilarity], result of:
        0.022010224 = score(doc=1736,freq=1.0), product of:
          0.082997315 = queryWeight, product of:
            1.0318726 = boost
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.016586915 = queryNorm
          0.265192 = fieldWeight in 1736, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.0546875 = fieldNorm(doc=1736)
      0.093920425 = weight(abstract_txt:formalismus in 1736) [ClassicSimilarity], result of:
        0.093920425 = score(doc=1736,freq=1.0), product of:
          0.173305 = queryWeight, product of:
            1.0543495 = boost
            9.909708 = idf(docFreq=5, maxDocs=44421)
            0.016586915 = queryNorm
          0.5419372 = fieldWeight in 1736, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            9.909708 = idf(docFreq=5, maxDocs=44421)
            0.0546875 = fieldNorm(doc=1736)
      0.036273424 = weight(abstract_txt:gibt in 1736) [ClassicSimilarity], result of:
        0.036273424 = score(doc=1736,freq=2.0), product of:
          0.091910146 = queryWeight, product of:
            1.0858649 = boost
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.016586915 = queryNorm
          0.3946618 = fieldWeight in 1736, product of:
            1.4142135 = tf(freq=2.0), with freq of:
              2.0 = termFreq=2.0
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.0546875 = fieldNorm(doc=1736)
      0.024592008 = weight(abstract_txt:eine in 1736) [ClassicSimilarity], result of:
        0.024592008 = score(doc=1736,freq=4.0), product of:
          0.06444474 = queryWeight, product of:
            1.1136109 = boost
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.016586915 = queryNorm
          0.38159835 = fieldWeight in 1736, product of:
            2.0 = tf(freq=4.0), with freq of:
              4.0 = termFreq=4.0
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.0546875 = fieldNorm(doc=1736)
      0.13203749 = weight(abstract_txt:gebäude in 1736) [ClassicSimilarity], result of:
        0.13203749 = score(doc=1736,freq=1.0), product of:
          0.2740181 = queryWeight, product of:
            1.8749242 = boost
            8.811096 = idf(docFreq=17, maxDocs=44421)
            0.016586915 = queryNorm
          0.48185682 = fieldWeight in 1736, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            8.811096 = idf(docFreq=17, maxDocs=44421)
            0.0546875 = fieldNorm(doc=1736)
      0.60400164 = weight(abstract_txt:mathematik in 1736) [ClassicSimilarity], result of:
        0.60400164 = score(doc=1736,freq=7.0), product of:
          0.5993261 = queryWeight, product of:
            5.1875186 = boost
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.016586915 = queryNorm
          1.0078014 = fieldWeight in 1736, product of:
            2.6457512 = tf(freq=7.0), with freq of:
              7.0 = termFreq=7.0
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.0546875 = fieldNorm(doc=1736)
    0.24 = coord(6/25)
  2. Neunzert, H.: ¬Die Zukunft der Mathematik : nicht mehr Königin, aber wichtiger Partner von Wissenschaft und Technik (2002) 0.16 
    0.16120891 = sum of:
  0.16120891 = product of:
    0.6717038 = sum of:
      0.015721587 = weight(abstract_txt:mehr in 130) [ClassicSimilarity], result of:
        0.015721587 = score(doc=130,freq=1.0), product of:
          0.082997315 = queryWeight, product of:
            1.0318726 = boost
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.016586915 = queryNorm
          0.18942285 = fieldWeight in 130, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.0390625 = fieldNorm(doc=130)
      0.018320847 = weight(abstract_txt:gibt in 130) [ClassicSimilarity], result of:
        0.018320847 = score(doc=130,freq=1.0), product of:
          0.091910146 = queryWeight, product of:
            1.0858649 = boost
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.016586915 = queryNorm
          0.19933432 = fieldWeight in 130, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.0390625 = fieldNorm(doc=130)
      0.00878286 = weight(abstract_txt:eine in 130) [ClassicSimilarity], result of:
        0.00878286 = score(doc=130,freq=1.0), product of:
          0.06444474 = queryWeight, product of:
            1.1136109 = boost
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.016586915 = queryNorm
          0.13628513 = fieldWeight in 130, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.0390625 = fieldNorm(doc=130)
      0.029549487 = weight(abstract_txt:erst in 130) [ClassicSimilarity], result of:
        0.029549487 = score(doc=130,freq=1.0), product of:
          0.12640563 = queryWeight, product of:
            1.2734364 = boost
            5.98444 = idf(docFreq=303, maxDocs=44421)
            0.016586915 = queryNorm
          0.23376718 = fieldWeight in 130, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            5.98444 = idf(docFreq=303, maxDocs=44421)
            0.0390625 = fieldNorm(doc=130)
      0.03445489 = weight(abstract_txt:1999 in 130) [ClassicSimilarity], result of:
        0.03445489 = score(doc=130,freq=1.0), product of:
          0.14003406 = queryWeight, product of:
            1.3403275 = boost
            6.2987905 = idf(docFreq=221, maxDocs=44421)
            0.016586915 = queryNorm
          0.2460465 = fieldWeight in 130, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            6.2987905 = idf(docFreq=221, maxDocs=44421)
            0.0390625 = fieldNorm(doc=130)
      0.5648742 = weight(abstract_txt:mathematik in 130) [ClassicSimilarity], result of:
        0.5648742 = score(doc=130,freq=12.0), product of:
          0.5993261 = queryWeight, product of:
            5.1875186 = boost
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.016586915 = queryNorm
          0.9425156 = fieldWeight in 130, product of:
            3.4641016 = tf(freq=12.0), with freq of:
              12.0 = termFreq=12.0
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.0390625 = fieldNorm(doc=130)
    0.24 = coord(6/25)
  3. Ortlieb, C.P.: Heinrich Hertz und das Konzept des mathematischen Modells (200x) 0.16 
    0.1609427 = sum of:
  0.1609427 = product of:
    0.67059463 = sum of:
      0.031443175 = weight(abstract_txt:mehr in 86) [ClassicSimilarity], result of:
        0.031443175 = score(doc=86,freq=1.0), product of:
          0.082997315 = queryWeight, product of:
            1.0318726 = boost
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.016586915 = queryNorm
          0.3788457 = fieldWeight in 86, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.078125 = fieldNorm(doc=86)
      0.036641695 = weight(abstract_txt:gibt in 86) [ClassicSimilarity], result of:
        0.036641695 = score(doc=86,freq=1.0), product of:
          0.091910146 = queryWeight, product of:
            1.0858649 = boost
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.016586915 = queryNorm
          0.39866865 = fieldWeight in 86, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.078125 = fieldNorm(doc=86)
      0.01756572 = weight(abstract_txt:eine in 86) [ClassicSimilarity], result of:
        0.01756572 = score(doc=86,freq=1.0), product of:
          0.06444474 = queryWeight, product of:
            1.1136109 = boost
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.016586915 = queryNorm
          0.27257025 = fieldWeight in 86, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.078125 = fieldNorm(doc=86)
      0.041911367 = weight(abstract_txt:buch in 86) [ClassicSimilarity], result of:
        0.041911367 = score(doc=86,freq=1.0), product of:
          0.10052352 = queryWeight, product of:
            1.1356066 = boost
            5.3367167 = idf(docFreq=580, maxDocs=44421)
            0.016586915 = queryNorm
          0.41693097 = fieldWeight in 86, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            5.3367167 = idf(docFreq=580, maxDocs=44421)
            0.078125 = fieldNorm(doc=86)
      0.08181484 = weight(abstract_txt:drei in 86) [ClassicSimilarity], result of:
        0.08181484 = score(doc=86,freq=1.0), product of:
          0.17973456 = queryWeight, product of:
            1.8597541 = boost
            5.8265367 = idf(docFreq=355, maxDocs=44421)
            0.016586915 = queryNorm
          0.45519817 = fieldWeight in 86, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            5.8265367 = idf(docFreq=355, maxDocs=44421)
            0.078125 = fieldNorm(doc=86)
      0.46121785 = weight(abstract_txt:mathematik in 86) [ClassicSimilarity], result of:
        0.46121785 = score(doc=86,freq=2.0), product of:
          0.5993261 = queryWeight, product of:
            5.1875186 = boost
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.016586915 = queryNorm
          0.7695608 = fieldWeight in 86, product of:
            1.4142135 = tf(freq=2.0), with freq of:
              2.0 = termFreq=2.0
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.078125 = fieldNorm(doc=86)
    0.24 = coord(6/25)
  4. Stammbach, U.: ¬"Die Mathematik ist eine gar herrliche Wissenschaft" (2005) 0.16 
    0.16011205 = sum of:
  0.16011205 = product of:
    0.5718288 = sum of:
      0.01779248 = weight(abstract_txt:diesem in 95) [ClassicSimilarity], result of:
        0.01779248 = score(doc=95,freq=1.0), product of:
          0.07981844 = queryWeight, product of:
            1.0119189 = boost
            4.7554536 = idf(docFreq=1038, maxDocs=44421)
            0.016586915 = queryNorm
          0.2229119 = fieldWeight in 95, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            4.7554536 = idf(docFreq=1038, maxDocs=44421)
            0.046875 = fieldNorm(doc=95)
      0.018865906 = weight(abstract_txt:mehr in 95) [ClassicSimilarity], result of:
        0.018865906 = score(doc=95,freq=1.0), product of:
          0.082997315 = queryWeight, product of:
            1.0318726 = boost
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.016586915 = queryNorm
          0.22730742 = fieldWeight in 95, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.046875 = fieldNorm(doc=95)
      0.021985017 = weight(abstract_txt:gibt in 95) [ClassicSimilarity], result of:
        0.021985017 = score(doc=95,freq=1.0), product of:
          0.091910146 = queryWeight, product of:
            1.0858649 = boost
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.016586915 = queryNorm
          0.23920119 = fieldWeight in 95, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.046875 = fieldNorm(doc=95)
      0.018254831 = weight(abstract_txt:eine in 95) [ClassicSimilarity], result of:
        0.018254831 = score(doc=95,freq=3.0), product of:
          0.06444474 = queryWeight, product of:
            1.1136109 = boost
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.016586915 = queryNorm
          0.28326333 = fieldWeight in 95, product of:
            1.7320508 = tf(freq=3.0), with freq of:
              3.0 = termFreq=3.0
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.046875 = fieldNorm(doc=95)
      0.054485306 = weight(abstract_txt:nichts in 95) [ClassicSimilarity], result of:
        0.054485306 = score(doc=95,freq=1.0), product of:
          0.16831851 = queryWeight, product of:
            1.4694676 = boost
            6.905677 = idf(docFreq=120, maxDocs=44421)
            0.016586915 = queryNorm
          0.3237036 = fieldWeight in 95, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            6.905677 = idf(docFreq=120, maxDocs=44421)
            0.046875 = fieldNorm(doc=95)
      0.049088906 = weight(abstract_txt:drei in 95) [ClassicSimilarity], result of:
        0.049088906 = score(doc=95,freq=1.0), product of:
          0.17973456 = queryWeight, product of:
            1.8597541 = boost
            5.8265367 = idf(docFreq=355, maxDocs=44421)
            0.016586915 = queryNorm
          0.2731189 = fieldWeight in 95, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            5.8265367 = idf(docFreq=355, maxDocs=44421)
            0.046875 = fieldNorm(doc=95)
      0.39135632 = weight(abstract_txt:mathematik in 95) [ClassicSimilarity], result of:
        0.39135632 = score(doc=95,freq=4.0), product of:
          0.5993261 = queryWeight, product of:
            5.1875186 = boost
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.016586915 = queryNorm
          0.652994 = fieldWeight in 95, product of:
            2.0 = tf(freq=4.0), with freq of:
              4.0 = termFreq=4.0
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.046875 = fieldNorm(doc=95)
    0.28 = coord(7/25)
  5. Gödert, W.: ¬Die Literatur der Mathematik und ihre Fachbibliographische Verzeichnung : ein Bericht für die Jahre 1979-1985 (1985) 0.15 
    0.14636716 = sum of:
  0.14636716 = product of:
    0.60986316 = sum of:
      0.020757891 = weight(abstract_txt:diesem in 579) [ClassicSimilarity], result of:
        0.020757891 = score(doc=579,freq=1.0), product of:
          0.07981844 = queryWeight, product of:
            1.0119189 = boost
            4.7554536 = idf(docFreq=1038, maxDocs=44421)
            0.016586915 = queryNorm
          0.26006386 = fieldWeight in 579, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            4.7554536 = idf(docFreq=1038, maxDocs=44421)
            0.0546875 = fieldNorm(doc=579)
      0.022010224 = weight(abstract_txt:mehr in 579) [ClassicSimilarity], result of:
        0.022010224 = score(doc=579,freq=1.0), product of:
          0.082997315 = queryWeight, product of:
            1.0318726 = boost
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.016586915 = queryNorm
          0.265192 = fieldWeight in 579, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            4.849225 = idf(docFreq=945, maxDocs=44421)
            0.0546875 = fieldNorm(doc=579)
      0.025649186 = weight(abstract_txt:gibt in 579) [ClassicSimilarity], result of:
        0.025649186 = score(doc=579,freq=1.0), product of:
          0.091910146 = queryWeight, product of:
            1.0858649 = boost
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.016586915 = queryNorm
          0.27906805 = fieldWeight in 579, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            5.1029587 = idf(docFreq=733, maxDocs=44421)
            0.0546875 = fieldNorm(doc=579)
      0.021297304 = weight(abstract_txt:eine in 579) [ClassicSimilarity], result of:
        0.021297304 = score(doc=579,freq=3.0), product of:
          0.06444474 = queryWeight, product of:
            1.1136109 = boost
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.016586915 = queryNorm
          0.33047387 = fieldWeight in 579, product of:
            1.7320508 = tf(freq=3.0), with freq of:
              3.0 = termFreq=3.0
            3.4888992 = idf(docFreq=3686, maxDocs=44421)
            0.0546875 = fieldNorm(doc=579)
      0.06356619 = weight(abstract_txt:nichts in 579) [ClassicSimilarity], result of:
        0.06356619 = score(doc=579,freq=1.0), product of:
          0.16831851 = queryWeight, product of:
            1.4694676 = boost
            6.905677 = idf(docFreq=120, maxDocs=44421)
            0.016586915 = queryNorm
          0.3776542 = fieldWeight in 579, product of:
            1.0 = tf(freq=1.0), with freq of:
              1.0 = termFreq=1.0
            6.905677 = idf(docFreq=120, maxDocs=44421)
            0.0546875 = fieldNorm(doc=579)
      0.45658234 = weight(abstract_txt:mathematik in 579) [ClassicSimilarity], result of:
        0.45658234 = score(doc=579,freq=4.0), product of:
          0.5993261 = queryWeight, product of:
            5.1875186 = boost
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.016586915 = queryNorm
          0.7618263 = fieldWeight in 579, product of:
            2.0 = tf(freq=4.0), with freq of:
              4.0 = termFreq=4.0
            6.965269 = idf(docFreq=113, maxDocs=44421)
            0.0546875 = fieldNorm(doc=579)
    0.24 = coord(6/25)