Document (#30131)

Author

Neunzert, H.

Title

¬Die Zukunft der Mathematik : nicht mehr Königin, aber wichtiger Partner von Wissenschaft und Technik

Source

Visionen. Hrsg.: Universität Kaiserslautern, H. Hofrichter

Imprint

Kaiserslautern : Universität

Year

2002

Pages

S.91-100

Abstract

Ich halte es nicht für sinnvoll, darüber zu spekulieren, wie sich eine Wissenschaft in den kommenden Jahrzehnten inhaltlich entwickeln könnte, Neue Theorien tauchen sehr schnell auf, gewinnen höchste Aufmerksamkeit und kehren dann langsam auf ein stabiles, bescheideneres Niveau zurück; man denke etwa an die Katastrophentheorie, an Chaos und Fraktale, an Fuzzy-Logik - vielleicht ist auch die Finanzmathematik schon in einem Normalisierungsprozess. Solche Entwicklungen, insbesondere das Auftreten solcher Phänomene, vorherzusagen, wäre Scharlatanerie. Aber es gibt natürlich auch langwellige Veränderungen des Charakters der Mathematik; so wechseln sich z.B. Phasen, in denen die "innere' Entwicklung der Mathematik dominiert, ab mit Phasen, in denen die Inhalte der Mathematik durch ihre Wechselwirkung mit anderen Wissenschaften bestimmt werden, Solche Phasen sind nie "rein" - immer gab es Mathematiker, die sowohl in reiner wie auch in angewandter Mathematik Bedeutendes leisteten, z.B. B. Riemann, H. Poincare, F. Klein oder N. Wiener. Aber Dominanzen waren unschwer zu erkennen, z.B. die Dominanz der reinen Mathematik im vergangenen Jahrhundert. Ebenso deutlich scheint es mir zu sein, dass wir uns seit wenigen Jahrzehnten im Phasenübergang befinden: Die Mathematik nähert sich wieder den anderen Wissenschaften - nicht nur der Physik, sondern auch der Chemie, Biologie und Medizin; sie nähert sich der Technik, z.B. den Informations- und Kommunikationstechnologien, der Werkstoffwissenschaft, der Robotik usw. Es gilt aber auch das Umgekehrte: Nicht nur Naturwissenschaft und Technik benötigen die Mathematik in steigendem Umfang, selbst Sozial- und Geisteswissenschaften "mathematisieren". Die Disziplinen insgesamt wachsen stärker zusammen: Ist dies vielleicht der Zukunftstrend? Hubert Markl, Präsident der Max-Planck-Gesellschaft, antwortet auf die Frage, ob die Biologie zur "Leitwissenschaft" des 21. Jahrhunderts wird: "Das immer rascher fortschreitende, tiefgründige Zusammenwachsen aller naturwissenschaftlichen Disziplinen, gemeinsam mit der praktischen Mathematik, zu einer einzigen umfassenden Wissenschaft von der Natur, die auch in weite Bereiche von Philosophie, Psychologie, Soziologie und Medizin vordringen wird, dürfte für die Wissenschaftsentwicklung des nächsten Jahrhunderts viel bestimmender sein als ein vermeintlicher Vorrang der Biologie. Erst diese Verbindung von Mathematik, Physik, Chemie und Biologie hat es möglich gemacht und wird weiter immer mehr Grundlage dafür sein, dass die Biowissenschaften sich endlich auch jenen Problemen stellen können, die ihnen ohne disziplinübergreifende Hilfestellung zu schwierig wären - nämlich alle Lebenserscheinungen bis hinein in die molekularen, ursächlichen Einzelheiten aufzuklären. " (aus "Visionen 2000", Brockhaus 1999).
Natürlich steht es mir nicht an, weiter über Biologie zu reden, aber die Einschätzung der künftigen Rolle der Mathematik, in enger Zusammenarbeit mit anderen Wissenschaften an der "Aufklärung" und Gestaltung der Welt zu arbeiten - diese Einschätzung teile ich vollkommen: Die Mathematik wird also weder "Königin der Wissenschaften" sein noch ihre Sklavin; sie wird, wie es sich für ein demokratisches Gemeinwesen gehört, ihre Aufgabe und ihren Sinn hauptsächlich als gleichberechtigter Partner von Informatik, Naturwissenschaften, Technik, von Wirtschafts- und Sozialwissenschaften finden. Das spiegelt sich auch in einer sehr aktuellen Diskussion um den Bedarf an "Computerexperten" wider; die Debatte, die mit unscharfen Begriffen (was ist schon ein "Computerexperte"?) operiert und von geringem Fachwissen (wer von den Diskutanten hat sich je in Indien umgesehen oder wenigstens mit Indern ausführlich gesprochen?) beeinträchtigt wird, zeigt trotzdem, dass wir sowohl schnell auszubildende Softwareprogrammierer wie eben auch sogenannte MINT-Professionals brauchen. MINT - ich habe den Ausdruck in der Industrie gehört - heißt Mathematik + Informatik + Naturwissenschaft + Technik; solche Professionals werden wir nur selten im Ausland "einkaufen" können - sie sind auch dort rar und nicht nur in Deutschland Mangelware, Wir müssen solche MINT-Professionals schon selbst ausbilden - ich komme am Ende auf diese Ausbildungsfrage zurück.

Field

Mathematik

Similar documents (author)

1. Neunzert, H.: Mathematische Modellierung : ein "curriculum vitae" (2012) 5.94

   5.937289 = sum of:
     5.937289 = weight(author_txt:neunzert in 2255) [ClassicSimilarity], result of:
       5.937289 = fieldWeight in 2255, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.499662 = idf(docFreq=8, maxDocs=44218)
         0.625 = fieldNorm(doc=2255)
   

2. Neunzert, H.: Vom Nutzen der Mathematik (1995) 5.94

   5.937289 = sum of:
     5.937289 = weight(author_txt:neunzert in 6839) [ClassicSimilarity], result of:
       5.937289 = fieldWeight in 6839, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.499662 = idf(docFreq=8, maxDocs=44218)
         0.625 = fieldNorm(doc=6839)
   

3. Neunzert, H.: "Denn nichts ist für den Menschen als Menschen etwas wert, was er nicht mit Leidenschaft tun kann" (2001) 5.94

   5.937289 = sum of:
     5.937289 = weight(author_txt:neunzert in 2828) [ClassicSimilarity], result of:
       5.937289 = fieldWeight in 2828, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.499662 = idf(docFreq=8, maxDocs=44218)
         0.625 = fieldNorm(doc=2828)
   

4. Neunzert, H.: Oskar Perron : einer der bedeutendsten pfälzischen Wissenschaftler (2017) 5.94

   5.937289 = sum of:
     5.937289 = weight(author_txt:neunzert in 626) [ClassicSimilarity], result of:
       5.937289 = fieldWeight in 626, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.499662 = idf(docFreq=8, maxDocs=44218)
         0.625 = fieldNorm(doc=626)
   

5. Neunzert, H.; Rosenberger, B.: Oh Gott, Mathematik? (1997) 4.75

   4.749831 = sum of:
     4.749831 = weight(author_txt:neunzert in 2312) [ClassicSimilarity], result of:
       4.749831 = fieldWeight in 2312, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.499662 = idf(docFreq=8, maxDocs=44218)
         0.5 = fieldNorm(doc=2312)
   

Similar documents (content)

1. Rötzer, A.: ¬Die Einteilung der Wissenschaften : Analyse und Typologisierung von Wissenschaftsklassifikationen (2003) 0.37

   0.36761102 = sum of:
     0.36761102 = product of:
       0.65644825 = sum of:
         0.014200427 = weight(abstract_txt:ihre in 684) [ClassicSimilarity], result of:
           0.014200427 = score(doc=684,freq=1.0), product of:
             0.07521718 = queryWeight, product of:
               4.8330836 = idf(docFreq=956, maxDocs=44218)
               0.015562979 = queryNorm
             0.18879233 = fieldWeight in 684, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.8330836 = idf(docFreq=956, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.034852926 = weight(abstract_txt:jahrzehnten in 684) [ClassicSimilarity], result of:
           0.034852926 = score(doc=684,freq=1.0), product of:
             0.11955797 = queryWeight, product of:
               1.0294023 = boost
               7.462781 = idf(docFreq=68, maxDocs=44218)
               0.015562979 = queryNorm
             0.29151487 = fieldWeight in 684, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.462781 = idf(docFreq=68, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.035057865 = weight(abstract_txt:medizin in 684) [ClassicSimilarity], result of:
           0.035057865 = score(doc=684,freq=1.0), product of:
             0.12002618 = queryWeight, product of:
               1.0314159 = boost
               7.4773793 = idf(docFreq=67, maxDocs=44218)
               0.015562979 = queryNorm
             0.29208514 = fieldWeight in 684, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.4773793 = idf(docFreq=67, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.02238327 = weight(abstract_txt:immer in 684) [ClassicSimilarity], result of:
           0.02238327 = score(doc=684,freq=2.0), product of:
             0.08085778 = queryWeight, product of:
               1.0368177 = boost
               5.0110264 = idf(docFreq=800, maxDocs=44218)
               0.015562979 = queryNorm
             0.27682272 = fieldWeight in 684, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.0110264 = idf(docFreq=800, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.044333637 = weight(abstract_txt:chemie in 684) [ClassicSimilarity], result of:
           0.044333637 = score(doc=684,freq=1.0), product of:
             0.14035933 = queryWeight, product of:
               1.1153637 = boost
               8.085969 = idf(docFreq=36, maxDocs=44218)
               0.015562979 = queryNorm
             0.31585816 = fieldWeight in 684, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.085969 = idf(docFreq=36, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.020436075 = weight(abstract_txt:schon in 684) [ClassicSimilarity], result of:
           0.020436075 = score(doc=684,freq=1.0), product of:
             0.095877 = queryWeight, product of:
               1.1290123 = boost
               5.456611 = idf(docFreq=512, maxDocs=44218)
               0.015562979 = queryNorm
             0.21314888 = fieldWeight in 684, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.456611 = idf(docFreq=512, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.023963924 = weight(abstract_txt:wissenschaft in 684) [ClassicSimilarity], result of:
           0.023963924 = score(doc=684,freq=1.0), product of:
             0.10661576 = queryWeight, product of:
               1.1905625 = boost
               5.754088 = idf(docFreq=380, maxDocs=44218)
               0.015562979 = queryNorm
             0.22476906 = fieldWeight in 684, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.754088 = idf(docFreq=380, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.013513878 = weight(abstract_txt:wird in 684) [ClassicSimilarity], result of:
           0.013513878 = score(doc=684,freq=1.0), product of:
             0.09168806 = queryWeight, product of:
               1.5613953 = boost
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.015562979 = queryNorm
             0.14738972 = fieldWeight in 684, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.028522717 = weight(abstract_txt:aber in 684) [ClassicSimilarity], result of:
           0.028522717 = score(doc=684,freq=2.0), product of:
             0.112680726 = queryWeight, product of:
               1.5801222 = boost
               4.5821176 = idf(docFreq=1229, maxDocs=44218)
               0.015562979 = queryNorm
             0.25312862 = fieldWeight in 684, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               4.5821176 = idf(docFreq=1229, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.021828534 = weight(abstract_txt:nicht in 684) [ClassicSimilarity], result of:
           0.021828534 = score(doc=684,freq=2.0), product of:
             0.10018419 = queryWeight, product of:
               1.632135 = boost
               3.9441223 = idf(docFreq=2327, maxDocs=44218)
               0.015562979 = queryNorm
             0.21788403 = fieldWeight in 684, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.9441223 = idf(docFreq=2327, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.047801334 = weight(abstract_txt:sich in 684) [ClassicSimilarity], result of:
           0.047801334 = score(doc=684,freq=10.0), product of:
             0.10874243 = queryWeight, product of:
               1.963475 = boost
               3.5586145 = idf(docFreq=3422, maxDocs=44218)
               0.015562979 = queryNorm
             0.4395831 = fieldWeight in 684, product of:
               3.1622777 = tf(freq=10.0), with freq of:
                 10.0 = termFreq=10.0
               3.5586145 = idf(docFreq=3422, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.18844219 = weight(abstract_txt:wissenschaften in 684) [ClassicSimilarity], result of:
           0.18844219 = score(doc=684,freq=9.0), product of:
             0.22308324 = queryWeight, product of:
               1.9885858 = boost
               7.208251 = idf(docFreq=88, maxDocs=44218)
               0.015562979 = queryNorm
             0.8447169 = fieldWeight in 684, product of:
               3.0 = tf(freq=9.0), with freq of:
                 9.0 = termFreq=9.0
               7.208251 = idf(docFreq=88, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.058133252 = weight(abstract_txt:auch in 684) [ClassicSimilarity], result of:
           0.058133252 = score(doc=684,freq=7.0), product of:
             0.1503117 = queryWeight, product of:
               2.5809362 = boost
               3.742164 = idf(docFreq=2848, maxDocs=44218)
               0.015562979 = queryNorm
             0.38675135 = fieldWeight in 684, product of:
               2.6457512 = tf(freq=7.0), with freq of:
                 7.0 = termFreq=7.0
               3.742164 = idf(docFreq=2848, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
         0.10297823 = weight(abstract_txt:biologie in 684) [ClassicSimilarity], result of:
           0.10297823 = score(doc=684,freq=1.0), product of:
             0.334115 = queryWeight, product of:
               2.720908 = boost
               7.890225 = idf(docFreq=44, maxDocs=44218)
               0.015562979 = queryNorm
             0.30821192 = fieldWeight in 684, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.890225 = idf(docFreq=44, maxDocs=44218)
               0.0390625 = fieldNorm(doc=684)
       0.56 = coord(14/25)
   

2. Thesaurus der exakten Wissenschaften : Unter Mitarb. von Charles Auffray u.a (2001) 0.35

   0.35361305 = sum of:
     0.35361305 = product of:
       0.6800251 = sum of:
         0.014200427 = weight(abstract_txt:ihre in 2414) [ClassicSimilarity], result of:
           0.014200427 = score(doc=2414,freq=1.0), product of:
             0.07521718 = queryWeight, product of:
               4.8330836 = idf(docFreq=956, maxDocs=44218)
               0.015562979 = queryNorm
             0.18879233 = fieldWeight in 2414, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.8330836 = idf(docFreq=956, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.031654727 = weight(abstract_txt:immer in 2414) [ClassicSimilarity], result of:
           0.031654727 = score(doc=2414,freq=4.0), product of:
             0.08085778 = queryWeight, product of:
               1.0368177 = boost
               5.0110264 = idf(docFreq=800, maxDocs=44218)
               0.015562979 = queryNorm
             0.39148644 = fieldWeight in 2414, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               5.0110264 = idf(docFreq=800, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.03569635 = weight(abstract_txt:physik in 2414) [ClassicSimilarity], result of:
           0.03569635 = score(doc=2414,freq=1.0), product of:
             0.1214791 = queryWeight, product of:
               1.0376399 = boost
               7.5225 = idf(docFreq=64, maxDocs=44218)
               0.015562979 = queryNorm
             0.29384765 = fieldWeight in 2414, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.5225 = idf(docFreq=64, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.044333637 = weight(abstract_txt:chemie in 2414) [ClassicSimilarity], result of:
           0.044333637 = score(doc=2414,freq=1.0), product of:
             0.14035933 = queryWeight, product of:
               1.1153637 = boost
               8.085969 = idf(docFreq=36, maxDocs=44218)
               0.015562979 = queryNorm
             0.31585816 = fieldWeight in 2414, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.085969 = idf(docFreq=36, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.063402586 = weight(abstract_txt:wissenschaft in 2414) [ClassicSimilarity], result of:
           0.063402586 = score(doc=2414,freq=7.0), product of:
             0.10661576 = queryWeight, product of:
               1.1905625 = boost
               5.754088 = idf(docFreq=380, maxDocs=44218)
               0.015562979 = queryNorm
             0.59468305 = fieldWeight in 2414, product of:
               2.6457512 = tf(freq=7.0), with freq of:
                 7.0 = termFreq=7.0
               5.754088 = idf(docFreq=380, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.03601469 = weight(abstract_txt:sein in 2414) [ClassicSimilarity], result of:
           0.03601469 = score(doc=2414,freq=3.0), product of:
             0.10675177 = queryWeight, product of:
               1.3756198 = boost
               4.986364 = idf(docFreq=820, maxDocs=44218)
               0.015562979 = queryNorm
             0.33736858 = fieldWeight in 2414, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               4.986364 = idf(docFreq=820, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.019111509 = weight(abstract_txt:wird in 2414) [ClassicSimilarity], result of:
           0.019111509 = score(doc=2414,freq=2.0), product of:
             0.09168806 = queryWeight, product of:
               1.5613953 = boost
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.015562979 = queryNorm
             0.20844054 = fieldWeight in 2414, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.045098376 = weight(abstract_txt:aber in 2414) [ClassicSimilarity], result of:
           0.045098376 = score(doc=2414,freq=5.0), product of:
             0.112680726 = queryWeight, product of:
               1.5801222 = boost
               4.5821176 = idf(docFreq=1229, maxDocs=44218)
               0.015562979 = queryNorm
             0.4002315 = fieldWeight in 2414, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               4.5821176 = idf(docFreq=1229, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.026734386 = weight(abstract_txt:nicht in 2414) [ClassicSimilarity], result of:
           0.026734386 = score(doc=2414,freq=3.0), product of:
             0.10018419 = queryWeight, product of:
               1.632135 = boost
               3.9441223 = idf(docFreq=2327, maxDocs=44218)
               0.015562979 = queryNorm
             0.26685235 = fieldWeight in 2414, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               3.9441223 = idf(docFreq=2327, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.052363735 = weight(abstract_txt:sich in 2414) [ClassicSimilarity], result of:
           0.052363735 = score(doc=2414,freq=12.0), product of:
             0.10874243 = queryWeight, product of:
               1.963475 = boost
               3.5586145 = idf(docFreq=3422, maxDocs=44218)
               0.015562979 = queryNorm
             0.48153913 = fieldWeight in 2414, product of:
               3.4641016 = tf(freq=12.0), with freq of:
                 12.0 = termFreq=12.0
               3.5586145 = idf(docFreq=3422, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.0888325 = weight(abstract_txt:wissenschaften in 2414) [ClassicSimilarity], result of:
           0.0888325 = score(doc=2414,freq=2.0), product of:
             0.22308324 = queryWeight, product of:
               1.9885858 = boost
               7.208251 = idf(docFreq=88, maxDocs=44218)
               0.015562979 = queryNorm
             0.39820337 = fieldWeight in 2414, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.208251 = idf(docFreq=88, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.038057145 = weight(abstract_txt:auch in 2414) [ClassicSimilarity], result of:
           0.038057145 = score(doc=2414,freq=3.0), product of:
             0.1503117 = queryWeight, product of:
               2.5809362 = boost
               3.742164 = idf(docFreq=2848, maxDocs=44218)
               0.015562979 = queryNorm
             0.2531882 = fieldWeight in 2414, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               3.742164 = idf(docFreq=2848, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
         0.18452506 = weight(abstract_txt:mathematik in 2414) [ClassicSimilarity], result of:
           0.18452506 = score(doc=2414,freq=1.0), product of:
             0.6777878 = queryWeight, product of:
               6.24884 = boost
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.015562979 = queryNorm
             0.27224606 = fieldWeight in 2414, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.0390625 = fieldNorm(doc=2414)
       0.52 = coord(13/25)
   

3. Körkel, T.: Internet für Hörer aller Fakultäten (2002) 0.28

   0.28123105 = sum of:
     0.28123105 = product of:
       0.46871838 = sum of:
         0.009940298 = weight(abstract_txt:ihre in 1219) [ClassicSimilarity], result of:
           0.009940298 = score(doc=1219,freq=1.0), product of:
             0.07521718 = queryWeight, product of:
               4.8330836 = idf(docFreq=956, maxDocs=44218)
               0.015562979 = queryNorm
             0.13215463 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.8330836 = idf(docFreq=956, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.024540504 = weight(abstract_txt:medizin in 1219) [ClassicSimilarity], result of:
           0.024540504 = score(doc=1219,freq=1.0), product of:
             0.12002618 = queryWeight, product of:
               1.0314159 = boost
               7.4773793 = idf(docFreq=67, maxDocs=44218)
               0.015562979 = queryNorm
             0.2044596 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.4773793 = idf(docFreq=67, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.024987444 = weight(abstract_txt:physik in 1219) [ClassicSimilarity], result of:
           0.024987444 = score(doc=1219,freq=1.0), product of:
             0.1214791 = queryWeight, product of:
               1.0376399 = boost
               7.5225 = idf(docFreq=64, maxDocs=44218)
               0.015562979 = queryNorm
             0.20569336 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.5225 = idf(docFreq=64, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.012512181 = weight(abstract_txt:anderen in 1219) [ClassicSimilarity], result of:
           0.012512181 = score(doc=1219,freq=1.0), product of:
             0.08768785 = queryWeight, product of:
               1.0797201 = boost
               5.2183776 = idf(docFreq=650, maxDocs=44218)
               0.015562979 = queryNorm
             0.14269002 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.2183776 = idf(docFreq=650, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.029866548 = weight(abstract_txt:einschätzung in 1219) [ClassicSimilarity], result of:
           0.029866548 = score(doc=1219,freq=1.0), product of:
             0.13681814 = queryWeight, product of:
               1.1012038 = boost
               7.983315 = idf(docFreq=40, maxDocs=44218)
               0.015562979 = queryNorm
             0.21829377 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.983315 = idf(docFreq=40, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.043888062 = weight(abstract_txt:chemie in 1219) [ClassicSimilarity], result of:
           0.043888062 = score(doc=1219,freq=2.0), product of:
             0.14035933 = queryWeight, product of:
               1.1153637 = boost
               8.085969 = idf(docFreq=36, maxDocs=44218)
               0.015562979 = queryNorm
             0.3126836 = fieldWeight in 1219, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.085969 = idf(docFreq=36, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.014305252 = weight(abstract_txt:schon in 1219) [ClassicSimilarity], result of:
           0.014305252 = score(doc=1219,freq=1.0), product of:
             0.095877 = queryWeight, product of:
               1.1290123 = boost
               5.456611 = idf(docFreq=512, maxDocs=44218)
               0.015562979 = queryNorm
             0.14920421 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.456611 = idf(docFreq=512, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.016774746 = weight(abstract_txt:wissenschaft in 1219) [ClassicSimilarity], result of:
           0.016774746 = score(doc=1219,freq=1.0), product of:
             0.10661576 = queryWeight, product of:
               1.1905625 = boost
               5.754088 = idf(docFreq=380, maxDocs=44218)
               0.015562979 = queryNorm
             0.15733834 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.754088 = idf(docFreq=380, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.013378056 = weight(abstract_txt:wird in 1219) [ClassicSimilarity], result of:
           0.013378056 = score(doc=1219,freq=2.0), product of:
             0.09168806 = queryWeight, product of:
               1.5613953 = boost
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.015562979 = queryNorm
             0.14590837 = fieldWeight in 1219, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.019965902 = weight(abstract_txt:aber in 1219) [ClassicSimilarity], result of:
           0.019965902 = score(doc=1219,freq=2.0), product of:
             0.112680726 = queryWeight, product of:
               1.5801222 = boost
               4.5821176 = idf(docFreq=1229, maxDocs=44218)
               0.015562979 = queryNorm
             0.17719004 = fieldWeight in 1219, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               4.5821176 = idf(docFreq=1229, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.034167062 = weight(abstract_txt:nicht in 1219) [ClassicSimilarity], result of:
           0.034167062 = score(doc=1219,freq=10.0), product of:
             0.10018419 = queryWeight, product of:
               1.632135 = boost
               3.9441223 = idf(docFreq=2327, maxDocs=44218)
               0.015562979 = queryNorm
             0.34104246 = fieldWeight in 1219, product of:
               3.1622777 = tf(freq=10.0), with freq of:
                 10.0 = termFreq=10.0
               3.9441223 = idf(docFreq=2327, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.02792039 = weight(abstract_txt:solche in 1219) [ClassicSimilarity], result of:
           0.02792039 = score(doc=1219,freq=1.0), product of:
             0.16480789 = queryWeight, product of:
               1.7092274 = boost
               6.195629 = idf(docFreq=244, maxDocs=44218)
               0.015562979 = queryNorm
             0.16941173 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.195629 = idf(docFreq=244, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.021162553 = weight(abstract_txt:sich in 1219) [ClassicSimilarity], result of:
           0.021162553 = score(doc=1219,freq=4.0), product of:
             0.10874243 = queryWeight, product of:
               1.963475 = boost
               3.5586145 = idf(docFreq=3422, maxDocs=44218)
               0.015562979 = queryNorm
             0.19461173 = fieldWeight in 1219, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               3.5586145 = idf(docFreq=3422, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.04614184 = weight(abstract_txt:auch in 1219) [ClassicSimilarity], result of:
           0.04614184 = score(doc=1219,freq=9.0), product of:
             0.1503117 = queryWeight, product of:
               2.5809362 = boost
               3.742164 = idf(docFreq=2848, maxDocs=44218)
               0.015562979 = queryNorm
             0.30697438 = fieldWeight in 1219, product of:
               3.0 = tf(freq=9.0), with freq of:
                 9.0 = termFreq=9.0
               3.742164 = idf(docFreq=2848, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
         0.12916756 = weight(abstract_txt:mathematik in 1219) [ClassicSimilarity], result of:
           0.12916756 = score(doc=1219,freq=1.0), product of:
             0.6777878 = queryWeight, product of:
               6.24884 = boost
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.015562979 = queryNorm
             0.19057226 = fieldWeight in 1219, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.02734375 = fieldNorm(doc=1219)
       0.6 = coord(15/25)
   

4. Heintz, B.: ¬Die Innenwelt der Mathematik : Zur Kultur und Praxis einer beweisenden Disziplin (2000) 0.26

   0.25706968 = sum of:
     0.25706968 = product of:
       0.91810596 = sum of:
         0.019880597 = weight(abstract_txt:ihre in 736) [ClassicSimilarity], result of:
           0.019880597 = score(doc=736,freq=1.0), product of:
             0.07521718 = queryWeight, product of:
               4.8330836 = idf(docFreq=956, maxDocs=44218)
               0.015562979 = queryNorm
             0.26430926 = fieldWeight in 736, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.8330836 = idf(docFreq=956, maxDocs=44218)
               0.0546875 = fieldNorm(doc=736)
         0.02215831 = weight(abstract_txt:immer in 736) [ClassicSimilarity], result of:
           0.02215831 = score(doc=736,freq=1.0), product of:
             0.08085778 = queryWeight, product of:
               1.0368177 = boost
               5.0110264 = idf(docFreq=800, maxDocs=44218)
               0.015562979 = queryNorm
             0.27404052 = fieldWeight in 736, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.0110264 = idf(docFreq=800, maxDocs=44218)
               0.0546875 = fieldNorm(doc=736)
         0.026756112 = weight(abstract_txt:wird in 736) [ClassicSimilarity], result of:
           0.026756112 = score(doc=736,freq=2.0), product of:
             0.09168806 = queryWeight, product of:
               1.5613953 = boost
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.015562979 = queryNorm
             0.29181674 = fieldWeight in 736, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.0546875 = fieldNorm(doc=736)
         0.03055995 = weight(abstract_txt:nicht in 736) [ClassicSimilarity], result of:
           0.03055995 = score(doc=736,freq=2.0), product of:
             0.10018419 = queryWeight, product of:
               1.632135 = boost
               3.9441223 = idf(docFreq=2327, maxDocs=44218)
               0.015562979 = queryNorm
             0.30503765 = fieldWeight in 736, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.9441223 = idf(docFreq=2327, maxDocs=44218)
               0.0546875 = fieldNorm(doc=736)
         0.047320906 = weight(abstract_txt:sich in 736) [ClassicSimilarity], result of:
           0.047320906 = score(doc=736,freq=5.0), product of:
             0.10874243 = queryWeight, product of:
               1.963475 = boost
               3.5586145 = idf(docFreq=3422, maxDocs=44218)
               0.015562979 = queryNorm
             0.43516505 = fieldWeight in 736, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               3.5586145 = idf(docFreq=3422, maxDocs=44218)
               0.0546875 = fieldNorm(doc=736)
         0.08793969 = weight(abstract_txt:wissenschaften in 736) [ClassicSimilarity], result of:
           0.08793969 = score(doc=736,freq=1.0), product of:
             0.22308324 = queryWeight, product of:
               1.9885858 = boost
               7.208251 = idf(docFreq=88, maxDocs=44218)
               0.015562979 = queryNorm
             0.39420122 = fieldWeight in 736, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.208251 = idf(docFreq=88, maxDocs=44218)
               0.0546875 = fieldNorm(doc=736)
         0.6834904 = weight(abstract_txt:mathematik in 736) [ClassicSimilarity], result of:
           0.6834904 = score(doc=736,freq=7.0), product of:
             0.6777878 = queryWeight, product of:
               6.24884 = boost
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.015562979 = queryNorm
             1.0084136 = fieldWeight in 736, product of:
               2.6457512 = tf(freq=7.0), with freq of:
                 7.0 = termFreq=7.0
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.0546875 = fieldNorm(doc=736)
       0.28 = coord(7/25)
   

5. Janich, P.: Was ist Information? : Kritik einer Legende (2006) 0.24

   0.24191345 = sum of:
     0.24191345 = product of:
       0.75597954 = sum of:
         0.031654727 = weight(abstract_txt:immer in 1639) [ClassicSimilarity], result of:
           0.031654727 = score(doc=1639,freq=1.0), product of:
             0.08085778 = queryWeight, product of:
               1.0368177 = boost
               5.0110264 = idf(docFreq=800, maxDocs=44218)
               0.015562979 = queryNorm
             0.39148644 = fieldWeight in 1639, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.0110264 = idf(docFreq=800, maxDocs=44218)
               0.078125 = fieldNorm(doc=1639)
         0.0713927 = weight(abstract_txt:physik in 1639) [ClassicSimilarity], result of:
           0.0713927 = score(doc=1639,freq=1.0), product of:
             0.1214791 = queryWeight, product of:
               1.0376399 = boost
               7.5225 = idf(docFreq=64, maxDocs=44218)
               0.015562979 = queryNorm
             0.5876953 = fieldWeight in 1639, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.5225 = idf(docFreq=64, maxDocs=44218)
               0.078125 = fieldNorm(doc=1639)
         0.03574909 = weight(abstract_txt:anderen in 1639) [ClassicSimilarity], result of:
           0.03574909 = score(doc=1639,freq=1.0), product of:
             0.08768785 = queryWeight, product of:
               1.0797201 = boost
               5.2183776 = idf(docFreq=650, maxDocs=44218)
               0.015562979 = queryNorm
             0.40768576 = fieldWeight in 1639, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.2183776 = idf(docFreq=650, maxDocs=44218)
               0.078125 = fieldNorm(doc=1639)
         0.038223017 = weight(abstract_txt:wird in 1639) [ClassicSimilarity], result of:
           0.038223017 = score(doc=1639,freq=2.0), product of:
             0.09168806 = queryWeight, product of:
               1.5613953 = boost
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.015562979 = queryNorm
             0.41688108 = fieldWeight in 1639, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.773177 = idf(docFreq=2761, maxDocs=44218)
               0.078125 = fieldNorm(doc=1639)
         0.040337212 = weight(abstract_txt:aber in 1639) [ClassicSimilarity], result of:
           0.040337212 = score(doc=1639,freq=1.0), product of:
             0.112680726 = queryWeight, product of:
               1.5801222 = boost
               4.5821176 = idf(docFreq=1229, maxDocs=44218)
               0.015562979 = queryNorm
             0.35797793 = fieldWeight in 1639, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.5821176 = idf(docFreq=1229, maxDocs=44218)
               0.078125 = fieldNorm(doc=1639)
         0.12562813 = weight(abstract_txt:wissenschaften in 1639) [ClassicSimilarity], result of:
           0.12562813 = score(doc=1639,freq=1.0), product of:
             0.22308324 = queryWeight, product of:
               1.9885858 = boost
               7.208251 = idf(docFreq=88, maxDocs=44218)
               0.015562979 = queryNorm
             0.5631446 = fieldWeight in 1639, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.208251 = idf(docFreq=88, maxDocs=44218)
               0.078125 = fieldNorm(doc=1639)
         0.04394461 = weight(abstract_txt:auch in 1639) [ClassicSimilarity], result of:
           0.04394461 = score(doc=1639,freq=1.0), product of:
             0.1503117 = queryWeight, product of:
               2.5809362 = boost
               3.742164 = idf(docFreq=2848, maxDocs=44218)
               0.015562979 = queryNorm
             0.29235655 = fieldWeight in 1639, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.742164 = idf(docFreq=2848, maxDocs=44218)
               0.078125 = fieldNorm(doc=1639)
         0.36905012 = weight(abstract_txt:mathematik in 1639) [ClassicSimilarity], result of:
           0.36905012 = score(doc=1639,freq=1.0), product of:
             0.6777878 = queryWeight, product of:
               6.24884 = boost
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.015562979 = queryNorm
             0.5444921 = fieldWeight in 1639, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.078125 = fieldNorm(doc=1639)
       0.32 = coord(8/25)