ESHS/HSS Annual Meeting

From Concrete Forms to Abstract Structures: A Bibliometric Study of the Term ‘Structure’ in Mathematical Review Journals from 1889 to the 1960s

• In Event: Transformations of Mathematics in the 20th Century

English Abstract

The term ‘structure’ (lat. s
tructura) was initially used in technical and architectural
contexts, referring to the visible and stable arrangement of physical parts such as in
buildings. It described concrete, perceptible objects and no abstract relationships. Early
definitions of the term confirm this. With the rise of modern natural sciences in the 19th
century, the meaning of ‘structure’ expanded. Around 1900, many disciplines shifted
from focusing on objects to emphasizing relationships. This shift was also evident in
mathematics: The Bourbaki group e.g. formalized structure as a foundational concept,
identifying three fundamental so called ‘mother structures’: algebraic, topological, and
order structures, aiming to represent all mathematics as a unified system of interrela-
ted struc tures.
This research project explores the historical development of the use of the term ‘struc-
ture’ in mathematical discourse from 1889 to the 1960s, focusing on the review journals
the Jahrbuch über die Fortschritte der Mathematik , which was published in Germany
and was the first internationally extensive review journal in the history of mathematics,
and the Zentralblatt für Mathematik und ihre Grenzgebiete . The rise of structural
thematics is reflected in the Jahrbuch and can also be seen o n a bibliometric level in the
context of scientific publications. In my presentation I would like to present the first
results of my bibliometric analysis. Using data from the Jahrbuch , we can see that the
number of submitted papers containing the term ‘st ructure’ has increased both in abso-
lute numbers and percentages. On the other hand, the number of mathematical sub-
disciplines involved has also increased.

Author

• Elife Çetintaş, University of Wuppertal