Towards the prehistoric sources of mathematical thinking. From the Paleolithic to the Ancient Greece.

elective monographs

Classroom

The aim of the course is to familiarize participants

with evidences on sources of mathematical and

metrological perception in prehistory.

During the course, archaeological sources are

discussed, from the Palaeolithic to historical times,

concerning the shaping of numerosity and

measurement practices in prehistory. Evidences

such as cuts on Palaeolithic bones, ivory and

artworks, beads, Near Eastern tokens and the first

entries on clay tablets, beads, wires and sheets in

the Neolithic period, megalithic structures (the so-

called megalithic yard), metal ingots from various

regions of the Old World, administrative records,

balance scales and weights in the Near East, Egypt

and Europe, as well as the issue of money and coin

making are discussed. In addition, the philosophical,

theoretical and methodological content will be

presented, various interpretations of the above

mentioned finds and a holistic description of the

process of the formation of mathematical thinking in

history.

Carl B. Boyer i Uta C. Merzbach, A History of

Mathematics, 3rd edition (Hoboken, N.J: Wiley,

2010).

Alexander Marshack, „A Lunar-Solar Year Calendar

Stick from North America”, American Antiquity 50, nr

1 (styczeń 1985): 27–51,

https://doi.org/10.2307/280632.

Tomasz Gralak, Architecture, Style and Structure in

the Early Iron Age in Central Europe (PL:

Uniwersytet Wrocławski and author, 2017),

https://doi.org/10.23734/22.17.001.

Karl Petruso, Ayia Irini: The Balance Weights : An

Analysis of Weight Measurement in Prehistoric

Crete and the Cycladic Islands (Mainz on Rhine: P.

von Zabern, 1992).

Michał Heller, Bóg i geometria: gdy przestrzeń była

Bogiem (Copernicus Center Press, 2020).

Majolie Lenerz-de Wilde, „Bronzezeitliche

Zahlungsmittel”, Mitteilungen der Anthropologischen

Gesellschaft in Wien 132 (2002): 1–23.

Mihael Budja, „Clay Tokens - Accounting before

Writing in Eurasia”, Dokumenta Praehistorica 25

(1998): 219–35.

J. Peter Denny, „Cultural Ecology of Mathematics:

Ojibway and Inuit Hunters”, w Native American

Mathematics, red. Michael P. Closs (University of

Texas Press, 1996), 129–80.

Jacques Derrida, Edmund Husserl’s Origin of

Geometry, an Introduction (Lincoln: University of

Nebraska Press, 1989).

Jens Hoyrup, In Measure, Number, and Weight:

Studies in Mathematics and Culture (Albany: State

University of New York Press, 1994).

3

John David Barrow - Pi Razy Drzwi. Szkice O

Liczeniu, Myśleniu I Istnieniu.

Denise Schmandt-Besserat, Jak powstało pismo

(Warszawa: Agade, 2007).

Edmund Husserl, Kryzys nauk europejskich i

fenomenologia transcendentalna (Warszawa: vis-a-

vis, 2017).

Witold Kula, Miary i ludzie (Warszawa: Książka i

Wiedza, 2004).

Morley, I., & Renfrew, C. (Eds.). (2010). The

Archaeology of Measurement: Comprehending

Heaven, Earth and Time in Ancient Societies.

Cambridge: Cambridge University Press.

doi:10.1017/CBO9780511760822

Richard Seaford, Money and the Early Greek Mind:

Homer, Philosophy, Tragedy (Cambridge, UK ; New

York: Cambridge University Press, 2004).

Aleksander Dzbyński, From Seeberg to Colmar:

Early mathematical concepts in prehistoric Europe

at the interface between material culture, technology

and metaphors, Prahistorische Zeitschrift, 2014,

https://doi.org/10.1515/pz-2014-0001.

Aleksander Dzbyński, Rytuał i porozumienie :

racjonalne podstawy komunikacji i wymiany w

pradziejach Europy Środkowej = Ritual and

understanding : rational bases of communication

and exchange in prehistoric Central Europe,

Collectio Archaeologica Ressoviensis 8 (Rzeszów,

2008).

Aleksander Dzbynski, The Power of the Line:

Metaphor, Number and Material Culture in

European Prehistory (Newcastle upon Tyne, 2013).

Participants have in-depth knowledge of archaeological

evidences and their role in shaping the early stages of

mathematical thinking (K_W01). They have extended

knowledge (K_W03) about the possibilities of the

description and interpretation of these evidences

(K_W04). They understand the need for considering a

variety of disciplines, both humanistic and scientific

approaches in the study of number and measure in

prehistory (K_W10), they know and understand methods

of interpretation (K_W14).

Potrafią dostrzegać złożone zależności pomiędzy

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omawianymi artefaktami a dawnymi procesami

kulturowymi (K_U07).

Approve of attendance or an exam