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On Double-Entry Bookkeeping: The Mathematical Treatment

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  • David Ellerman

Abstract

Double-entry bookkeeping (DEB) implicitly uses a specific mathematical construction, the group of differences using pairs of unsigned numbers ('T-accounts'). That construction was only formulated abstractly in mathematics in the nineteenth century, even though DEB had been used in the business world for over five centuries. Yet the connection between DEB and the group of differences (here called the 'Pacioli group') is still largely unknown both in mathematics and accounting. The precise mathematical treatment of DEB allows clarity on certain conceptual questions and it immediately yields the generalization of the double-entry method to multi-dimensional vectors typically representing the different types of property involved in an enterprise or household.

Suggested Citation

  • David Ellerman, 2014. "On Double-Entry Bookkeeping: The Mathematical Treatment," Accounting Education, Taylor & Francis Journals, vol. 23(5), pages 483-501, October.
    • Handle: RePEc:taf:accted:v:23:y:2014:i:5:p:483-501
    DOI: 10.1080/09639284.2014.949803
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    Cited by:

    1. Anna Vysotskaya & Oleg Kolvakh & Greg Stoner, 2016. "Mutual calculations in creating accounting models: a demonstration of the power of matrix mathematics in accounting education," Accounting Education, Taylor & Francis Journals, vol. 25(4), pages 396-413, July.
    2. Renes, S., 2020. "When Debit=Credit. The balance constraint in bookkeeping, its causes and consequences for accounting," ERIM Report Series Research in Management ERS-2020-005-FA, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Frederico Botafogo, 2019. "The Syntax of the Accounting Language: A First Step," Papers 1906.10865, arXiv.org.
    4. Apostolou, Barbara & Dorminey, Jack W. & Hassell, John M. & Rebele, James E., 2015. "Accounting education literature review (2013–2014)," Journal of Accounting Education, Elsevier, vol. 33(2), pages 69-127.

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