Is a mathematical model equivalent to its computer implementation?

Submitted: February 24, 2024
Accepted: May 16, 2024
Published: June 18, 2024
Abstract Views: 371
PDF: 98
Publisher's note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.


A recent trend in mathematical modelling is to publish the computer code together with the research findings. Here we explore the formal question, whether and in which sense a computer implementation is distinct from the mathematical model. We argue that, despite the convenience of implemented models, a set of implicit assumptions is perpetuated with the implementation to the extent that even in widely used models the causal link between the (formal) mathematical model and the set of results is no longer certain. Moreover, code publication is often seen as an important contributor to reproducible research, we suggest that in some cases the opposite may be true. A new perspective on this topic stems from the accelerating trend that in some branches of research only implemented models are used, e.g., in artificial intelligence (AI). With the advent of quantum computers, we argue that completely novel challenges arise in the distinction between models and implementations.



PlumX Metrics


Download data is not yet available.


Jelizarow M, Guillemot V, Tenenhaus A, et al. Over-optimism in bioinformatics research. Bioinformatics 2010;26:437. DOI:
Milkowski M, Hensel WM, Hohol M. Replicability or reproducibility? on the replication crisis in computational neuroscience and sharing only relevant detail. J Comput Neurosci 2018;45:163. DOI:
Tiwari K, Kananathan S, Roberts MG, et al. Reproducibility in systems biology modelling. Mol Syst Biol 2021;17:e9982.
Stodden V, Guo P, Ma Z. Toward reproducible computational research: an empirical analysis of data and code policy adoption by journal. PloS One 2013;8:e67111.
McKiernan EC, Bourne PE, Brown CT, et al. How open science helps researchers succeed. Elife 2016;5:e16800.
Stodden V, McNutt M, Bailey DH, et al. Enhancing reproducibility for computational methods. Science 2016;354:1240. DOI:
Barton CM, Lee A, Janssen MA, et al. How to make models more useful. Proc Natl Acad Sci USA 2022;119:e2202112119.
Castellano C, Fortunato S, Loreto V. Statistical physics of social dynamics. Rev Mod Phys 2009;81:591. DOI:
Pereira EJAL, da Silva MF, Pereira HB. Econophysics: Past and present. Physica A 2017;473:251. DOI:
Holovatch Y, Kenna R, Thurner S. Complex systems: physics beyond physics. Eur J Phys 2017;38:023002. DOI:
Barthelemy M. The statistical physics of cities. Nat Rev Phys 2019;1:406. DOI:
Fan J, Meng J, Ludescher J, et al. Statistical physics approaches to the complex Earth system. Phys Rep 2021;896:1-84. DOI:
Kauffman SA. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 1969;22:437-67. DOI:
Bak P, Tang C, Wiesenfeld K. Self-organized criticality. Phys Rev A 1988;38:364. DOI:
Rodrigues FA, Peron TKD, Ji P, Kurths J. The Kuramoto model in complex networks. Phys Rep 2016;610:1-98. DOI:
Vieira LS, Laubenbacher RC. Computational models in systems biology: standards, dissemination, and best practices. Curr Opin Biotechnol 2022;75:102702. DOI:
Gleick J. Chaos: Making a new science. Penguin Books, London; 2008.
Lorenz EN. Deterministic nonperiodic flow. J Atmos Sci 1963;20:130-41. DOI:<0130:DNF>2.0.CO;2
Höpfl S, Pleiss J, Radde NE. Bayesian estimation reveals that reproducible models in systems biology get more citations. Sci Rep 2023;13:2695. DOI:
Farmelo G. It must be beautiful - great equations of modern science. Granta Books, London; 2002.
May RM. Uses and abuses of mathematics in biology. Science 2004;303:790-3. DOI:
Le Novere N, Bornstein B, Broicher A, et al. Biomodels database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Res 2006;34:D689-91.

How to Cite

Hiesmayr, B. C., & Hütt, M.-T. (2024). Is a mathematical model equivalent to its computer implementation?. Proceedings of the European Academy of Sciences and Arts, 3.