From linear measurements in multivariate analysis to computational palaeontology

Palaeontology, traditionally rooted in fieldwork and direct observation of fossil remains, is undergoing a transformativeshift thanks to technological and mathematical innovations. These advances have expanded the scope and depth of palaeontological research,improving our understanding of evolutionary processes, shape evolution, phylogenetic relationships, and taxonomic diversification. Statisticaltools, particularly phylogenetic comparative methods, have become essential for evaluating evolutionary rates and patterns across species.Geometric morphometrics has revolutionised the study of biological form, enabling more accurate reconstructions of fossilised organisms anddetailed analyses of evolutionary trends. Additionally, new imaging technologies, such as scanning electron microscopy (SEM) and synchrotronradiation, have enhanced the study of fossils and opened new avenues for detailed analysis. In the last few years, Artificial Intelligence (AI)and machine learning, though still in their early stages, are showing promise for automating fossil classification, identifying patterns in largedatasets, and even advancing image-based systematic taxonomy. While AI tools are not yet a replacement for expert palaeontologists, theyoffer significant support, particularly in curating large collections and facilitating rapid classification processes. However, the integrationof all these statistical and technological tools into palaeontological practice presents challenges, particularly in terms of interpreting resultsaccurately. This underscores the need for palaeontologists to develop a foundational understanding of the algorithms and statistical methodsthey employ, ensuring proper application and reducing the risk of erroneous inferences. As these mathematical and computational toolscontinue to evolve, they are set to revolutionise palaeontology, enabling more efficient, accurate, and innovative research. Furthermore,these advancements are contributing to the growing field of conservation palaeobiology, with potential applications in understanding climatechange, extinction events, and species adaptation, offering critical insights into contemporary conservation efforts.