Lagrange and Mozart as critics of Descartes

This article traces three lines of positive and negative influence which emanated from Descartes's Discours sur la méthode (1637), orat least were closely linked to it. Three areas of concern are involved: the relationship between geometry and algebra, celestial mechanics, and physiological psychology. The two critics of the title were contemporaries: reasons for their surprising conjunction will emerge at the en

In memoriam Kurt Go¨del: His 1931 correspondence with zermelo on his incompletability theorem

SummariesShortly after publishing his now famous incompletability theorem in 1931, Kurt Go¨del and Ernst Zermelo corresponded about the nature and significance of Go¨del's result. The texts of the surviving letters are presented, preceded by an explanation of the circumstances of the correspondence and an indication of the historical significance of the points discussed

Using experimental research designs to explore the scope of cumulative culture in humans and other animals

In humans, cultural evolutionary processes are capable of shaping our cognition, because the conceptual tools we learn from others enable mental feats which otherwise would be beyond our capabilities. This is possible because human culture supports the inter-generational accumulation of skills and knowledge, such that later generations can benefit from the experience and exploration efforts of their predecessors. However, it remains unclear how exactly human social transmission supports the accumulation of advantageous traits, and why we see little evidence of this in the natural behaviour of other species. Thus, it is difficult to know whether the cognitive abilities of other animals might be similarly scaffolded by processes of cultural evolution. In this article I discuss how experimental studies of cultural evolution have contributed to our understanding of human cumulative culture, as well as some of the limitations of these approaches. I also discuss how similar research designs can be used to evaluate the potential for cumulative culture in other species. Such research may be able to clarify what distinguishes human cumulative culture from related phenomena in nonhumans, shedding light on the issue of whether other species also have the potential to develop cognitive capacities that are outcomes of cultural evolution

The Historical Context of the Gender Gap in Mathematics

This chapter is based on the talk that I gave in August 2018 at the ICM in Rio de Janeiro at the panel on "The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective". It provides some examples of the challenges and prejudices faced by women mathematicians during last two hundred and fifty years. I make no claim for completeness but hope that the examples will help to shed light on some of the problems many women mathematicians still face today

On the relations between historical epistemology and students’ conceptual developments in mathematics

There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students’ conceptual developments in mathematics. We problematize this attempt to link the two fields on the basis of Grattan-Guinness’ distinction between “history” and “heritage”. We argue that when parallelism claims are made, history and heritage are often mixed up, which is problematic since historical mathematical definitions must be interpreted in its proper historical context and conceptual framework. Furthermore, we argue that cultural and local ideas vary at different time periods, influencing conceptual developments in different directions regardless of whether historical or individual developments are considered, and thus it may be problematic to uncritically assume a platonic perspective. Also, we have to take into consideration that an average student of today and great mathematicians of the past are at different cognitive levels

The whole and its parts : why and how to disentangle plant communities and synusiae in vegetation classification

Most plant communities consist of different structural and ecological subsets, ranging from cryptogams to different tree layers. The completeness and approach with which these subsets are sampled have implications for vegetation classification. Non‐vascular plants are often omitted or sometimes treated separately, referring to their assemblages as “synusiae” (e.g. epiphytes on bark, saxicolous species on rocks). The distinction of complete plant communities (phytocoenoses or holocoenoses) from their parts (synusiae or merocoenoses) is crucial to avoid logical problems and inconsistencies of the resulting classification systems. We here describe theoretical differences between the phytocoenosis as a whole and its parts, and outline consequences of this distinction for practise and terminology in vegetation classification. To implement a clearer separation, we call for modifications of the International Code of Phytosociological Nomenclature and the EuroVegChecklist. We believe that these steps will make vegetation classification systems better applicable and raise the recognition of the importance of non‐vascular plants in the vegetation as well as their interplay with vascular plants