Introduction: The origins of numerical abilities.

Abstract

The papers in this theme issue are based on a discussion meeting at Royal Society in London on 20 and 21 February 2017, and at their Kavli Centre at Chicheley Hall in Buckinghamshire on the 22 and 23 February. In addition to the scientific presentations, two distinguished mathematicians, Fields Medallist, Cedric Villani and Professor of Mathematics at Oxford University, Marcus du Sautoy, summed up the implications of our new understanding of the origins of numerical abilities for mathematics and for mathematics education. Audio recordings of the talks and the subsequent discussions can be accessed at https://royalsociety.org/science-events-and-lectures/2017/02/numerical-abilities/, https://royalsociety.org/science-events-and-lectures/2017/02/numerical-abilities-future/. It is clear that humans have a sense of number. This is evident from their ability to count using counting words, such as one, two, three, … and counting symbols, such as 1, 2, 3, … or I, II, III, IV, … . In fact, Pagel & Meade [1] argue that reconstructions of the deep history of cognates from diverse language families show that counting words are among the longest-surviving words in all languages. Even when the culture fails to provide words or symbols to notate counting, humans are still able to enumerate objects in their environment, as evidence from work with Australian Aboriginal children [2], suggesting that the symbolic forms, perhaps especially the number words, arose to denote a pre-existing concept of number. One of the oldest questions in Western philosophy is what is a number that we may have a sense of it. Giaquinto [3], in his paper in this issue, notes that Euclid defined a number as ‘a multitude of units’ where a unit is a single individual thing. According to this view, ‘any pair of items is a 2 and so there are many 2 s; any trio is a 3 …