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Evidence is discussed about the use of geometric information for spatial orientation and the association between space and numbers in non-human animals. A variety of vertebrate species can reorient using simple Euclidian geometry of the environmental surface layout, i.e. in accord with metric and sense (right/left) relationships among extended surfaces. There seems to be a primacy of geometric over non-geometric information in spatial reorientation and, possibly, innate encoding of the sense of direction. The hippocampal formation plays a key role in geometry-based reorientation in mammals, birds, amphibians and fish. Although some invertebrate species show similar behaviours, it is unclear whether the underlying mechanisms are the same as in vertebrates. As to the links between space and number representations, a disposition to associate numerical magnitudes onto a left-to-right-oriented mental number line appears to exist independently of socio-cultural factors, and can be observed in animals with very little numerical experience, such as newborn chicks and human infants. Such evidence supports a nativistic foundation of number–space association. Some speculation about the possible underlying mechanisms is provided together with consideration on the difficulties inherent to any comparison among species of different taxonomic groups. This article is part of a discussion meeting issue ‘The origins of numerical abilities'.

Comparative cognition of number and space: the case of geometry and of the mental number line