Man's language ability is due to a more general, deep-seated cognitive ability characteristic of the species. It is argued that man's ability for mathematical thinking is a product of the same species-specific form of cerebration as language. The basis for mathematical constructs seems to be contained in the basis for language constructs; apparently, for every mathematical notion there is a homologous one in the sphere of language, the former always being more restricted and well defined than the latter. Mathematical ability may therefore be regarded as a special case of the more general ability that also generates language, and this point is further emphasized by certain similarities in the formal structure of mathematics (arithmetic in particular) and language. Taking advantage of the commonalities between language and arithmetic, it is possible to use the latter to illustrate important general characteristics of the former. The insights gained are relevant to biology at large, and to comparative zoology and neurology in particular. The zoologist who wishes to compare animal communication with language must know what the nature of language is-how (or whether) one might analyze it into components. He must know what might constitute a primitive or simple language. It is shown that the irreducible elements of the two systems under study (language and arithmetic) are processes (i.e., processes of "relating," or simply "relations") and that these processes combine into interrated systems. The systems have ontogenetic histories that might, perhaps, furnish a criterion for the notion of simplicity. We do not yet know what might be a homologous phylogenetic "cousin" of the basic human ability under consideration; howerver, we should expect it to be "homeomorphic" to the human system if it is derived from a common ancestral ability. Homeomorphic mapping is therefore the most reliable criterion so far for phylogenetic relatedness. By characterizing language and arithmetic simultaneously (in order to get at their common biological foundations) it is also possible to sharpen up the questions that the student of language should put to the neurophysiologist. The quest for innovation or differences in brain processes and functions now appears to be the primary one, whereas a description of structural changes in the human brain would be of interest only insofar as this would elucidate how brain functions might have become modified by them.