overall goals. But each different culture mathematics may be assigned different roles and parts to play, as a contribution to these goals. Thus the purposes of mathematics in a culture may be religious, artistic, practical.technological, study for its own sake, and so on. Whichever it is, the mathematics of each culture presumably serves its own purposes efficiently and well, since it has evolved to meet certain needs and survived. Consequently, the mathematics of each culture is equally valuable, since all cultures are equally valid.
An objection to this argument can be anticipated. To claim that all culture forms of mathematics are equally valuable, is to deny the power of what migh be termed Western academic mathematics. This is the discipline which lies at the heart of modern science and technology, and industry and production. Great progress has been achieved in these fields, and Western mathematics has made a critical contribution. In harnessing the forces of nature and enhancing industrial production the mathematical component of Western culture is immensely efficient, and has no rival.
But it is a fallacy to arque this that consequently Western academic mathematics is more valuable or efficient than the mathematics of any other culture.
For claims of the value or efficiency of mathematics assume a system of values. Each culture has value that are a part of its view of the world, its overall goals, and the purposes it give to its members. Each culture, like each individual, has the right to integrity. Thus, the system of values of each culture are ab initio, equally valid. In absolute terms, there is no basis for asserting that the system of values of one culture or society is superior to all others. It cannot be asserted, therefore, that Western mathematics is superior to any other forms because of its greater power over nature. This would be to commit the fallacy of assuming that the values of Western culture and mathematics are universal.
The acknowledgment of the culture-bound nature of mathematics leads inevitably to the acknowledgment of its value-laden nature. There is a growing literature which recognizes the values implicit in mathematics, and the need for their critical examination. Bell et al.(1973) raised the issues of military involvement in mathematics, and the moral issues raised. More recently such as Maxwell (1984), Restivo (1985), Eenest (1986), Bishop (1988), have raised the question of the value implicit in mathematics, mostly from an educational standpoint.