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The philosophy of mathematics poses a number of problems for Marxists. Firstly, mathematics is the most abstract of subjects -- the symbols in mathematics rarely represent concrete objects, they may sometimes stand for numbers, but frequently they refer to completely formal structures. This means that a demonstration of the materialist root of mathematical ideas will be harder to produce than for other sciences. Secondly, mathematics is not usually considered an experimental subject, and so the second feature of the scientific method appears not to hold. Thus, if mathematics is not tested in practice, what claim does it have to be different to religion or any other mystical belief?

Yet, mathematics is an integral part of virtually every science. Contrary to one of the myths, science is not a mechanical process where masses of data are collected, patterns observed and eventually theories emerge. In many cases the scientific theory is developed on the basis of mathematics and logic far in advance of any experimental justification. A good example of this is Einstein's general theory of relativity, developed mathematically way ahead of the experimental science, though subsequent experimental work has confirmed the predictions of the theory to an extraordinary degree of accuracy. A second example is in Chaos Theory where pure mathematicians such as Cantor, Julia and Fatou had produced a theoretical framework for the subject long before the computer technology had been developed to make it applicable. So any weakness in the methodology in mathematics is also a weakness in the way science is done.