Mathematics teaching is democratic education

It is a commonly held belief that mathematics teaching has no political effects. Astonishingly, however, the fact is that the style of argument now used in mathematics everywhere was not developed originally to do mathematics. Originally its function was to counteract the teaching by the early Greek sophists of rhetoric. Their training gave the rich and privileged such an advantage in public speaking that democracy was threatned. Making respectable a new form of argument, in which evidence and logical structure predominated, was a very radical act of enlightened democratic education. Mathematics teaching in the form of open critical dialogue between teacher and taught remains a powerful form of education in democratic attitudes. Ambitions to produce political ideas as infallible as mathematics have a modern origin. In the early part of this century, mathematics education was again becoming universal throughout Europe. In the same period the belief arose that mathematics could eventually be completed as a single structure of truth. This transformed mathematics into a paradigm of democracy in which unorthodoxy must necessarily be eliminated. Communicated to people everywhere by universal education, this belief increased respect for similar political ideas. Gödel’s proof that mathematics can never be completed came too late to correct these political effects, but modern teachers can again use mathematics as a proof of the value and success of democratic attitudes and ideas. Whilst mathematics itself is ethically neutral, the ethical principles which produced both democracy and mathematics and which can be converyed in mathematics teaching are highly relevant to the modern world, and should be understood and taught by teachers everywhere.