Abstract
This paper can be considered as a self criticism of the author. He was advocating formal mathematics and formal teaching of mathematics since writing his PhD thesis in 1978. He has started to change his views in 1994 in favour of humanizing mathematics and humanizing mathematics teaching.
The paper includes the three main theories of mathematical truth leading to a formal view to mathematics and formal teaching of the subject, then deals with recent developments in science, mathematics and suggestions to modify the three theories in order to cope with these developments, Paradigm shifts in mathematics education were presented and the study was concluded with two urgent suggestions to reform mathematics education.
