The mathematics I am interested in includes the use of category theory to relate relationships between differing mathematical theories such as geometry, algebra and analysis; the meaning of the number line through perception, completion and extension; the use of symbols flexibly as process or concept, which I name ‘procept’; the various notions of infinity; the historical development of mathematical ideas; the various meanings of mathematical proof. My research centering on mathematics includes my proof of the structure of ordered extensions of the complete ordered field; my introduction of the superreal numbers as polar series in a single infinitesimal and their properties. I do not produce research articles on mathematics, as I seek the essential simplicity of concepts with rich internal structure that can be used in flexible ways. My views of the past and future of Mathematics Education Research at large involve the realization that different cultural communities have differing objectives and differing ways of interpreting mathematical ideas. My personal experience co-operating internationally with mathematics educators in different communities around the world shows that experiences embraced by some communities may be rejected by others. To move into the future, I seek simple experiences that novices and experts can share to make sense of mathematics in their own interpretation.