Seeing Mathematics and Seeing Mathematicians

Natural Vision and Mathematics: Seeing Impossibilities

The Turing-inspired Meta-Morphogenesis project investigates forms of biological information processing produced by evolution since the earliest life forms, especially information processing mechanisms that made possible the deep mathematical discoveries of Euclid, Archimedes, and other ancient mathematicians. Such mechanisms must enable perception of possibilities and constraints on possibiliti...

Seeing and not seeing.

Recent studies revealed that although subterranean mammals inhabit a dark underground environment, they can still perceive light stimuli and use this to entrain their circadian activity rhythm. Regarding spatial orientation, olfactory and tactile cues are employed for short-distance; whereas for long-distance, subterranean mammals employ the earth's magnetic field and self-generated (vestibular...

Seeing Seeing

This paper discusses several key issues concerning consciousness and human vision. A brief overview is presented of recent developments in this area, including issues that have been resolved and issues that remain unsettled. Based on this, three Hilbert questions are proposed. These involve three related sets of issues: the kinds of visual experience that exist, the kinds of visual attention th...

Mathematics, Mathematicians, and Mathematics Education

I am one of a growing number of research mathematicians who are substantially engaged with school mathematics education. Such outreach has a long and honorable tradition. In this lecture, I illustrate some of the ways that I think this can be helpful, and even essential. Upon his retirement in 1990 as president of the ICMI, Jean Pierre Kahane spoke perceptively of the intimate connection betwee...

Seeing more is seeing better.