In 1570, at the University of Oxford, a young lecturer called Henry Savile opened his lecture course on mathematical astronomy by telling the story of Aristippus the Socratic philosopher. According to the Roman writer Vitruvius, Aristippus was shipwrecked on the coast of Rhodes, and struggling with his comrades out of the storm-tossed waves came to a beach on which there were geometric drawings in the sand. ‘Be of good cheer’ he said to his comrades, ‘for I see the marks of human-kind’. Humanity is defined and characterised by its being a mathematizing species; wherever there is mathematics there is civilisation. The image from antiquity became a symbol of the University of Oxford’s mathematical aspirations, forming a background to common beliefs about the significance and role of mathematics in the ensuing centuries. This use of the past as a guide and inspiration, testifying to mathematics as a symbol and characterization of humanity, can be seen as forming a thesis which we can hold up in opposition to a second image, also produced in Oxford, three centuries later. In a book called Picture logic: a attempt to popularise the science of reasoning (1874), Alfred Swinburne drew a picture showing all the living world passing into a monster logical sausage-machine, emerging in uniform parcels under the watchful gaze of Professor Logic, who cheerily reflected: ‘It’s with our machine here as it is with the ordinary sausage machine, never mind what the material is so long as the shape is right. Large or small, young or old, flesh or stone, you must all pass through, for Professor Logic isn’t particlular about the matter, all he concerns himself with is the form’. This symbolic image can be taken to stand for the numerous interventions down the ages suggesting that mathematics is involved in something inhuman, mechanical; that mathematical modeling misses the point and unweaves the rainbow; that mathematics teaching is an anti-humanistic shuttering, a closing down, of human aspirations. And as we will see, the critique made of mathematics and mathematics education as being mechanistic can be extended to the educational policies within which the education is experienced. Somewhere in the historical dialectic between the conceptions underlying these two images there may lie a resolution which with strength and energy can be used in constructing the best possible framework for mathematics learners of the future. I’ll come back to these symbols later and draw more out of them for this purpose, after making some observations on internationalism in our community. (ZDM/Mathdi)