Loss of vision: How mathematics turned blind while it learned to see more clearly
To discuss the developments of mathematics that have to do with the introduction of new objects, we distinguish between ‘Aristotelian’ and ‘non-Aristotelian’ accounts of abstraction and mathematical ‘top-down’ and ‘bottom-up’ approaches. The development of mathematics from the 19th to the 20th century is then characterized as a move from a ‘bottom-up’ to a ‘top-down’ approach. Since the latter also leads to more abstract objects for which the Aristotelian account of abstraction is not well-suited, this development has also lead to a decrease of visualizations in mathematical practice.
Bernd Buldt and Dirk Schlimm. "Loss of vision: How mathematics turned blind while it learned to see more clearly" Philosophy of Mathematics: Sociological Aspects and Mathematical Practice (2010).
Available at: http://works.bepress.com/bebuldt/4
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