The well-designed young mathematician

The well-designed young mathematician

This paper complements McCarthy’s “The well designed child”, in part by putting it in a broader context, the space of possible well designed progeny, and in part by relating design features to development of mathematical competence. I first moved into AI in an attempt to understand myself, especially hoping to understand how I could do mathematics. Over the ensuing four decades, my interactions...

The well-designed child

This article is inspired by recent psychological studies confirming that a child is not born a blank slate but has important innate capabilities. An important part of the “learning” required to deal with the three dimensional world of objects, processes, and other beings was done by evolution. Each child need not do this learning itself. By the 1950s there were already proposals to advance arti...

Beyond Well-designed SPARQL

SPARQL is the standard query language for RDF data. The distinctive feature of SPARQL is the OPTIONAL operator, which allows for partial answers when complete answers are not available due to lack of information. However, optional matching is computationally expensive – query answering is PSPACE-complete. The well-designed fragment of SPARQL achieves much better computational properties by rest...

Viii. Final Perspectives Viii.6 Advice to a Young Mathematician

Borwein, J., D. H. Bailey, and R. Girgensohn. 2004. Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A. K. Peters. Calkin, N., and H. S. Wilf. 2000. Recounting the rationals. American Mathematical Monthly 107:360–63. Ferguson, H. R. P., and R. W. Forcade. 1979. Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two. Bulletin ...

The mathematician as a formalist