Finland

Rene Descartes

nationality

American

British

occupation / innovator as

novelist

science fiction writer

historian of mathematics

mathematician

innovator in the field of

combinatorics

scientist

scientific organization

National Academy of Sciences

is a country which sophisticated Europeans even today barely consider civilized, especially for its queer custom of paying its debts.

is responsible for having broken with the Greek tradition of admitting only the first, second, and third powers ('lengths,' 'areas,' and 'volumes') in geometry, recognizing that representability as figures in Euclidean space for all of the terms in an equation is irrelevant to the geometrical interpretation of the analysis.

Descartes devised the notation x, x2, x3, x4,... for powers, and made the final break with the Greek tradition of admitting only the first, second, and third powers ('lengths,' 'areas,' and 'volumes') in geometry. After Descartes, geometers freely used powers higher than the third without a qualm, recognizing that representability as figures in Euclidean space for all of the terms in an equation is irrelevant to the geometrical interpretation of the analysis.

is responsible for an analytic reformulation of geometry that didn't just make possible a systematic investigation of known curves, but, also potentially created a whole universe of geometric forms beyond conception by the synthetic method.

The implications of Descartes' analytic reformulation of geometry are obvious. Not only did the new method make possible a systematic investigation of known curves, but, what is of infinitely greater significance, it potentially created a whole universe of geometric forms beyond conception by the synthetic method. Descartes also saw that his method applies equally as well to surfaces... but he did not develop this. With the extension to surfaces, there was no reason why geometry should stop with equations in three variables; and the generalization to systems of equations in any finite number of variables was readily made in the nineteenth century. Finally, in the twentieth century, the farthest extension possible in this direction led to spaces of a non-denumerable infinity of dimensions. ...The path from Descartes to the creators of higher space is straight and clear; the remarkable thing is that it was not traveled earlier than it was.

Eric Temple BellThinkers

Eric Temple Bell