I realize modern algebraic notation is fairly new but for as long as there have been recorded chess games, every square I think was referred to using two coordinates, in old descriptive notation a column named after a piece and a row which I think would always have been a number from 1 to 8. Come to think of it, the game of Go would have had no good way other than two integer coordinates to refer to the intersections on which stones were placed.

Is there any evidence that Descartes or earlier mathematicians had been inspired by recorded chess or Go games, perhaps even introducing their ideas using the game boards? Go and chess are of course ancient games and I know recorded chess games predate Descartes by centuries and assume that Go also was recorded long ago.

It seems not even hard to imagine that before Descartes someone noticed that the distance between two points on the Go or chess board could be calculated using coordinates.

EDIT: Regarding Go notation: As I understand it, a very cumbersome way to record Go games was/is in use until fairly recently or still which actually displays successive positions. I guess the value is, just recording the moves would be very hard to follow for all but the best players (I emphasize "guess" because I barely know the rules of Go) could follow a game using algebraic notation. But I suspect had coordinates been used 2000 years ago, something like Cartesian geometry would have been the almost inevitable result -- who knows what that would have meant for China combined with other advances? I realize this is speculation, of course.

  • 2
    $\begingroup$ The point was not coordinates as such, but their adaptation to solving geometric problems. The latitude-longitude coordinates were used in geography and astronomy since Eratosthenes and Hipparchus, and did not influence geometry much, although Oresme did call his axes after them. Discrete grid of chess was even less relevant. Apollonius used some proto-coordinates in Conic Sections, and that was the main influence on Descartes, along with Vieta's conversion of geometric problems into equations with lengths. $\endgroup$
    – Conifold
    Jan 23, 2023 at 11:30
  • $\begingroup$ @Conifold: would using coordinates on a map of two locations to calculates the distance between them not be an example of them being used to solve a geometric problem? if so, did no one do something like this prior to Descartes? $\endgroup$
    – releseabe
    Jan 23, 2023 at 11:56
  • $\begingroup$ That is done with the Pythagorean theorem (or its spherical variant), and coordinates only clutter the view. Descartes had to demonstrate that he could solve problems previously intractable or greatly simplify/unify known solutions. $\endgroup$
    – Conifold
    Jan 23, 2023 at 12:08
  • $\begingroup$ On a map, why would you use the Pythagorean theorem? If u calculate the legs of the triangle lengths, why not just directly calculate the length of the hypotenuse? i am assuming they would simply use the scale of the map to multiple the length calculated directly. $\endgroup$
    – releseabe
    Jan 23, 2023 at 12:14
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    $\begingroup$ See this post for details: originally Descartes used non-orthogonal coordinates. $\endgroup$ Jan 23, 2023 at 13:52


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