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I am curious to know when the right-hand-rule for vector product was established and used consistently in mathematics.

I read here

Who gave right hand thumb rule for circular loop of current conducting wire?

that in physics it was established by Ambrose Fleming in the late 19th century. I assume that in math it was commonly adopted later to have everything compatible with physics.

My reason for asking is that I am reading an introductory algebraic geometry text by Victoria Scott from 1894. I have noticed that she seems to use a left hand rule for the computation of vector product: in order to compute an area of a triangle she does a product of the sides (that I assume is the vector product) but, with the order chosen, she should get a negative area. And when she wants a negative area (to remove from another area)... the result should be positive with the modern convention. Since at the end she is just interested in plane geometry, consistency of the signs is the only thing that she needs, and she gets it. But this has raised my curiosity about the history of the right-hand-rule and the orientation of axes in the Euclidean 3-space...

Thank you for your help!

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  • $\begingroup$ I guess the right short naming is "Fleming" or "Ambrose Fleming" but I could be wrong. $\endgroup$
    – Mauricio
    Sep 27 at 17:09
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    $\begingroup$ Also on Math overflow $\endgroup$
    – J. W. Tanner
    Sep 28 at 3:18
  • $\begingroup$ Thanks for linking! I asked fist there and was redirected here! $\endgroup$
    – Sofia Tirabassi
    Sep 28 at 7:53
  • $\begingroup$ Eugene Wigner was known to do all his physics computations using the left hand rule, and then adjust the sign appropriately at the end. Actually seems pretty natural to use the (majority) non-writing hand to work out the vector directions. $\endgroup$
    – Jon Custer
    Sep 28 at 13:12
  • $\begingroup$ It might interest you that there is also a Maxwell's corkscrew rule. $\endgroup$
    – Mauricio
    Sep 29 at 8:44

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