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I would like to write a paper on the fundamentals of Continuum Mechanics using the Geometric Algebra approach popularized by David Hestenes.

Is Hestenes's Geometric Algebra a wide accepted theory? I'm concerned because this previous Math.SE Answer describes it as "somewhat controversial". Also I see a previous Physics.SE Question (now closed as off-topic) about using Geometric Algebra as a curriculum replacement for linear algebra and vector calculus received an Answer that was highly critical of its pedagogical value.

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  • $\begingroup$ I'm curious to know in what context the issue of trust (versus doubt?) occurs here. One can use Google Scholar and other resources to see an author's work is frequently cited, as one measure of "wide acceptance". $\endgroup$
    – hardmath
    Mar 30, 2017 at 21:44
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    $\begingroup$ As the words here in this forum are so important, I've read the word "controversial" in this answer about geometric algebra: math.stackexchange.com/a/84159/423621 $\endgroup$
    – Roberto Dias Algarte
    Mar 30, 2017 at 23:25
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    $\begingroup$ And this other answer shows clearly that the author does not trust (oops, sorry), the author does not agree with Hastenes' Geometric Algebra: physics.stackexchange.com/a/19863 $\endgroup$
    – Roberto Dias Algarte
    Mar 30, 2017 at 23:31
  • $\begingroup$ That is why I made my simple question. $\endgroup$
    – Roberto Dias Algarte
    Mar 30, 2017 at 23:34
  • $\begingroup$ Okay, I took your Comments and combined them with the original text as best I could. Please review to check if unintentionally I've changed your meaning. $\endgroup$
    – hardmath
    Mar 31, 2017 at 0:25

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Yes, geometric algebra is a totally valid and accepted part of math. The proofs are correct.

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    $\begingroup$ Well, valid yes, but it does not make a lot of sense to say "Hestenes' approach is widely accepted." The problem is that it has very little to distinguish itself from Clifford algebra, and the people who use that particular nomenclature are a very small population. Very few mathematicians are even aware of this particular field. The fact of the matter is that nobody has been very impressed with the results of the program. As the OP mentioned in the posts, some people do not see it as much more than a repackaging of Clifford algebra. $\endgroup$
    – rschwieb
    May 8, 2017 at 17:24
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    $\begingroup$ Frankly it still surprises me how much the issue is clouded by Hestenes' name alone. The struggle to integrate Hamilton and Clifford's approaches to vector algebra with our current systems has been going on since the mid-19th century, and the contentious issues seem pretty much the same to me. Hestenes just seems to have re-ignited the same discussion. $\endgroup$
    – rschwieb
    May 8, 2017 at 17:29
  • $\begingroup$ Well, by "accepted" I just meant "people don't think it's false". But it's interesting to learn more about how people view this subject. $\endgroup$
    – littleO
    May 8, 2017 at 18:22
  • $\begingroup$ Hestenes added a derivative, which makes it a calculus as well as an algebra. I haven’t heard that this is controversial. $\endgroup$
    – NicNic8
    Nov 19 at 4:05

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