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I recall reading years ago in a linear algebra book that Gauss was accused of witchcraft for his (re)discovery of what we now call the row reduction algorithm for solving linear equations. Has anyone else encountered the same story? Is there possibly any truth to it?

The context, I believe, was the use of the algorithm in "equation solving competitions" that were apparently held in the 19th century; most participants would use substitutions together with some clever tricks, but Gauss' algorithm was much faster for large linear systems. But I can't verify any of this.

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    $\begingroup$ By the way, I would be sympathetic to the argument that "debunk this story" questions ought to be off-topic for this site; the question may have a good answer if the story is true, but if the story is false then it may be difficult to produce evidence of its falsehood. $\endgroup$ – Paul Siegel Dec 3 '14 at 19:53
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    $\begingroup$ We've allowed similar questions in the past, e.g. hsm.stackexchange.com/questions/333. While it's difficult to prove the falsehood of a story, there is usually at least some circumstantial evidence, even if it's just that no one at the time wrote anything down related to a story. $\endgroup$ – Logan M Dec 3 '14 at 22:39
  • $\begingroup$ Can anyone find something relevant in this link? I got it directly from a search engine. $\endgroup$ – HDE 226868 Dec 3 '14 at 22:52
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It seems incredibly unlikely that Gauss was (in a serious way) accused of witchcraft for his contributions to linear algebra. Instead of trying to look for anecdotal evidence, we can reason from general historical context.

Firstly, note that it is easily found on Wikipedia that witch-hunts were mostly a thing of the 17th century and before, and instances of serious accusations were a rarity after 1750. In particular, we find the quote

In the later 18th century, witchcraft had ceased to be considered a criminal offense throughout Europe.

Secondly, it turns out that 'Gaussian elimination' was, in fact, well known before Gauss even was born (more reading material by the same author can be found here). As the above paper shows, Newton already knew of, and described, the method of solving simultaneous linear equations that we now call Gaussian elimination. The work by Newton predates Gauss' birth by over a hundred years. The method was already widely taught to students before Gauss ever worked on it. It therefore seems quite ridiculous that Gauss would be accused of witchcraft for a mathematical method that had been known for over a hundred years (in the Western world; some sources argue that the technique had already been known for over a millennium by Eastern mathematicians).

So, the question arises: Why do we even call it Gaussian elimination? In the same paper by Grcar one finds a section arguing that there was little use for the method introduced by Newton, until the invention of the method of least squares... and that's where Gauss comes in:

It is not often that a mathematical discovery is immediately useful, as was the case with the method of least squares. And it was the method of least squares which finally created a recurring need to solve simultaneous linear equations. When a use for schoolbook Gaussian elimination finally arose, Carl Friedrich Gauss invented something better for the problem at hand.

Gauss' main contribution consisted of inventing a new (bracket) notation for the method, which was more convenient, and subsequently adapted by 'professional computers', i.e. human calculators. Note, however, that Gauss did not come up with the now universally used matrix notation.

From the second half of the 19th century onward, textbooks started referring to Gauss when treating what was then simply 'elimination'. In the early 20th century, it was realized that Gauss' method could be generalized to solving matrix equations in the way that we all know and love. Grcar also offers an explanation for the fact that the method is now (mistakenly) called Gaussian elimination:

The invention of electronic computers led to new university faculties for instruction in the new way of computing which drew people of diverse training to the field. They extrapolated opinions of its history from whatever heritage they knew. Geodesy at one time accounted for the bulk of the simultaneous linear equations that were solved professionally, so its terminology may have appeared to be authoritative.

The citations that precisely described the contribution of Gauss had already been shortened to an unspecific “Gauss’s procedure.” This usage was misinterpreted as attributing ordinary, common, schoolbook elimination to Gauss, but only after World War II. Von Neumann was apparently the last prominent mathematician to simply write 'elimination' as Lacroix and Gauss had done.

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