Karl Friedrich Gauss made many discoveries that he did not publish and that remained unknown until later mathematicians (re)discovered them. When Gauss's personal notebooks were later examined, it turned out that he had made the same discoveries decades earlier.

For example, in Visual Complex Analysis Tristan Needham discusses how Hamilton and Rodrigues were apparently the first to discover quaternions in 1843 and 1840, respectively. Only later did it turn out that Gauss had preceded them by more than 20 years. Needham writes:

"Hamilton and Rodrigues are just two examples of hapless mathematicians who would have been dismayed to examine the unpublished notebooks of the great Karl Friedrich Gauss. There, like just another log entry in the chronicle of his private mathematical voyages, Gauss recorded his discovery of the quaternion rule in 1819."

What other significant discoveries did Gauss make but not publish that were rediscovered by and attributed to later mathematicians?

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    $\begingroup$ It went the other way a number of times. For example, the proof of the impossibility of the trisection of the general angle by ruler and compass is often attributed to Gauss, but is in fact due to Pierre Wantzel. $\endgroup$ – André Nicolas Mar 6 '12 at 23:25
  1. Non-Euclidean geometry.

  2. Cooley-Tukey Fast Fourier Transform

Details readily available via websearch.

  • $\begingroup$ well, mentioning FFT understates Gauss' genius. Gauss' work on Fourier series itself, predated that of Fourier. $\endgroup$ – Chan-Ho Suh Apr 29 '17 at 17:30

The Gauss–Seidel method for solving systems of linear equations was described by Gauss as early as 1823, but he did not publish it. It was published by Seidel in 1874.


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