11
$\begingroup$

Carl 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"Hamilton and Rodrigues are just two examples of hapless mathematicians who would have been dismayed to examine the unpublished notebooks of the great Carl Friedrich Gauss.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?

$\endgroup$
1
  • 2
    $\begingroup$ 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. $\endgroup$ Mar 6, 2012 at 23:25

3 Answers 3

9
$\begingroup$
  1. Non-Euclidean geometry.

  2. Cooley-Tukey Fast Fourier Transform

Details readily available via websearch.

$\endgroup$
1
  • 2
    $\begingroup$ well, mentioning FFT understates Gauss' genius. Gauss' work on Fourier series itself, predated that of Fourier. $\endgroup$ Apr 29, 2017 at 17:30
2
$\begingroup$

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.

$\endgroup$
0
$\begingroup$

I knew Gauss did a lot of work on elliptic function but didn't publish anything, his work contained most of the key points of Abel and Jacobi's work. And it seems that he also touched some ideas of the modular function which are out of Abel and Jacobi's work. In fact, from some notes I read that the idea of ideal numbers created by Kummer is also from Gauss. Another work is the class number formula which is firstly published by Dirichlet. But Gauss has known this formula long ago. I think he should have a proof. He also has the proof of quartic reciprocity law which is published by Eisenstein. The only problems which I knew he didn't solve is the solution of 5 degree equations and the Fermat theorem. But at that time he hasn't focus on math. So from all these, we can feel that Gauss has a unbelievable insight into mathematics. One of the most genius man in history.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .