Have there have been any interesting cases of one person stealing another mathematician's results and publishing them as his own? In particular, are there any interesting cases of this happening in the late 1800s or early 1900s?
There is the story of the "ergodic theorem". Young mathematician John von Neumann proved the so-called "mean ergodic theorem". He wrote it up and sent it to the Proceedings of the National Academy of Sciences. It was reviewed by one of the editors of the Proceedings, senior mathematician G. D. Birkhoff. In due course, Birkhoff recommended publication. It appeared in 1932. Meanwhile, inspired by von Neumann's result, Birkhoff worked furiously for a few months and obtained an improved result, the so-called "pointwise ergodic theorem". He had it published in the same journal. It appeared in 1931. Birkhoff's paper made no mention of von Neumann's paper. Only many years later, in a paper with Birkhoff as co-author, was it admitted that von Neumann had the priority.
A famous case from this time period concerns priority dispute between Hilbert and Einstein over the deriving the field equations of general relativity. Hilbert completed the general theory field equations "at least 5 days before" Einstein submitted his final paper in 1915, Einstein accused Hilbert of "nostrifying" him.
The word is interesting, "nostrification" officially means adoption of a foreign diploma, here it is applied to adoption of ideas. Borrowing chords is accepted in music, for example, and is even considered a boon to creativity. Van der Waerden characterized “nostrification” in 1930 as "reformulating other people’s best ideas with increased sharpness and generality, and from then on citing the local reformulation". But the line between that and plagiarism is not bright, Einstein was very unhappy. Corry writes in David Hilbert and the Axiomatization of Physics that the practice was widespread in Hilbert's Göttingen:
"It was widely understood, among German mathematicians at least, that “nostrification” encapsulated the peculiar style of creating and developing scientific ideas in Göttingen, and not least because of the pervasive influence of Hilbert. Of course, “nostrification” should not be understood as mere plagiarism. It was a central trait of a hectic scientific culture that stimulated an intense and sustained interaction between professors, young docents, and students, across departments and across universities. The Göttingen atmosphere implied a constant discussion and adoption of new ideas, techniques, and problems that had originally been created or suggested by others, either at home or outside. Whenever these ideas appeared to be fruitful and relevant to current concerns of the local community, they were immediately absorbed into the common scientific patrimony."
Weyl, for example, rediscovered the axioms of a vector space in 1918 without citing Peano's 1898 version, but, perhaps, he did not know. In Grundlagen der Geometrie "Hilbert “nostrified” much of the contributions of the Italian school, and the only work he explicitly referred to was that of Veronese". As for the dispute with Einstein, printer's proofs of his paper found by Corry in 1997 seem to back Einstein's opinion, at least in that Hilbert did not beat him to it. The version of the paper submitted "at least 5 days before" did not contain the correct equations. Einstein and Hilbert patched things up quickly, even before the publication. Einstein wrote in a private letter:
"There has been a certain resentment between us, the cause of which I do not want analyze any further. I have fought against the feeling of bitterness associated with it, and with complete success. I again think of you with undiminished kindness and I ask you to attempt the same with me. It is objectively a pity if two guys that have somewhat liberated themselves from this shabby world are not giving pleasure to each other."
Hilbert, after some meandering, added to the printed version of his paper a reference to Einstein’s paper and a concession of his priority. But the "Hilbert first" story continued to circulate widely. Here is from the Belated Decision in the Hilbert-Einstein Priority Dispute by Corry, Renn and Stachel (1997), where Corry's find was reported and analyzed:
"According to the commonly accepted view, David Hilbert completed the general theory of relativity at least 5 days before Albert Einstein submitted his conclusive paper on this theory on 25 November 1915. Hilbert’s article, bearing the date of submission 20 November 1915 but published only on 31 March 1916, presents a generally covariant theory of gravitation, including field equations essentially equivalent to those in Einstein’s paper. A close analysis of archival material reveals that Hilbert did not anticipate Einstein. The first set of proofs of Hilbert’s paper shows that the theory he originally submitted is not generally covariant and does not include the explicit form of the field equations of general relativity.
[...] Both the proofs and the final version of Hilbert’s first communication (3) are dated “submitted on 20 November 1915,” presumably referring to the original manuscript. A copy of the proofs, preserved in his archives and marked in his own hand “First proofs of my first note,” bears a printer’s stamp dated 6 December 1915 (Fig. 1). However, the cover of the issue in which the heavily revised published version appeared is dated 31 March 1916. Its first note cites Einstein’s conclusive paper, in which he reached the final form of his generally covariant theory (11), submitted on 25 November 1915 and published on 2 December 1915. Thus, Hilbert could have revised his paper in response to Einstein’s work. Differences between the proofs and this published version of Hilbert’s paper confirm this view.
[...] To summarize: Initially, Hilbert did not give the explicit form of the field equations; then, after Einstein had published his field equations, Hilbert claimed that no calculation is necessary; finally, he conceded that one is. Taken together, this sequence suggests that knowledge of Einstein’s result may have been crucial to Hilbert’s introduction of the trace term into his field equations."
No. The question is badly conceived and phrased. You cannot 'steal' a result and proving the theft is unconvincing. There is a sensible difference between a priority dispute and crime. It was not the Facebook Age and people were more interested in valid results and not in the person behind them. Objective validity is impersonal and, except for taking out papers from somebody's drawer, stealing is a metaphor. There might have been bad feelings and rivalities but it is obvious that accusations are hard to prove. Freeman Dyson recounts about Feynman saying (see)he was
"Always giv[ing] the bastards more credit than they deserve."
(Of course this not how Einstein felt, nor his hagiographers. But that seems to be the spirit that prevailed then in science and mathematics)