As silly as this sounds, I can't find a proof that the axiom of dependent choice (DC) does not imply that the reals are well-orderable. My memory is that this is a fairly early result in the history of independence proofs in set theory. So, my question is twofold. First, the history part:
When/by whom was it first proved that DC does not imply that the reals are well-orderable?
Second, the mathematical part:
How does the proof go?
(To be clear, I am looking for a proof that $ZF+DC+$"the reals are not well-orderable" is consistent relative to $ZFC$; I am not interested in proofs which require assumptions of extra consistency strength. For example, both $AD$ (which implies that the reals are not well-orderable) and $DC$ are consequences in $L(\mathbb{R})$ of large cardinals, so this gives a relative consistency proof from large cardinals - but that's not what I'm looking for.)
The first proof is by Solomon Feferman. It was published as an abstract in 1964:
As for the original proof, I don't know if it were ever published in full. Going through another paper of Feferman from that year which dealt with forcing, I can tell you that the methods are not pretty and completely unclear to anyone who didn't sit to study the original forcing papers in depth (not just Cohen's, but also the ones that were immediately published after that).
Added:
Truss published a generalization of Solovay's argument, as well as Feferman's argument (from the second paper, not the citation in the first part) in which he investigated models of $\sf ZF$.
The discussion on the Feferman-type of construction begins after Lemma 2.2, and continues until the end of the second section.
The construction, essentially is adding $\kappa$ many Cohen reals (finite functions from $\kappa\times\omega$) say $x_\alpha$ for $\alpha<\kappa$. Then considering the model generated by the sequences of $\langle x_\alpha\mid\alpha<\beta<\kappa\rangle$.
In terms of symmetric extensions this is the same as taking permutations of $\kappa$, applying them in the obvious way, and considering the ideal of bounded supports for generating filter. Moreover, this symmetric extension contains all the real numbers of the full generic extension, since every Cohen real is forced by a countable subforcing.