"Bob Powell"

OP
Can anyone here point me toward an authoritative history of hex head nuts and
bolts? I see square nuts and bolts in old
machinery and tools in museums, but I don't think I've seen
a hex head nut or bolt in anything built before 1900.

Bob
Hex stock had so many obvious advantages ... far more efficient use of
material to turn a bolt from bar stock ... less waste, far less machining
time ... ditto for simpler box wrenches, sockets etc. Less stress on
the box wrench corners, also more compact. Reckon it became the norm
pretty much as soon as the mills became capable of making it.

None of this applies to hot-forged or cold-formed bolt heads, and rolled
threads, that represent virtually all the common fasteners today. But there
was a long period where all machine screws and bolts were turned from hex
(or square) stock.

As Bob points out, all you need to make a hex-headed bolt or a hex nut is hex
stock. Part of the problem here is in the question. Most simple mechanical
devices do not have an original attribution, to a person or even to one
industry.

I don't have any really good early cites, but hex-headed bolts and nuts were
common in some applications in Western technology by at least mid-nineteenth
century. The oldest tradition probably comes out of hot forging with a header
(nail and bolt headers are common). But machinery for making screws was also
well developed by the 1840s. (I'm not talking about "screw machines," but about
machinery for making screws, such as bolt cutting machines and nut tapping
machines. Screws with tapered points show up, for example, about that time.)
Index milling machines for milling the sides of nuts and bolt heads are also in
evidence from about then--at least by the 1860s, in the U. S.
At the same time, much classic machinery, such as the common engine lathe,
retained the use of square-headed bolts/screws, more as part of the style than
not, I think, throughout most of the 1800s. Machine builders were conservative,
and would want to fulfill the buyer's expectations as to what the product
should look like, work like.

Frank Morrison