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Question:

I mean — where does this convention come from?

Screws themselves have either a #numeric value or a fractional value. This refers to shaft of the screw. But what of the head and the tools used on them?

Answer:

According to Fastener Engineer, Lee Dougan of the Phillips Screw Company:

. . . The original Phillips Screw driver bit goes back to the 1930’s. But prior to the invention of the Phillips® cruciform drive system, Robertson invented the Robertson® Square drive which was a marked improvement over the conventional slotted drive system that had been around for centuries. These drive systems were designated #0, #1, #2, and #3.

A #2 Phillips driver bit is approximately the same size that would fit into the equivalent screw head that would use a # 2 Square. Similarly, the #1 Phillips and #1 Square fit into similarly sized screw heads. So I think that is where the Phillips Screw designation came from. (It) takes you back to the Robertson square designation. A simple numbering system is an easy way to distinguish similar looking parts. It may be as simple as that . . . .

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Note from the Host

Please read below in the Comments section for the complete journey to our best answer above. I welcome continued discussion on this. A follow up post of sorts, here >> The Skinny on Screws :: A Guide to Common Screws.  

Screws are one of the wonderous Six Simple Machines. More on all of them there. Thanks. ~jb @BuildingMoxie