There are lots of ways to design chips, and almost everyone uses synthesis. But not for CPUs. For CPUs, almost everyone uses synthesis, but the people who design the best chips tend to use it for as little as they can get away with.
The idea is that your architects write a description of the chip’s logical behavior in a synthesizable language (typically verilog, but other possibilities include VHDL, various C++ or C varieties, etc.)
So they may say something like:
A[8:0] = B[8:0] + C[8:0]
to create an 8-bit adder. Then, with synthesis, your logic designers would plunk all that into a “synthesis tool” (almost always from a company called Synopsis) to dump out a netlist (which lists the logic gates to be used and how they are wired together).
Then your physical designer takes that netlist and lays it out to create the chip mask. (Typically using automated place-and-route tools, often from a company called Cadence)
That’s not at all how I ever did it at any of the three companies I worked at.
We always “hand-synthesized” the logic. And hand placed the gates. And hand-routed at least some of the wires.
Because we were real men (even the women!)
I mean, one time I literally loaded the mask into vi and edited two wires on the day of takeout. Did I mention I’m very manly?