As is widely known, Alan Turing discovered/invented the Turing Machine in his classic 1936 paper. Here he also gave how these machines are specified in terms of their machine states and instructions on how they operate. Is there any official or widely accepted name for this "first" mathematically defined programming language$^*$ $L$ that consists of a specification of a Turing Machine together with its transition function? Clearly by definition this language is Turing complete and hence can simulate any other algorithmic programming language. For instance here would be how program of $L$:
//Some specification of the machine $M$'s states, initial state, final state, allowable tape symbols, blank tape symbol, etc.
<0, 0, 1, R, 2> // If $M$ is in state 0 and sees a 0, then write 1, move right, and enter state 2
<2, 0, 0, R, 3> // If $M$ is in state 2, sees a 0, then write 0, move right, and enter state 3
<2, 1, 0, L, 3> // etc
*By first mathematically defined programming language, I'm ignoring for the moment innovations like automated loom printing or natural programming languages like DNA/RNA which are definitely algorithmic, and instead focusing on a particular strand of algorithmic specification that most closely matches what is commonly thought of as a programming language today. There are also other mathematically defined systems that were shown to be Turing equivalent around the same time as Turing, but none of these really caught on in terms of influence as Turing machines and their programming language did.