So when <c___> showed up it was because they imported some other header, but made it so in practice it was similar to the use of <___.h>? If it wasnt already there already (which you said <cmath> has been around since the beginning) So what about <iostream>? it uses namespaces now, and has cout and stuff, so its an "import" too? when did they do that.. was it somewhat 4 years ago? or further back and people just didnt notice when they were making C++ books.
The CRT headers were "imported" into the C++ standard by removing the .h and prepending a c. The new C++ headers simply were created without a .h, as far as the standard is concerned. In practice, many of the C++ headers were headers that older compilers commonly used, with the .h removed.