Q. Is it better when not legally necessary to avoid using the Gregorian calendar and use the Hebrew date, or it does not matter today anymore since it is globally used as a civil non-Christian calendar?
A. Some Poskim maintain one may incur even a Biblical prohibition in the use of the Gregorian date (Maharam Shik Y.D. 171., Chasam Sofer – Droshos: Teves: 5593). Consequently, they add to the civil date the word L'misparam, or to "their counting", connoting that we agree to a different reckoning (ibid., Mishmeres Sholom – Smochos 40: 84.) We indeed find numerous quotations of the civil date in diverse s'forim with the above addition (Tshuvos Remoh 51, Shvus Yakov 3:11, Chavos Yoir 184, to mention a few.)
Ramban (Shemos 12: 2) mentions another prohibition and that is using a different numerical count for the months than the one established by the Torah, where Nisan is the first of the months.
Horav Shlomo Miller's Shlit"a opinion is to be lenient when necessary as in legal forms and documents, since today the civil date does not carry religious connotations. (See next answer)
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a
Important Numbers
