Sir William Taylor of Norwich
The expression “mathematical nudity” appears on p. 144 of Mathematics without Apologies. Google tells me it was used once before, in a letter of Sir William Taylor to Robert Southey, dated August 16, 1799, in this sentence:
The rival partisans of the different possible theories appear to me, like dogmatizing sectaries, not always to wield with equal skill the weapons of controversy; not always to construct their technology with equal philological precision; not always to lay snares for phaenomena with a readiness equally inventive, or to syllogize with the same mathematical nudity of language but always to consider truth both as their pursuit and their possession.
The “different possible theories” to which Taylor refers are the phlogiston theory, the oxygen theory, and two other theories of “combustion, respiration, &c.” Taylor kept busy with his studies of electricity and light (he thought they were both acids) and with his “left-handed reading of the cabbalistic squares.” He asked Southey whether he thought it was plausible to “translate a text or two in the Bible” to help him establish a chronology of Persian emperors; I have not been able to determine whether or not he found mathematical nudity there.