Acuteness, n.
1. The quality of being acute or pointed; sharpness; as, the acuteness of an angle.
2. The faculty of nice discernment or perception; acumen; keenness; sharpness; sensitiveness; -- applied to the senses, or the understanding. By acuteness of feeling, we perceive small objects or slight impressions: by acuteness of intellect, we discern nice distinctions. Perhaps, also, he felt his professional acuteness interested in bringing it to a successful close. Sir W. Scott.
3. Shrillness; high pitch; -- said of sounds.
4. (Med.)
2 more senses
Violence of a disease, which brings it speedily to a crisis.
Syn. -- Penetration; sagacity; keenness; ingenuity; shrewdness; subtlety; sharp-wittedness.
Shades of meaning
Fernald has no entry of its own for acuteness; he lists it under acumen.
Where he writes about it:
Sharpness, acuteness, and insight, however keen, and penetration, however deep, fall short of the meaning of acumen, which implies also ability to use these qualities to advantage. — from acumen
We speak of the acuteness of an observer or a reasoner, the insight and discernment of a student, a clergyman, or a merchant, the sagacity of a hound, the keenness of a debater, the shrewdness of a usurer, the penetration, perspicacity, and acumen of a philosopher. — from acumen
The astute mind adds to acuteness and keenness an element of cunning or finesse. — from astute