Sharp, keen, acute can all mean having a fine point or edge, but it is in several of their extended senses that they are most likely to come into comparison.
As applied to persons or their qualities, especially of intellect, all three can indicate possession of alert competence and clear understanding. In such use sharp is likely to suggest an incisive self-centered quality, sometimes manifest in alert rationality, sometimes in devious cunning.
Keen (see also EAGER ) usually stresses eager enthusiasm, clear-sightedness, and quick penetrating character of mind, but it may imply no more than shrewd astuteness.
Acute (see also ACUTE ) may come close to keen in implying a penetrating quality of mind but it is more likely to stress sensitivity and depth and effectiveness of perception especially in the making of subtle distinctions.
As applied to something perceptible through the senses sharp often suggests a disagreeably cutting or biting quality or it may emphasize distinctness or clearness of definition.
Keen, in contrast, may suggest a bracing, zestful, or piquant quality.
Acute, less common in this sense, may impute an intensely perceptible and often distasteful quality to what it qualifies.
As applied to the senses themselves, all imply exceptional functional efficiency and choice is predicated on idiom; thus, sharp is used especially of sight and hearing, keen, of sight and smell, and acute, of hearing. As characterizing pleasures and pains, sharp suggests most definitely something that seems to cut or pierce, keen implies intensity, and acute implies poignancy.