**Core Concept**
Progressive supranuclear palsy (PSP) is a rare neurodegenerative disorder characterized by progressive damage to the brain, particularly affecting the supranuclear gaze control centers, leading to difficulties in eye movements and balance. This condition often presents with a combination of cognitive decline, motor symptoms, and autonomic dysfunction.

**Why the Correct Answer is Right**
The patient's symptoms, including difficulty in downward gaze, ataxia, and frequent falls, are classic features of PSP. This is due to the involvement of the midbrain, particularly the rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF) and the superior colliculus, which are responsible for controlling vertical eye movements. The cognitive decline in PSP is often less pronounced than in Alzheimer's disease, and the patient's history of frequent falls is a significant clue to the diagnosis. Additionally, PSP is often associated with rigidity, bradykinesia, and postural instability, which are similar to those seen in Parkinson's disease, but the presence of supranuclear gaze palsy is a distinctive feature of PSP.

**Why Each Wrong Option is Incorrect**
**Option A:** Parkinson's disease is a common neurodegenerative disorder that presents with tremors, rigidity, bradykinesia, and postural instability, but it typically does not cause difficulty in downward gaze or supranuclear gaze palsy.

**Option C:** Alzheimer's disease is a progressive neurodegenerative disorder that affects cognitive function, memory, and language, but it does not typically cause difficulty in eye movements or balance.

**Option D:** While PSP is a rare condition, it is a distinct clinical entity that should not be dismissed as "none of the above."

**Clinical Pearl / High-Yield Fact**
PSP is often referred to as " Steele-Richardson-Olszewski syndrome" after the three neurologists who first described the condition in 1964. This is a classic example of a neurodegenerative disorder that requires a high index of suspicion for diagnosis.

✓ Correct Answer: B. Progressive supranuclear gaze palsy