Step 1: Frame the condition. Alzheimer's disease is a relentless, progressive brain disorder and the leading cause of dementia, marked by memory loss and confusion.
Step 2: Verify the true claims. Epidemiology supports about one in ten over age 65 being affected, and dementia is its defining clinical syndrome, so both are accurate.
Step 3: Expose the falsehood. Treatments such as cholinesterase inhibitors only temporarily relieve cognitive and behavioral symptoms; they neither stop nor reverse the disease. Therefore calling Alzheimer's curable is incorrect.
No cure exists, so the curable statement is the false one.\[\boxed{\text{Alzheimer's disease is curable}}\]