In an NYT op-ed (a dicey place to get nutrition advice, but we'll go with it for the moment), Mark Bittman asks, Is Alzheimer's Type 3 Diabetes?
Bitman's question is based on a cover story in New Scientist (available for free but annoying download here) on research on the way that the brains of rats and rabbits brains respond to insulin. By using drugs or diet to interfere with these animals' insulin metabolism, researchers have been able to generate Alzheimer's-like changes in their brains, including a telltale rise in beta-amyloid proteins.
The usual disclaimers about animal research apply -- not only are there ethical difficulties in experimenting on animals, but results don't always carry across species. Is there any evidence that this is relevant to humans? Yes. Steven Arnold of the University of Pennsylvania took brain samples from human cadavers and soaked them in insulin. The samples from people who has not had Alzheimer's responded strongly, showing an insulin response; those from Alzheimer's patients showed little response, showing a resistance to insulin signaling.
If Alzheimer's is "type 3 diabetes", then it's possible that plant-based diets may have the same prevention and management benefits for Alzheimer's that they have for diabetes. (See here for a good summary, and here and here and here and here and here for studies.) Exercise also helps, as does avoiding endocrine disrupting chemicals such as BPA.