The links between aluminium cookware and Alzheimer's are inconclusive. From your article:
It can migrate to food from cookware and packaging materials such as foil and cartons. One study found that around 20 per cent of aluminium in the diet came from the use of aluminium cookware and foil, according to the Food Standards Agency. Tomatoes, rhubarb, cabbage and many soft fruits should not be cooked in aluminium pans, it says.
Older studies into the relation between aluminium and Alzheimer's have shown that aluminium has neurotoxic effects. A direct link between aluminium exposure and contracting Alzheimer's was only found recently:
Overall, these results suggest very strongly that occupational exposure to aluminium contributed significantly to the untimely death of this individual with Alzheimer's disease.
Now inhaling aluminium dust through a dust mask is a lot different from cooking in aluminium pans, but I won't say the link is weak at best.
This remains very difficult to study, due to the long-term effects, and unfortunately also due to little funding and pushbacks from the aluminium industry itself.
Aluminium cookware has some advantages - especially for very large pans.
And if you're worried about aluminium using different pans is only removing a small amount from your lifestyle - it's used everywhere. http://www.telegraph.co.uk/health/9119528/Is-aluminium-reall...