Articles like Gout May Protect Against Alzheimer's Disease have been around for quite some time. Indeed there's plenty of evidence for the protective effect of gout, or rather, uric acid, on Alzheimer's disease. I just want to point out that there does exist conflicting evidence from other researches, such as this 2-page report, No association between gout and Alzheimer's disease: results of a case–control study in older people in Taiwan(Int J Geriatr Psychiatry 2013; 28: 1205-1206). In case you can't read it, here's one passage (emphasis added):
Both studies [in Italy and Portugal] have conveyed the message that high level of uric acid may increase the risk of Alzheimer's disease. In this present study, we found that no association is detected between gout and Alzheimer's disease in both gender, whether gouty patients had ever used urate-lowering drugs or not. Because conflicting results exist, further studies are required to confirm the association between gout and Alzheimer's disease.