Cancer and Alzheimer’s disease are two of the most feared diagnoses in medicine, but they rarely strike the same person. For years, epidemiologists have noticed that people with cancer seem less likely to develop Alzheimer’s, and those with Alzheimer’s are less likely to get cancer, but nobody could explain why.

A new study in mice suggests a surprising possibility: certain cancers may actually send a protective signal to the brain that helps clear away the toxic protein clumps linked to Alzheimer’s disease.

Alzheimer’s is characterised by sticky deposits of a protein called amyloid beta that build up between nerve cells in the brain. These clumps, or plaques, interfere with communication between nerve cells and trigger inflammation and damage that slowly erodes memory and thinking.

In the new study, scientists implanted human lung, prostate and colon tumours under the skin of mice bred to develop Alzheimer‑like amyloid plaques. Left alone, these animals reliably develop dense clumps of amyloid beta in their brains as they age, mirroring a key feature of the human disease.

But when the mice carried tumours, their brains stopped accumulating the usual plaques. In some experiments, the animals’ memory also improved compared with Alzheimer‑model mice without tumours, suggesting that the........

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