He is also known for his consulting and advocacy on behalf of alleged victims of statistical misrepresentation, including the reversal of the murder conviction of a Dutch nurse who had been jailed for six years.

[1] He obtained a Ph.D. in mathematics in 1979,[2] with the thesis Censoring and Stochastic Integrals,[1] which was supervised by Jacobus Oosterhoff and Carel Scheffer [nl] of the Vrije Universiteit, which awarded the doctorate.

[3] Gill has said that he was "not much of an activist" as a student, but now feels guilty about not speaking up more at the time about perceived injustices, saying that this is partly because of an incident when working as a statistician in the 1970s when he helped on an experiment that severed the front legs of rats to investigate whether it would lead to the reshaping of their skulls.

[6] After receiving his Ph.D., he continued to collaborate with Danish and Norwegian statisticians for ten years, co-authoring Statistical models based on counting processes, by Andersen, Borgan, Gill, and Keiding.

[1] Gill has lobbied for retrials for nurses whose criminal convictions were based in part on statistical evidence, including Lucia de Berk and Benjamin Geen.

[14][15][16] After a campaign in which Gill helped, a retrial was ordered and de Berk was found not guilty; she received a public apology from the Dutch government, which also began negotiating financial compensation.