As mentioned in the article, several scientists have (apparently) uncovered math errors in Mallett’s calculations. Even ignoring those, there’s always been the problem of translating math (however robust it might be) into engineering - to actually
build a device that has a chance of working. For instance, there’s something called the “Tipler cylinder.” This is a cylinder that’s so gigantic that when it spins, it drags spacetime around with it. So it could, in theory, function as a time machine. The problem is, the cylinder would have to be infinitely long - which is a bit of an obstacle to practical construction.
Finally, most “realistic” models of time travel are constrained by the spacetime geometry created by the machine, itself. This means that backward travel can only go as far back as the point when the machine was created. So with such a device, you
could travel to the future and then
return to the present. But you
couldn’t visit the dinosaurs or assassinate a young Adolf Hitler.