Well, I know I can multitask - for example, I can sometimes talk and think at the same time (plus, I could also be doing the work of sitting)..
Proving a negative (ex. “One can never multitask”) versus proving a positive are two widely asymmetrical efforts. The burden of proof that something does not exist vs that something does exist is infinitely greater. Proof of existence has to demonstrate ONE occurrence to satisfy the proof. Proof of non-existence requires evidence that under every possible scenario, a given event or phenomenon cannot occur.
Bertrand Russel’s china teapot analogy is a perfect example. Essentially, he postulates that if “between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense.” If someone can produce a single photograph from a continuous video of the universe where the teacup is floating, you will have solid proof. Otherwise, you can’t say it does not exist, however absurd the idea seems. For example, I do not believe for a moment that humans can live forever (as Ray Kurzweil hopes), or that all human diseases can be cured, but I can’t prove it. Maybe a “flash card” of an individual’s brain with all its memories could be made in the future and implanted into a new organic or inorganic life form, effectively producing a form of immortality? These are all interesting questions to ponder. Denial of denial is another interesting philosophical dilemma.