The validity of this claim is highly dependent on your definition of "solution".
If the "solution" is for the waste to magically disappear with no trace at zero cost, then that is indeed impossible, but that's also an unreasonable definition of a solution.
Four projects seem to have succeeded, for example, the Waste Isolation Pilot Plant in USA is already operating and began accepting military transuranic waste in 1998. Two other projects, the planned final storage facilities at Gorleben in Germany and Yucca Mountain in the USA, were cancelled or put on hold indefinitely.
The extremely long lifes of waste are usually obtained due to a misapplication of a rule of thumb for short-lived isotopes, which says that a sample is no longer radioactive after 10 half-lifes.
Certain designs of reactors that are not cost effective yet, but known to be practical, can reuse high level waste as fuel, because it still contains around 95% of its energy.
Two of them are already operating in Russia and Japan.These were the two repositories for intermediate and low-level nuclear waste (e.g.not spent fuel) that were built in Germany: Asse II and Morsleben.Currently it's uneconomical on its own as means of producing more nuclear fuel, but makes sense from a long-term waste management perspective.The anti-nuclear movement opposes reprocessing, because it believes it could lead to more nuclear proliferation (see further below) and that it pollutes the environment with radioactivity (wrong).But it's also the public that stages and participates in those protests.When you divide world reserves of uranium by the current consumption, you get about 70 years as the time horizon for uranium depletion.However, there is no reason to believe this problem is insoluble.Here are some claims made by the anti-nuclear movement in reference to the waste issue.It does not necessarily reflect the views expressed in Rational Wiki's Mission Statement, but we welcome discussion of a broad range of ideas.Unless otherwise stated, this is original content, released under CC-BY-SA 3.0 or any later version. Feel free to make comments on the talk page, which will probably be far more interesting, and might reflect a broader range of Rational Wiki editors' thoughts.