Minerals such as zircon are routinely used by geochronologists to confidently provide the U-Pb and Pb-Pb ages which underpin the conventional multi-millions-of-years' timescale. These dating methods and the underlying assumptions are reviewed. The recognition of Pb loss from minerals after they form to explain discordant dates has resulted in the demonstration that both U and Pb mobility can occur in them. But how much U and Pb have been mobilized and how far they have migrated cannot be known with certainty. The radiation released by U decay damages crystal lattices and volume expansion generates micro-fractures, providing preferential pathways for U and Pb migration. Heat aids U and Pb mobility, but also causes recrystallization and defect recovery, locking migrated U and Pb atoms into their new locations. The current locations of U and Pb atoms within minerals can be studied at the atomic level. But there can be no certainty as to whether those atoms have always been in those locations, or whether they have migrated there. Also, there is no way of knowing what and how much migration happened in the past. Thus, even if the outer portions of crystals are removed before isotopic analysis and the U-Pb ages obtained for the cores of crystals are concordant, there can be no certainty that they represent the dates when the crystals formed. These uncertainties are compounded by the underlying unprovable assumptions on which the radioisotope dating methods are based, especially the assumption of time-invariant decay rates, built on the foundation of an assumed deep time history. The resultant U-Pb and Pb-Pb ages obtained are thus subjective, even though geochronologists take numerous precautions to make the U-Pb and Pb-Pb methods still have a strong semblance of validity. Nevertheless, since the amount of U and Pb mobility in most cases has been small, then the determinations can be used to provide useful relative ages. Thus, those absolute ages cannot be used to dismiss the history of the earth and its chronology provided in God's infallible Word.