The Doctor's exact age has long been a point of contention among fans of Doctor Who, but one episode of the classic series suggested a solution. Rather than having lost count or lying about their age, the various versions of The Doctor may have simply employed different standards of measurement to describe the time they had lived.
The question of The Doctor's age has been debated by fans of Doctor Who since the show's earliest years. When the original series came to a close in 1989, the Seventh Doctor was somewhere past 953 years old (the age the Seventh Doctor claimed in his first appearance) yet the Ninth Doctor said he was 900 years old in his first appearance as the New Who era began. The debates have become even more intense in the wake of season 12 and the revelation that The Doctor was a being known as The Timeless Child; an immortal of indeterminate age who was the true source of the Time Lords' regenerative powers.
Various solutions have been suggested by different Doctor Who showrunners. The most common explanations for any discrepancies in The Doctor's age are that The Doctor had been lying about their age out of vanity or that they had become so old that it is all but impossible for them to keep track. The Eleventh Doctor admitted to both possibilities in "The Day of The Doctor", replying that he was "Twelve hundred and something, I think, unless I'm lying. I can't remember," when the War Doctor asked him his age.
Surprisingly, an actual solution was offered in the Second Doctor episode "Tomb of the Cybermen," where the Second Doctor was asked his age. After taking a moment to think, the Second Doctor replied that "if we count in Earth terms, I suppose I must be about... four hundred and fifty years old. " The qualifier "in Earth terms" is the key distinction, as the term "year" refers to the amount of time it takes a planet to complete one revolution around the star it orbits and the length of a "year" varies from planet to planet. This means that a year on The Doctor's homeworld of Gallifrey could be shorter or longer than a year on Earth, much like how a year on Mercury is the same length as 88 days on Earth or a year on Neptune is the same as 165 years on Earth.
Without a standardized constant year as defined by the Galactic Federation or some other central authority, there's no way to know if The Doctor was measuring their lifespan according to Earth years or Gallifreyian years when giving their age, except in those rare cases (as in "Tomb of the Cybermen") where a specific standard of measurement was noted. This would explain one of the major inconsistencies in the classic series, where the Third Doctor claimed to have lived for "several thousand years" in both "Doctor Who and The Silurians" and "The Mind of Evil." Assuming that Gallifrey had a faster rate of revolution than the Earth, The Doctor could have been truthful in both instances; by the standards of Gallifrey, he could be thousands of years old while still being hundreds of years old in Earth years. While it's certainly easier for the current crop of Doctor Who writers to say he was lying or lost count, it seems truer to the spirit of the show to think that, as with all things tied to time, everything is relative.