Less than versus fewer than

I completed my Doctoral Degree in less than four years.

I completed my Doctoral Degree in fewer than four years.

Both are grammatically correct. However, using "fewer" here is quite unlikely.

Since you already now that "less" is for uncountable nouns and "fewer" is for countable nouns, it should be simple to see how those can modify the word "year".

When "less" is used, the time to complete the Doctoral can be anywhere between 0 and 4 years, like 3 years + 6 months, which is 3.5 years.

When "fewer" is used, it means the number of years should be an integer or whole number. Here, it can be 0, 1, 2 or 3 years. "3 years and 6 months" is 3.5 years, which isn't an integer number of years, and should go with "less" instead of "fewer".

Yes, both are correct although the former is far more likely.

In less than four years means than in less than this amount of time.

In fewer than four years, which is much less common, means in not as many years.

It comes down to whether you are regarding the time involved as a continuum or as individual years. The same principle applies where other measures such as weights or volumes are concerned.

https://books.google.com/ngrams/graph?content=less+than+four+years%2Cfewer+than+four+years