Less or Fewer?
Which of these two sentences is correct?
His troubles are less than mine
His troubles are fewer than mine
The answer is, it depends on whom you ask. According to Strunk and White, "less" refers to quantity and "fewer" refers to number. "His troubles are less than mine" mines "His troubles are not so great as mine." He has a lower quantity of troubles than I do. If you are referring to number, you should use "fewer", as in "His troubles are fewer than mine." This means "His troubles are not so numerous as mine."
This is one time where Strunk and White have fallen behind the times. We no longer draw distinctions between quantity and number as such, especially in scientific writing. The distinction depends only on whether the noun modified by less/fewer is a mass noun or a countable noun.
Mass Nouns vs. Countable Nouns
Another way to think about the question is to consider whether the noun being modified is a mass noun or a countable noun. A mass noun is one that you cannot assign a number to, and is never constructed in the plural (e.g., "air"). Mass nouns take the definite article "the", never the indefinite article "a, an". A countable noun is the opposite: you can assign a number to it, you can construct plurals and you can use the indefinite article (e.g. "a dog", "two dogs").
The adjective "less" modifies mass nouns
The adjective "fewer" modifies countable nouns
A few examples:
There is less money in the bank than there used to be ("money" is a mass noun).
There are fewer bills in my wallet than there used to be ("bill" is a countable noun).
A little less conversation, a little more action, please (apologies to Elvis, but it's a great example: "conversation" in this context is a mass noun, although it can be a countable noun in other contexts).
When we will have less dog, we will have fewer fleas. This is a literal translation of the French saying "Quand nous aurons moins de chien, nous aurons moins de puces". The meaning of the saying is that when you have fewer things, you have less to worry about (see what I did there?). Notice that in French, their is only one word (moins) for "less" or "fewer". In English, we need to ask whether the noun modified is a mass noun or a countable noun. Whereas "dog" is usually a countable noun, in this (metaphorical) context, we are talking about a generalized dog (i.e., a problem). "Fleas" here is a countable noun.
OK, Dr. Lindeman, how come the sign in the supermarket checkout line says "10 Items or Less"?
In other words, shouldn't the sign say "10 Items or Fewer"? Yes, it should. This is a historical artifact. When English was a new language, circa 1066 AD, the ancestor to the word "less" was all we had, and we used it for both countable and mass nouns. "Few" was incorporated into English later. Old habits die hard, and the old usage still sounds correct in the ears of many English speakers.
It Gets Tricky, Though
For writers of scientific articles, there are some tricky areas you need to be aware of.
Weight
Even though we express weight in countable units, we often refer to weights as mass nouns. For example:
"Panda bears weigh less than 200 grams at birth".
"The average control group weights were consistently less than 75 kg."
Time
Even though we count time in countable units, the units can sometimes function as mass nouns. For example:
"Jane has been at her job for less than 5 years." (note that I used the numeral 5 instead of the word "five", but that is a discussion for another post).
"James had less than 5 seconds to defuse the bomb".
Percentages
This one is really tricky. To decide whether to use "less" or "fewer", you need to ask yourself the question "a percentage of what?". In other words, is the whole a countable or mass noun? For example:
Fewer than eight percent of the world’s people have blue eyes. ("People" in this context is a countable noun, so we use "fewer")
The animals ate less than ten percent of their rations. ("rations" in this context is an mass noun, and therefore takes "less")
More Troubles
So, to return to our initial example, the correct answer is "His troubles are fewer than mine", because "troubles" in this context is a countable noun. One can have more than one trouble at a time, unfortunately.
I hope that this post has helped reduce your troubles, at least by a factor of one.
If you still have troubles, though, particularly with getting your scientific paper published. I can help.