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Is "thousands of thousands" grammatically correct? Why does it seem that "thousands upon thousands" sounds better, even though the former is closer to the logical truth? Is there any difference at all?

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The answers by AUAnonymous and pavium hit on the crux of the matter. I might also add, that to me "thousands upon thousands" has a stronger connotation of compounding, and possibly even of indefinite thousands. I would be inclined to use the former in a literal sense and the latter in a more figurative sense. – Brendon Jul 14 '11 at 7:18
I have never heard "thousands of thousands". Only "thousands upon thousands" and "thousands and thousands". – tenfour Jul 14 '11 at 13:54
@tenfour The phrase "thousands of thousands", is in the King James Bible. It means "Millions". – TecBrat Feb 15 '13 at 13:57

I realize this is an English language question site, but to answer this question in terms of math:

"Thousands of thousands" = 1000 x 1000 (or more)
"Thousands upon thousands" = A x 1000 (where A is any relatively small number)

So in simple terms, "thousands of thousands" is a lot more than "thousands upon thousands", although I do agree with you the latter does sound better.

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Well, actually your first equation should be X * 1000 x 1000 where X is greater than 1. But, strict math aside I think this would be a normal interpretation of of. Consider an easier example like "5 bags of 5". Or consider expressions like "the 3rd daughter of the 5th son". So I would say of tends to always refer to multiplication or sets of some kind. – edA-qa mort-ora-y Jul 14 '11 at 7:59
nitpicking version: m x 10^3 x n x 10^3 vs m x 10^3 + n x 10^3 where m, n ∈ {2,3,4,5,6,7,8,9} – Unreason Jul 14 '11 at 13:55

To my ear, thousands upon thousands could just mean "several thousands" or "many thousands".

I've never understood it to mean thousands of thousands, which would amount to millions — which the speaker would probably use, if that was meant.

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the main reason for thousands of thousands is that the concept of millions is only good for abstract readers and conceptual thinkers, where much wider audience has direct experience with thousands, so 'thousands of thousands' can be more easily imagined compared to millions. – Unreason Jul 15 '11 at 12:59

To my ears, thousands of thousands is a really large number (possibly a million) at a specific moment (as already indicated in other answers)

However, thousands upon thousands might imply a progress in time: a thousand followed by another thousand later followed by yet another thousand even later and so on.

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Thousands upon thousands is an undetermined number. Rather than multiplying which would be the case with the word "of" as in thousands of thousands we instead have thousands upon thousands which would indicate adding thousands upon thousands.

With thousands upon thousands we only know that the thousands are plural so the lowest number would be two thousand plus two thousand. From that we know that four thousand is the lowest number we can come up with for thousands upon thousands.

Unless a specific number of thousands is given we have NO idea how many thousands upon how many thousands are being added together. It could mean as little as four thousand to an infinitely higher number of thousands. We only know it is the plural usage of thousands upon thousands.

(thousands upon thousands is equal to thousands added to thousands)

Thousands of thousands is also an indeterminate number because we do not know how many thousands times how many thousands unless a specific number of thousands is given. The lowest number thousands of thousands could represent is two thousand times two thousands which equals four million. I say that is the lowest because of the plurality of "thousands."

Here again the number could be infinitely higher because there is no limitation on how many unlimited thousands of unlimited thousands. The only limitation is each number has to be at least two thousand because of plural usage.

Grammatically speaking, either one is fine. It depends upon what you are trying to say and how you want to say it or how you want it to sound. If the exact number is critical to your message then I suggest using exact numbers. i.e. ten thousands of ten thousands which is one hundred million or ten thousands upon ten thousands which is twenty thousand.

If you want to leave it open to the imagination of the reader either thousands of thousands or thousands upon thousands could be used because either "could be" an infinite number.

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