This is intended as a clarification of the "correctness" of using data as a mass noun, for those strict-minded sticklers (there's plenty of them) who might be unconvinced by Kosmonaut's "languages borrow words and do whatever they want with them":
1 - "Datum" and "data (plural)" are historically correct, so "data (mass noun)" must be wrong. How can "data" have a mass noun form as well as a singular and plural?
You'd never say "Oh, I spilled rice on the floor. Wait, it's okay, I only
spilled 4 rices". There's a separate noun phrase for the singular and
plural ("grains of rice").
Consider potato. It has a singular form, meaning one distinct root vegetable, a plural form, meaning multiple distinct root vegetables, and a mass form, meaning an amount of foodstuff made from potatoes. Imagine a dinner table, where each diner has a baked potato on their plate (singular), and everyone is sharing a platter of roast potatoes (plural) and a bowl of mashed potato (mass) (hopefully among other things...). If you ask someone to "pass the potato", they'll understand that you mean the bowl of mass mash, not the tray of plural potatoes or the singular potato on their plate.
2 - There can be such a thing as "a datum" in a way which is not true
for "a water". Imagine someone looking at a database full of data and
saying, "There is so much data in this, I can't see where to start".
Surely this is like standing in a migration of birds and saying "There
is so much bird in the sky, I can't see the sun..."? Since data can be
countable, surely "data" can't be primarily a mass noun?
Data is not necessarily countable. Data in a neat Excel sheet might have countable cells, but what about the data that is lost when photo editors talk about "data loss" when increasing the contrast of a digital photo made of binary machine code data? There's no clear way of defining where one datum starts and the next one stops — would a datum in this context be a bit, a byte, or the data defining one pixel? Such a line would be arbitrary, like looking for units of rice in a processed flat rice cracker. It's an amount measured in units of mass — 67kb of data in a jpg, 2 grams of rice in a rice cracker.
Even seemingly trivial cases aren't so trivial. What's one datum in a modern relational database? One value, one row? What about where there are table joins and foreign keys? Is a structural definition a datum? You can create a convention-specific definition, but it's not a universal definition like one bird.
3 - Following that pattern, shouldn't the mass noun of data be datum
(the singular), like how the mass noun of potatoes is potato?
No. It's rare, but not completely unique, for a count noun to develop from a plural, in cases where the singular over time becomes less and less universally meaningful. "Physics" used to mean the set of countable, defined, distinct natural sciences - until the field developed such that it became clear that the lines between one physic and another wasn't as sharp or universal as previously thought.
You could answer "What's happening at CERN?" with "A lot of physics", but you wouldn't expect the reply "How many?". This is because there's no longer a clear established universal dividing line between one physic and another. Your answer would interpret the question as, "How much?" and would be a measurement of amount: "Enough to occupy 4,000 physicists". In the same way, you could answer "What does this supercomputer store?" with "A lot of data", but the reply "How many?" would incorrectly assume that all data has one clear common countable unit and that there is a clear universal dividing line between one datum and another across all contexts. Even if this data did happen to have a consistent countable convention, replying "7 million data" would be ambiguous unless the asker already knew this convention. A more useful answer would be to interpret it as "How much?" and give an answer in terms of a measurement of amount: "Nearly 220 petabytes".