My initial thought was that if Math can be performed that produces the same results Encrypted vs Unencrypted, is that it isn't very well encrypted. My understanding is that the better encryption techniques approaches what looks like static (randomness).
It's strong. Very strong.
Problem is, there's a tradeoff in time/speed and operations you can do. There are general algorithms that let you do a wide variety of operations, but they are very slow - on the order of a million times slower than unencrypted.
Faster algorithms usually restrict the operations you can do. on the data, and performance is almost equal that of unencrypted.
Note that you don't simply say "I want to add these two numbers" , encrypt them, then just do a simple add - no, the operation after encryption may be a multiplication, or other operation.
And this is actually very useful - because it lets you store critical data in the cloud, and perform manipulations of that data in the cloud, without the cloud provider having to have the encryption key. If the data is stolen, the hacker gets encrypted garbage.
So the current operation is database - you put up an encrypted data in the cloud, and the cloud provider runs an encrypted database service. You can perform limited queries, and the cloud provider will return you the encrypted rows as encrypted blobs to you. You use the key (kept onsite for security), and marvel that you just did a transaction in the cloud, the cloud provider executed the operation, and you got back the rows that you wanted, and at no time other than on your PC was it ever in plaintext.
You could be more fancy - say you want to add up a column - you tell the database server to add it up (encrypted), and the final result is sent back, as encrypted data. You use your key and get your answer.
That's the primary use case for this sort of encryption. Do it right and even in house database can be completely encrypted. So stuff like health information and banking records will never be in plain text until you need it so breaches won't be as harmful.