What problems do BTC miners solve?

[OfficialGratejoy]

I was have a discussion with one of my very good friend who is into shitcoins,we had an argument on mining BTC and he asked me this specific question. what problems do BTC miners solve?

[NotFuzzyWarm]

If you mean 'what does BTC miner hardware do?", they take data from a block header and apply pseudo-random numbers to the sha256 algo to try to get a result that exceeds the current diff. When they succeed, they signal Block Found confirming all the Tx's in the block and it is added to the chain - but it is NOT fully confirmed yet.
From https://kano.is/index.php?k=mining

What does a Bitcoin miner actually do?

A Bitcoin miner creates a Bitcoin block header of 80 bytes, using the work it is given e.g. by a pool, and hashes it using the SHA256 hash algorithm.
Within those 80 bytes, there is a 4 byte value called the nonce - that it cycles from 0 to approximately 4 billion and hashes it for each nonce value.
The SHA256 hash algorithm gives a pseudo-random result for each hash done.
If a hash results in a Difficulty value greater than or equal to the limit specified by the work it was given, it will return the information required to produce the same 80 byte block header it hashed.
A Difficulty value of 1 is expected to occur, on average, once every approximately 4 billion hashes attempted.
If the hash result has a Difficulty value greater than the Bitcoin network Difficulty, then that means the miner found a Bitcoin block!

That result is broadcast to the network and most of the time other miners then use that block header as new work to start building upon. Only once at least 1 block *after it* using that new work is found can that previous block start to be considered as 'confirmed' as it could still be pushed out by a chain reorganization which is caused by a different block being built upon faster. 2 competing blocks is called an Orphan Race. Typically a block must be confirmed at least 3x before it is considered safely confirmed because at that point is is very very unlikely that a different block would cause a reorg. The more blocks that are built on it, the safer it is. After 101 confirmations only then can the block be called fully confirmed.

Bitcoin miners are not 'solving complex equations' as many folks wrongly insist on saying/quoting. It is a very simple and straightforward operation. A deeper dive into the mechanics is at https://kano.is/index.php?k=minedet

[stwenhao]

What problems do BTC miners solve?

They enforce the proper order of transactions. Without mining, you can have a valid chain, where Alice sent coins to Bob, and another valid chain, where the same coins were sent to Charlie. If you have no mining, then you have two (or more) valid chains, with valid signatures, and you don't know, which history is the correct one.