If you see bitcoin as a currency, mining is issuing new bitcoins. It is analogous to a central bank issuing (or printing) new currency.

What product is produced for the world? Mining for coal produces coal to be used for energy production. Mining for precious minerals provides metals for use in products all humanity can use.

You could ask the same question to the central bank example. If The Fed issues $ 1 trillion what product is it producing for the world? The difference with bitcoin is that there is no central authority that chooses when to issue new currency but an algorithm and the issued currency instead of going to the banks in a form of loan, are given to the user who mines the next block.

Satoshi Nakamoto in his famous white paper presented a solution to the problem of consensus among decentralized and not trustworthy peers via Proof-of-work.

Bitcoin mining is to secure the network of decentralized and trustless nodes.

Bitcoin mining adds value by providing security to the network.

The primary purpose of Bitcoin mining is not to produce value for its owners. Value is produced just to incentivize nodes to contribute more to Proof-of-work network power.

... but as best as I can tell the math is for no other purpose than to generate value for the owner.

Bitcoin does not have a concept of 'the owner'.

Mining generates value for the user initially, through the confirmation of new transactions in blocks. Without mining, there is no reliable way in Bitcoin for the transaction to be confirmed.

Since the currency is new, mining also serves the dual purpose of issuing new currency.

Since its inception in Bitcoin, mining has been seen as analogues to mining for gold. The miners are free to enter the mine and work (which is confirming transactions) and when they are successful in solving the mathematical puzzle needed to create a valid block they receive the transaction fees (BTC already in circulation) and the block reward (newly minted BTC). As time progresses the block reward is regularly halved, the last new Bitcoins are expected to be issued in approximately the year 2040.

The process of mining is valuable for the user of Bitcoin primarily and the miner is paid for their work.