The value of solving problems is (as I understand it) if you are a successful miner, you get a Block Reward and a Fee Per Confirmed Transaction.
You are a successful miner if your computer solves the problems first. The problems are the hashing problem, the byzantine generals problem, and the double-spending problem.
Bitcoin is speculative so you run the risk of running up massive energy costs, for little or no return.
Early on (e.g. 2009) you could mine 50 coins every 10 minutes, now each new block mined returns 6.25 BTC.
Currently, the daily total revenue from mining Bitcoin globally is 41 million USD.
BUT
The mathematical problems are so immense, and require so much computing power that you need enormous farms of ASIC's to make it worthwhile.
Bitcoin mining is at its essence burning coal for profit. If nothing else it will increase plant life with all that dastardly CO2!