The comparison and contrast between Banks and Bitcoin is a pretty good one.

Banking computers sit around adding and subtracting numbers to keep track of people's money:

• Who made their car payment?
• Who received a paycheck?
• Who is spending more money than they have, and what are the consequences?

Is any of this useful to the human race?

At the end of the day, no one has any more food or lives a longer life because of a banker's math. But we all know this is important basic element of infrastructure to keep society running smoothly.

Bitcoin miners do the same thing, they keep detailed accounting of people's money. They don't directly feed anyone, but providing an accounting and a means to exchange money is important to the functioning of society.

Mining makes tradeoffs that are different from banks.

On one hand, they use a lot more electricity than banks, but on the other hand, they break the reliance and necessary trust that banks are acting responsibly.

This is especially important when we saw during the 2008 Financial crisis that banks were not trustworthy. They intentionally made bad loans, took huge risks, and damaged the economy to enrich themselves.

Because of bankers actions then, bad things did happen to society. Rates of bankruptcy increased, and that is not an abstract financial situation. Financial stressors are closely correlated with increased rates of suicide, divorce, alcoholism, spouse and child abuse, etc. These bankers literally ruined lives with their irresponsible decisions to enrich themselves.

Bitcoin (probably) won't ever do that.
Is that good for society? Is it worth the increased electricity and computing costs? Maybe or maybe not. No one is entirely sure. But it is certainly a worthwhile experiment to investigate.

"What kind of problems does miner's computer solve?" suggests that the questioner may have been influenced by a misleading yet common image used by journalists. The image is of miners' computers solving "complex" or "difficult" "problems" or "puzzles." "Difficult" is correct only in the sense that what miners are trying to do takes, on average, a relatively large amount of computation. But the computation itself is quite mundane, and is not anything that would intellectually challenge a person who understands the basics of computer computation. It's a process of tediously trying different input values for a computation on some data derived from the current block until one of those values generates a valid output value. There is no way to predict or guess which input values will work. The first miner to come up with a good value wins the block reward.

So any implication that the mining process's "proof of work" in itself solves general problems for the human race or any member thereof is misleading. (Also misleading: the most common illustration for popular articles about Bitcoin -- a stack or pile of metallic-looking coins.)

Solving hashes isn't useful onto itself. However, it does provide an effective "proof of work" that Bitcoin makes use of. In particular, it makes it expensive to cheat, yet profitable to play by the rules. This allows Bitcoin to be self-regulating without central control.

So, how does this help the human race? There are many potential answers to this question, but they are all speculative. That's your own opinion.