I have come for some advice. If one of the PCs' main strength is their immense pool of wealth...

I have come for some advice. If one of the PCs' main strength is their immense pool of wealth, how do you challenge them, keep them busy and keep them entertained? Picture almost entirely unrelated.

Give us lots more details on the player and setting and quest.

I can tell you 2 obvious solutions: make something so fucking expensive that they care, or put them up against something that can't be bought.

Give them a problem that wealth wouldn't solve, but don't cut them off or keep them from using it altogether.
Have something in mind that will actually make them benefit from not spending their wealth, or have it be a resource they will need to spend with caution, and have their reputation at stake.

Physical and mental challenges that money can't solve. If they hire people to handle it, all those people die or otherwise fail. Pose a challenge that has no interest in money. Find a way to challenge their personal ability in a way that their wealth cannot intervene.

Money doesn't grow on trees. Keep track of the expenses and deplete as necessary.

Attack their wealth.

Wealth and liquid assets are two different things.

The wealth is a strength yes but also a weakness, its not hard to attack it somehow or take it away.

Enjoy the fun as the PC becomes horrible paranoid and protective of it, and stops shelling it out so easily.

I'm not extremely familiar with the player, but he's a pretty cool guy from what I know of him. The setting is a science fiction world where Earth has been abandoned for over 2000 years and other planets have become the new homes of humans, There are no known aliens and so far the only major obstacle in his plan is that there is an AI run satellite making a lot of drones to kill any humans that enter Earth space, since he wants to reclaim Earth and I get the feeling that is what he is gonna get the rest of the group to work on too.
Presenting him with problems he can't buy his way out of may help a little, but I need something for the long term.
Having him have to take care of things with his own two hands is a nice suggestion, but what I really need help with I think is coming up with something to make him have to make careful decisions with his spending.
The problem with that is that he is for all intents and purposes just an old business man acting as a patron of sorts for the other PCs, so aside from his wealth and raw intellect, he doesn't have much in the way of personal ability.
This could help, depending on how large his regular expenses are.
I was considering having a certain group at least take a large part of his wealth out of his reach until he manages to solve the conflict with them, but I don't want to cripple him entirely if that goes down badly. It's still worth considering.

Just how wealthy is this PC? Is he a millionaire? billionaire? Bill Gates? Rogue Trader?

Somewhere in the multimillionaire range. I think the cost of his mercenary army will put a notable dent in his wealth, but I want to make managing it filled with difficult strategic decisions and through that make the role a fun one to play.

What is the source of his wealth? Money bin? Equity and Debt security equivalents held for value growth or periodic dividend or interest payments? Legal monopoly on invention or process? Huuuuge... tracts of land?

All of them are vulnerable, one way or the other, to sabotage.

Have the AI start trying to undermine his wealth. So he can't just fund an offensive against it, he has to co-ordinate a defensive at the same time.

Shareholder lawsuits, proxy votes against him, debt defaults, the brave but dangerous sir Lancelot, calls for nationalization or removal of legal monopolies, Beagle boys, that kind of thing.

>take it away
That's lazy.

Sounds to me you need to scale the conflicts. Fabulously wealthy, intensely political people don't tend to sit in a vacuum. Even if they're independently wealthy, someone purchasing a mercenary army to invade Earth is going to raise eyebrows. If they take him at his word, then everybody and their corporation is going to want a piece of the invasion pie, or exploit the situation to ruin him. If they don't take him at his word, he's buying a fucking mercenary army capable of planetary invasions. That's a hostile gesture that ought to be responded to.

If your party's power raises, then raise the stakes as well. It's probably worthwhile to read some advice for Rogue Trader GMs, since they tend to be dealing with the same power scale as your PC.

It's not that you should strip the player of his money, it's that, realistically speaking, there are a lot of people in the world that really want to get a hand on it. On this level it's all about prestige and status along other big league guys. There may be elite services that cost ridiculously high - but look as ridiculously glamourous and fancy and "everybody does that". As an example - gambling or stock trading. Other than that it's security and fame - many elite class thiefs/"robin hoods" may know about his possessments. Render guards for hire "why do you think I pay you???" kind of impotent against such threats. Also remember that some lawful-good NPCs with strict morale may consider all wealthy people morally wrong (commies, in other words).

Most of it I believe is from his business, but he does have a substantial amount of income from investments. I've already considered the fact that his business has begun expanding into areas the government of the moon his company is based on wouldn't be happy with as a reason for them to freeze his accounts or something until he does as they want him to.

The problem with the AI acting to undermine him at the moment is that it is currently unaware of him and his plans, and that it currently has no means to spread beyond the satellite that is still orbiting Earth to get to make any attempt on the system in which his wealth is stored. Otherwise, that is a decent idea. I'd considered that there would be governments unhappy with it, but somehow rival corporations interests didn't come to mind. Thank you for the suggestion. Now I just have to figure out how the other corporations will make his life difficult since I am no expert on business.
I already expect purchasing all his help will be quite expensive, but that his wealth itself might have him at odds with some people is definitely worth considering. Another thing I might have to consider is that he is technically playing himself as a lot more feeble than he really is, and has his son as the current face of his business and his puppet.

>multimillionaire
>immense pool of wealth
Are you playing Unknown Armies or something?

The point is its something to have him defend, it adds tension and gives a powerful character a clear weakness.

Lazy would be pretending the PC can just flash insane levels of wealth around to solve problems and never have anyone start gunning for it.

You basically said the same thing i did, but more specifically after calling me lazy for your lack of reading comprehension, pretty impressive.

GURPS actually.

Ah, that clear information regarding setting and tone has cleared up the situation marvelously.

It's space with lots of nice big railguns, many different types of governments of many different sizes across a galaxy and people are as apathetic and warmongering as they always have been. Does that help?

It helps in that it clarifies, but it also supports my suspicions that a mere multimillionaire will not be rich enough to do anything meaningful. The grander the setting, the greater the difference between the rich and the poor.

Slightly off topic, but what's the AI's motivation?

You could have some rival interest who wants to make sure this little project bleeds him white get in touch with the AI. That offers a chance to expand, as well as mutual betrayal, infighting, and backstabbing.

You may be right, but he isn't just a multimillionaire is the number of actual space bucks he has, he is a multimillionaire in how much it's actually all worth.
It's a very old AI that's more limited in the speed and capacity for growth, so it's still trying to fulfill the same goal it had way back then, which was to prevent any invasions or attacks of one country on another specifically on Earth. It bombarded Earth with chemical weapons until there was no more life on the planet after one country tried to knock it out with missiles. Most people in the setting learned about it in school.

That depends on the monetary system in play. A multimillionaire in an economy with a very strong currency is richer than a numerically equivalent multimillionaire in an economy with a weak currency.

OP here, it's late and I should be getting ready for tomorrow. Thanks for the suggestions everyone.

(1. use money to gain more money
(2. buy armor and weapons for fellow PCs (quest weapons might be stronger but you can just equip the parts they are lacking).
(3. mercenaries, don't even have them fight with the party just throw them on missions to fuck the BBEG's operations and have them report to you every session