Different tax loopholes depending on region etc, but basically like this:

I’m a billionaire earning $100M this year.

I owe $40M as taxes for that. (Too much!)

I find a dumb banana painting by a starving artist.

I buy it from him for $1000.

I wait 6 months.

I go to a museum to get it appraised by “professionals”.

I pay the professional appraiser’s wife $50K as a gift.

The appraiser says the painting is now worth $30M!

Wow that’s awesome, I have such a keen eye for art.

You know what, I’m gonna donate this painting to a museum instead because I’m such a patron of art and culture.

Oh, look at that, I get a tax rebate for the value of my donated painting ($30M)

Now I only have to pay $40M - $30M = $10M in taxes on my $100M income.

There’s more nuance to it in practice, but that’s the gist of it.

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Edit: For some reason I can't reply to the comments below so I'm gonna do it here.

> That wouldn't explain the price here, since in your scam the whole idea is to buy cheap and donate dear. not buy for 139M

Now we're getting in the details but it's very suspicious for an appraiser to appraise a work of art from an unknown artist at millions. But it's not that suspicious if they take Van Gogh's Starry Night which was previously appraised at $500M to now be valued at $1B. this way the deca-billionaire still gets to save his taxes while appraiser avoids suspicion.

> As far as I know, that's not how taxes work. You can't get a rebate for the amount of taxes you would have paid, you can get a deduction for the amount of money you made.

There are a lot of loopholes in the complicated tax system for the ultra-wealthy, not for us. This video (still a simple explanation in an animated way) covers a few more of them: https://www.youtube.com/watch?v=dHy07B-UHkE

As far as I know, that's not how taxes work. You can't get a rebate for the amount of taxes you would have paid, you can get a deduction for the amount of money you made.

So:

You made $100M owe $40M in taxes.

Your painting is worth $30M! You have such a keen eye for art.

Now you made $130M and owe $50M in taxes.

You donate the painting, you're back at having made $100M and owing $40M.

Otherwise we'd all choose not to pay tax and donate our tax money to charitable institutions instead.

Yes, there are lots of “loopholes” available if you are willing to commit tax fraud! But that’s something anyone can do, it’s not particularly harder to lie about the value of charitable donations if you’re not ultra-wealthy.

That wouldn't explain the price here, since in your scam the whole idea is to buy cheap and donate dear. not buy for 139M

Your scheme involves getting a fake appraisal for a value higher than the market price. But this does not explain high prices at an auction.