Alternative Minimum Tax is based not just on your income, but moreso on the deductions you use. In short, if you have above the minimum AMT threshold of income (54k per your link), and pay a tiny amount of tax, you will pay AMT. AMT is used as an overall protection for the government to say "okay, you can use these deductions from your taxable income, but if you're making a lot of money, you should pay something, no matter what your deductions are". This extra AMT can be used to reduce your tax payment in a future year, if you pay regular tax again.
For example - if you have 60k in income, but have 60k in specific deductions from your income, you will pay zero regular tax [because your taxable income will be zero]. AMT would require you to pay some tax on your income above the minimum 54k threshold, which might work out to a few thousand bucks. Next year, if you have 60k in income, but only 15k in deductions, then you would pay some regular tax, and would be able to offset that regular tax by claiming a credit from your AMT already paid.
AMT is really a pre-payment of tax paid in years when you have a lot of deductions. Unless you have a lot of deductions every single year, in which case you might not be able to get all of your AMT refunded in the end.
Wikipedia has a pretty good summary of AMT in the US, here: https://en.wikipedia.org/wiki/Alternative_minimum_tax.
If you think AMT is unfair (and maybe in some cases you might pay it when you think it's "unfair"), look at the root causes of paying AMT listed in that Wikipedia article:
- Having Stock Option deductions;
- Having high interest costs on large investments;
- Having a large amount of depreciation for physical business assets; etc.
I am not trying to convince you that AMT is fair, just that it applies only when someone already has a very low tax rate due to deductions. If you have straight salary income, it would only apply in rare scenarios.