On Fox News Sunday, Paul Ryan said that he didn’t have time to explain the math behind his tax proposal. Fortunately I have a few minutes to spare, so I thought I’d pitch in.

Mr. Ryan and Mitt Romney have proposed a tax plan that would lower everyone’s tax rates by 20 percent. On Sunday, Mr. Ryan was asked to explain how the proposal can be revenue neutral — that is, not reduce the total amount of tax revenues collected — given this condition of substantially lower tax rates. He mentioned ending tax deductions starting with “people at the higher end” and broadening the tax base, and finally declared:

… it would take me too long to go through all of the math, but let me say it this way. You can lower tax rates by 20 percent across the board by closing loopholes and still have preferences for the middle class for things like charitable deductions, for home purchases, for health care.

There’s a reason why it would take too long — infinitely long, you could say — to go through the math that holds this policy proposal together: because math will never hold this particular policy proposal together.

You cannot lower tax rates as much as Mr. Romney and Mr. Ryan propose to do and keep all the existing tax expenditures for middle class Americans and still end up with the same total amount of tax revenue.

As the Tax Policy Center demonstrated, cutting individual income tax rates by 20 percent from today’s levels would reduce tax burdens by $251 billion per year (in 2015) among households with income above $200,000.

If you leave preferential tax rates for savings and investing (e.g., long-term capital gains and dividends) untouched, as Mr. Romney has said he would do, that leaves only $165 billion of available tax expenditures that can be eliminated from this same group of high-income earners once their marginal tax rates fall.

That means there’s an $86 billion shortfall — the difference between $251 billion in tax cuts and $165 billion in potential tax increases on this high-income group — that needs to be accounted for somewhere.

By process of elimination that somewhere must be the rest of the population, the 95 percent of households earning less than about $200,000 annually.

The taxes for this group, which Mr. Romney has called “middle income,” would have to go up. The only ways to get the taxes collected from this group to go up would be to raise their rates (which Mr. Romney and Mr. Ryan have already ruled out) and/or eliminate the major tax preferences they enjoy.

It’s arithmetically possible to achieve some subset of the main principles that the Romney-Ryan tax plan aims for: cutting current marginal income tax rates by 20 percent; preserving/enhancing incentives for saving and investment; eliminating the alternative minimum tax; eliminating the estate tax; maintaining revenue neutrality; and not raising the tax burden on the middle class.

But not all of those principles can coexist so long as basic arithmetic survives.