Sounds like an interesting concept, although, as I am not a mathematician, just a recreational math hobbyist, I can’t say that it’s “all perfectly transparent” to me. Nor do I think it is to most other readers of the Chronicles.
Care to elaborate? I love to learn new stuff.

I don’t imagine that most of us want to multiply two 100-digit numbers often, but when we do, it’d be great to have a superior method.

In the meantime, I can’t see how it would effect that fact that if we were taking 28 students on a field-trip, and each had to pay 12 dollars, there’d be a better way to figure out the total owed than with mental math.

Constantly seeking more efficient methods, the above could even be done more easily than with the “mystery algorithm.” Readers can try that here.

You are right, mental math is great for small numbers. The “mystery algorithm”, with a small tweak, and pencil and paper (just to write the answer, not to do any “work”), is pretty easy to do with multiplications up to six digits by six digits long.
Even with numbers larger than that, it remains much easier than the “standard” algorithm.

But my point in the Chronicles isn’t that “my” way is the best. The point is that there generally is a better way to do anything. Apparently the method you suggest is much better for very large numbers, and I’d love to learn it.

I have to admit that I am not familiar with fourier transforms. They probably aren’t within the scope of this site, but I certainly would like to learn about them.

Let’s consider your points of:

“I can’t get excited about finding alternative ways to do it (which most parents won’t know).” That’s the point. That’s where this site comes it. I’m trying to change that. Most people don’t eat right either (that would include me) but isn’t it better to try to be one of the ones who do?

“There doesn’t seem to be any compelling ‘efficiency’ reason to do that.” The “mystery algorithm” is easier, requires no “props” like pencil, paper, or calculator, is faster, and is easier to learn. That seems more efficient to me. Most people I teach it to react the same way, too.

“… remember this is a country that couldn’t convert to metric…” Indeed I do. Most of that was due to fear of change. Math Mojo readers hopefully do not succumb to that so easily. People are here because they want something better.

I’d hope you will share with us a detailed description of the method you mentioned.

Thanks for writing in!

Brian