> This new method will be marginally faster if you ever need to multiply two numbers on a scale where writing down the bits fills every plank-length cube in the known universe.

If we're talking about physical implementations then you would also have to take the delay between those planck volumes into account

> “The best we can hope for is we’re three times faster,” van der Hoeven said.

And they talk about billions of digits elsewhere in the article. I doubt that only applies for the ~8.46e184 digits you seem to be talking about.

From last time this came up, the number of bits in the numbers involved is 2^(9^12). Storing a count of the number of bits takes about 930 billion digits. Actually storing the bits or digits of the numbers per se takes a whole lot more, to say the least.

https://hal.archives-ouvertes.fr/hal-02070778/document

Surely a practical benefit can come from this result being used in other proofs/systems, which then have real-world impact?

Yes, this result will be used to save a few printed symbols each time the topic comes up in future mathematics papers, and the beauty of the slightly simpler mathematical expressions will spark joy in mathematicians reading them.