
Mathematicians Discover the Perfect Way to Multiply - pseudolus
https://www.quantamagazine.org/mathematicians-discover-the-perfect-way-to-multiply-20190411/
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spuz
Previous discussion:
[https://news.ycombinator.com/item?id=19474280](https://news.ycombinator.com/item?id=19474280)

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hannob
The title is a bit misleading, though they do explain it in the text.

It seems they cannot show right now that this is the perfect way to multiply.
It's faster than any previously existing way and they hope to be able to
proove in the future that there is no faster way.

I found this interesting because coming from cryptography I know that it's
very hard to have any lower bounds for algorithm speed. Which is why we can't
have provably secure cryptography (yet?).

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rollthehard6
Q - how do you multiply something like 25x63 example in your head? Personally,
I'd break that down also, by doing -

5 x 63 = 315 x 5 = 1575

reminds me a little of the Feynman story about his duel with the abacus
master.
[https://news.ycombinator.com/item?id=5849665](https://news.ycombinator.com/item?id=5849665)

~~~
docdeek
For that example I would be thinking 60 x 25 = 1500 (4 x 25=100, so that's the
simple part for me) and then 3 x 25 = 75, and add the two products.

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pseudolus
Here's a link to the actual paper:

[https://hal.archives-ouvertes.fr/hal-02070778/document](https://hal.archives-
ouvertes.fr/hal-02070778/document) (PDF)

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amichail
The second author is the creator of TeXmacs btw.

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lower
Previous discussion:

[https://news.ycombinator.com/item?id=19474280](https://news.ycombinator.com/item?id=19474280)

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rawwar
Aren't algorithms for multiplying integers in O(n log n) using DFT known for a
long time (eg. Cooley-Tukey)?

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eesmith
According to the article, Schönhage and Strassen introduced the use of fast
Fourier transform to integer multiplication in 1971, giving n × log n ×
log(log n). "The technique has been the basis for every fast multiplication
algorithm since."

"Over the past decade, mathematicians have found successively faster
multiplication algorithms, each of which has inched closer to n × log n,
without quite reaching it. Then last month, Harvey and van der Hoeven got
there."

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JustSomeNobody
25 X 63

25 X 6 X 10 = 1500

25 X 3 = 75

1500 + 75

1575

This is easier for me to do in my head than juggle as many steps as the
"perfect way"

