[markgall]

Can anyone provide a link that "Some are going as far as to suggest that the entire foundations of computer engineering and machine learning should be re-built as a result of this", or anything similarly grandiose?

I am a professional mathematician, though nowhere near this kind of thing. The result seems amusing enough, but it doesn't really strike me as something that would be surprising. I confess that this thread is the first I've heard of it...

[saithound]

It's a fun, but unsurprising undergrad-level result. It got picked up and overhyped on HN [1] and /r/math [2] earlier this week.

Some of my favorites:

DoctorOetker: "I'm still reading this, but if this checks out, this is one of the most significant discoveries in years."

cryptonektor: "Given this amazing work, an efficient EML operator HW implementation could revolutionize a bunch of things."

zephen: "This is about continuous math, not ones and zeroes. Assuming peer review proves it out, this is outstanding."

[1] https://news.ycombinator.com/item?id=47746610

[2] https://www.reddit.com/r/math/comments/1sk63n5/all_elementar...

[DoctorOetker]

:)

I still consider the article important, as it demonstrates techniques to conduct searches, and emphasizes the very early stage of the research (establishes non-uniqueness for example), openly wonders which other binary operators exist and which would have more desirable properties, etc.

Sometimes articles are important not for their immediate result, but for the tools and techniques developed to solve (often artificial or constrained) problems. The history of mathematics is filled with mathematicians studying at-the-time-rather-useless-constructions which centuries or millennia later become profound to human interaction. Think of the "value" of Euclid's greatest common divisor algorithm. What starts out as a curiosity with 0 immediate relevance for society, is now routinely used by everyone who enjoys the world wide web without their government or others MitM'ing a webpage.

If the result was the main claimed importance for the article, there would be more emphasis on it than on the methodology used to find and verify candidates, but the emphasis throughout the article is on the methodology.

It is far from obvious that the tricks used would have converged at all. Before this result, a lot of people would have been skeptical that it is even possible to do search candidates this way. While the gradual early-out tightening in verification could speed up the results, many might have argued that the approach to be used doesn't contain an assurance that the false positive rate wouldn't be excessively high (i.e. many would have said "verifying candidates does not ensure finding a solution, reality may turn out that 99.99999999999999999% of candidates turn out not to pass deeper inspection").

It is certainly noteworthy to publish these results as they establish the machinery for automated search of such operations.

[renewiltord]

This result itself is being described in those terms[1]:

> If this is true, then this blog post debunking EML is going to up-end all of mathematics for the next century.

This is very concerning for mathematics in general.

1: https://news.ycombinator.com/item?id=47775105

[seanhunter]

Why on earth would it upend all of mathematics? Secondly, even if it did that, why would that be concerning for mathematics?

[renewiltord]

Yes or no, it's too early to tell.