Terence Tao solves the Erdős Discrepancy Problem | Hacker News Reader

Terence Tao solves the Erdős Discrepancy Problem

nature.com

285 pointsjonbaer27 comments

There are at least three exciting things here:

1. A well-known conjecture in number theory has been proven (by Terry Tao, natch).

2. Several elements in the proof arose from an innovative collaborative approach to mathematical research (the Polymath Project, specifically Polymath5).

3. The result will be published in a newly announced cost-effective open-access journal, giving the new journal a big early prestige boost.

Every one of these is a big deal; taken together, they give us a glimpse of the future of mathematics (which, per William Gibson, is already here, just not very evenly distributed).

I hope it's the future for a lot of fields, not just mathematics, but I'm very glad to see things like this happening and big kudos are deserved by all involved.

Even the article here is better than most--I love how it linked even to the blog comment that gave Tao the impetus to investigate the connection and I would love to see things like this become standard for proper scientific reporting (i.e. if something happened online, give us a link). That should be standard practice, but it's so often neglected that it makes this article much more thorough than the average.

>> Though the proof has not undergone a rigorous peer review, experts expressed no concern over whether it would survive a critical look.

Such is people's confidence in Terence Tao - not unfounded by any means - but the result has not been peer reviewed yet. Tim Gowers has said that they'll be conservative in their review process [0] so any errors will probably be picked up quickly.

[0] https://gowers.wordpress.com/2015/09/10/discrete-analysis-an...

Any use of the word "conservative" outside a quantitative comparison should at least be disregarded and at most set off alarm bells that a deceit is underway. In no case should you draw any further conclusions about the outcome based on some presumed directionality of such a qualitative modifier. "Conservative compared to what?"

... what?

Discussion from a few days back on the paper itself: https://news.ycombinator.com/item?id=10238373

There's also https://news.ycombinator.com/item?id=10247132.

The OP is a pretty fun article to read, so let's not count it as a dupe.

While we're on Erdős and Terrance Tao, Terrance has an Erdős number of 2 (https://en.wikipedia.org/wiki/List_of_people_by_Erd%C5%91s_n...) so whilst having met Erdős as a boy (https://en.wikipedia.org/wiki/Terence_Tao#Personal_life) he never collaborated with him on a paper. (Probably due to differences in ages).

It's amazing to see the influence Paul Erdős had on people. There is a children's story (that I read to my kids) about his incredible life. http://www.amazon.com/The-Boy-Who-Loved-Math/dp/1596433078

*Terence

It would be cool if somenone annotated this paper on Fermat's Library, would to get a better grasp of it: http://fermatslibrary.com/s/the-erdos-discrepancy-problem

Anyone? =)

anyone know where the comment was made?

Looks like https://terrytao.wordpress.com/2015/09/06/sign-patterns-of-t...

Yes, it's listed on the nature article...

Not sure why this was downvoted. There is a link to the comment at the end of the article, which surprised me a little in a good way.

$500 is close to $6.5K inflation adjusted. Although it makes sense to frame it.

When a chemist makes a discovery , do they call them a "chem whizz"?

Subtitle: "Terence Tao successfully attacks the Erdős Discrepancy Problem by building on an online collaboration."

First paragraph: "A mathematical puzzle that resisted solution for 80 years — including computerized attempts to crack it — appears to have yielded to a single mathematician."

This irks me.

Yeah, esp since Tao admits that a comment on his blog gave him the necessary insight.

Yes as the Nature article says, the commenter who gave Tao the initial idea is Uwe Stroinski, who received a PhD in mathematics from the University of Tübingen.

Just repeating his name here because i think his contribution should not be missed.

> by building on an online collaboration." [...] appears to have yielded to a single mathematician."

>This irks me.

It didn't bother me because I don't interpret the "collaboration" and "single mathematician" as contradictory. In other words, all mathematics is built upon group contributions whether the collaboration happens digitally online or via letters transported across 17th century continental Europe.

In this case, "single mathematician" doesn't mean a person who discovered every insight and connected all the dots. Instead, it means the one who connected the last dot. So far, it looks like Tao solved the last step of the puzzle and no one else independently solved it and submitted a proof at the same time. Contrast this situation to the invention of calculus which was simultaneously created by Newton and Leibniz.

> Contrast this situation to the invention of calculus which was simultaneously created by Newton and Leibniz.

There were plenty of precursors to calculus, coming from the likes of Descartes, Fermat and Pascal. For example: http://www-history.mcs.st-and.ac.uk/HistTopics/The_rise_of_c...

Echoing what jasode said, I don't think this blog comment makes this much less of a Tao accomplishment, even if the comment was absolutely crucial. Tons of scientific insights can traced back to off-hand conversations with colleagues; the fact that this happened on a blog rather than over coffee in person is not relevant to priority claims. When insights aren't traced in this way, it's usually because the person just hasn't kept an exhaustive record of all the useful conversations in his head (rather than because there were no such useful conversations).

In other words, if you think this degree of collaboration is enough to characterize the discovery as not individual, then there have been no individual discoveries ever. But that's not a very useful definition, because there are clearly some discoveries that are much more collaborative than others.

> The second is a logarithmically averaged version of the Elliott conjecture, established recently by the author

The proof relies on a variation of a recently proven conjecture.

See also the blogpost on Tim Gowers' blog : https://gowers.wordpress.com/2015/09/20/edp28-problem-solved... :).

Indeed, and submitted here:

https://news.ycombinator.com/item?id=10247132

The title there was:

    Gowers on Terrence Tao's solution
    to the Erdős discrepancy problem

The title here started out as:

    Maths whizz solves
    a master's riddle

I suspect the click-baity title helped this submission get early views and early votes. The other, more factual title was probably just mostly ignored. It would be interesting to know how many click-throughs that earlier submission got.

Am I the only one who noticed the smoothest self-promotion ever in the comment section?

Very interesting post, such a good read. Glad I came across it. Flitwick Blinds often use advanced mathematics when calculating conservatory roof blinds or shaped shutters at http://www.flitwick-blinds.co.uk*

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