A community blog for Math.SE

Question

Starting a community blog has been proposed a couple of times, to a fair amount of support, but nothing has ever gotten off the ground. StackExchange already has a platform for site blogs, and a number of our sister sites have successful blogs.

I'm proposing the idea once again, but in light of the previous threads I am going to assume there is some interest and jump right into figuring out the details.

• Scope:

  • Highlighting and expanding on great posts on the main site.

  • Short exposition pieces on interesting mathematics, primarily at the advanced high school to advanced undergraduate level.

  • Current events of interest to the mathematical community, such as major conferences, outreach efforts like Mathematics Awareness Month, and major awards like the Fields and Abel medals.

  • Very general outlines of the work behind recent major breakthroughs, or concerning the status of potential breakthroughs, such as Mochizuki's claimed proof of the ABC conjecture.

  • Reviews of new math books (or even old ones that contributors have read recently).

• Non-scope: There are some things which a site blog might well contain which I think we should avoid.

  • Posts about Math.SE itself: I think these should stay on meta.

  • Posts at a very high level: Posts on a site blog should be accessible to a large portion of the community. At a high level, not only does someone need to be very advanced to understand it, but they will probably also have to work in the same field, severely limiting the scope.

• Frequency: 1 post/week but subject to change. We have a large community of active and involved users, so I think this is quite achievable. For example, this would only require 12 contributors posting every 3 months. The ideal frequency is high enough so that people's posts come out not too long after being submitted, but low enough that we can maintain a small buffer in order to stay on schedule.

• Management: I think the blog should have 2-3 administrators, who can approve posts for publishing and could maintain a Google spreadsheet with the schedule for upcoming posts. Post ideas could be proposed and discussed through a dedicated chat room. Posts in progress could be shared via Google documents or a similar such service. The process would look roughly like the following:

  1. Post idea is proposed in chat and okay'ed by community and at least one admin.

  2. Contributor writes rough draft of post and shares it with the community. The community offers suggestions to approve the post.

  3. The contributor produces a final draft which is okay'ed by an admin and added to the schedule.

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I have two questions for the community:

• Are you interested?

• What changes would you like to see in this proposal?

Assuming there's interest, I will incorporate the feedback into a revised outline for the blog and make a new thread soliciting starting administrators and contributors.

Answer 1

This answer is mainly to gather a list of interested potential contributors.

Edit it to add your display-name, and a very brief description of a topic if you would be willing and prepared to have a suitable blog post ready for submission by 17 May 2014. If your display-name is not unique, also include a link to your user profile, so everyone can identify you.

_{IMPORTANT! Be honest. It is likely that the undersigned will be called upon to submit the first few blog posts. Don't add someone else's display-name in the hopes of suckering encouraging some other poor sap user into this dirty work endeavour. Also, don't remove other users' proposals.}

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When your proposal is ready for publication: Please preface your entry with [Ready for posting] so we know who is ready, and who is not.

1. Alex Becker: The Complex Real Roots of $x^3-3x+1$. (Level: Moderate-Advanced Undergraduate.) Once you know the quadratic formula, $x^3-3x+1$ is about the simplest nontrivial polynomial you can come up with. However, it is also an example of the casus irreducibilis. All $3$ of its roots are real, and can be expressed in terms of square and cube roots, but not without using imaginary numbers!

2. Blue: The Seven Faces of a Tetrahedron. (Level: Advanced High School.) A Law of Cosines for dihedral angles in a tetrahedron reveals the figure's three "pseudo-faces", which can be used to devise a variety of formulas, such as a Heron-esque formula for volume in terms of the seven total face areas. (Note: The material lays a conceptual foundation for a topic that extends into Hyperbolic Space at a higher academic level and admits numerous open questions.) [May have to drop out of first wave. Sorry!]

3. Ron Gordon: Uses and misuses of the residue theorem in evaluating real integrals and sums. (Level: Advanced Undergraduate) The residue theorem is a fantastic tool for evaluating some integrals and sums, and there are many examples in Math.SE of its effective use. Unfortunately, there are also a number of examples in which the theorem, or its applicability, is completely misunderstood. The blog posts will address the use of the residue theorem as a practical tool to evaluate integrals and sums, as opposed to its use because the professor demanded it be used to evaluate such-and-such an integral.

4. [Ready for posting] Michael Greinecker: Matching theory. (Level: Early Undergraduate) Exposition of the Gale-Shapley algorithm and structural properties of stable matchings. Link

5. Goos: The coin-minting game. (Level: Advanced High School) Explanation and exploration of a game due to Conway. Symmetries related to the Coin problem; non-constructive proof of a winning strategy; proof that the game always ends despite its highly unbounded nature; open questions.

6. Daniel Rust: Sturmian Sequence. (Level: Moderate Undergraduate) An introduction to a special class of bi-infinite sequences comprised of two letters and the many ways they can be constructed and ultimately classified. Using continued fractions we can devise a 'test' to see whether two Sturmian sequences are 'equivalent' in a very general sense; links between geometry and combinatorics; open problems concerning higher dimensional analogues. <- I would like to do this post in the future, but I cannot have it ready by the deadline.

7. anorton: Dial Game (Level: Advanced High School.) Consider an arrangement of $5$ dials, each with $13$ possible settings (labled $0$ through $12$, inclusive). Given a set of possible "moves" (e.g. "move 1 rotates dials $1$ and $3$ clockwise, but $5$ counter-clockwise) and a starting configuration of the dials, what sequence of moves will point all dials towards $0$? Brute force is possible, but would take an exorbitant amount of time. Using linear algebra and modular arithmetic, solving the problem takes relatively little time. <- I would like to do this post in the future, but I cannot have it ready by the deadline.

8. [Ready for posting] anorton: Area of Polygons (Level: Advanced High School or Early Undergraduate.) Given an ordered list of points describing the vertices of a polygon, one can compute the area. This post will derive such a formula using Green's Theorem. [Side note: I don't really want to do two posts back-to-back, but I would do so if need be.] Link to current version.

9. Sanath Devalapurkar: Puzzles in the Foundation of Mathematics - Russell's paradox (Level: Advanced High School.) Naive set theory is usually what is (falsely) thought of, by people introduced to set theory, as set theory itself. This post will show one example of a paradox that arises from naive set theory, and lists and provides a basic explanation to a few alternatives to naive set theory, such as $\mathsf{ZFC}$ and topos theory.

10. [Ready for posting] Mark Dominus (MJD): When do the numbers $A$ and $2A$ have exactly the same (base-10) digits? (Level: advanced high school upwards) I will show how to prove that there are no such $A$ with fewer than 6 digits, and how to find examples with 6 or more digits without resorting to a brute-force computer search. The method I show will explain why all examples of 9 or fewer digits share a certain curious property. NOTICE My article needs editing. Email me if you are willing to read it over.

11. [ready] vzn. informally/briefly highlight/"gloss over" some advanced/challenging/research math already profiled in personal blog but from an undergrad pov, something like a brief TOC/overview/grab bag of some neat/deep subjects worthy of further study, some tend to cross with CS, some recent breakthroughs in field. namely: Collatz conjecture, Zhang twin prime proof, automated thm proving, Erdos discrepancy problem/Polymath, Erdos 100, P vs NP problem (Claymath prize etc), maybe others.

12. [First Draft] Jyrki Lahtonen. Two points determine a line, three a quadratic - what has that got to do with CDs? (Level: Advanced High School - Intermediate Undergraduate) An introduction to the algebra of error detection/correction on CDs driven by toy examples. Expected to be ready by the end of May.

13. [Ready for posting] Paramanand Singh. Playing with Partitions: Euler's Pentagonal Theorem (Level: Advanced High School - Early Undergraduate) Although this proof of Pentagonal theorem by Franklin is well known, I believe I already have my handwritten notes which are elaborate/simple enough to make sense to a high school student. I should be able to put it in blog format by next weekend (17th May 2014). See "Text version on dropbox" and "on stackedit.io"

14. [Ready for posting] Will Jagy As requested by Jyrki here Binary quadratic forms over Z and class numbers of quadratic fields. About ten pages in Latex, 12 point. No idea what happens next, don't know blogs or mathjax. Also never had any luck with dropbox or similar. Have files BLOG.pdf and BLOG.tex for anyone who does know what happens next and is willing to read the thing. My gmail address is most suitable. Today is 14th July, 2014. Would I lie? Tuesday, 15 July: no further changes came to mind, so I placed the final version, both pdf and .tex, at MMMEEEEEE just under my picture. Meanwhile, mixedmath seems to be at CONFERENCE. Alright, was able to post a draft and edit to some degree. Remaining big problem: I put lengthy computer outputs, I need them to to format the way my C++ program printed them. There does not seem to be a satisfactory blog edit command for a block of multi-line code, although there is a "code" button that does something or other.

Answer 2

I’m Grace Note, a Community Manager at Stack Exchange. I’m also the one in charge of maintaining our community-run blogs.

We’ve learned a lot by creating these per-site blogs for, essentially, anyone who asked for them. But in honesty, we have not been doing enough to make blogs work, not for the contributors nor for the communities that are associated with them. As such, going forward we at Stack Exchange are suspending the creation of new blogs until we make some changes. However, I see here 11 potential articles from 11 potential authors, and what appears to be a fairly large amount of push to try and make this not just a reality, but a spirited one at that. So we're going to make an exception here to consider setting up the Mathematics blog sooner. Two points here.

1. A major fallout in a lot of community-run blogs is that the project starts with a good number of enthusiastic writers all providing something to start it off. But then the steam is lost shortly afterwards and the system goes from a handful of writers to zero writers. Basically the blog is the sort of thing that they can submit if they have an idea but in lacking any sort of obligation or pull, they won't attempt to necessarily find ideas.

   To this point, it is recommended that there should probably be 1-2 people who want to take charge and "own" the blog, so to speak. This "owner" would be responsible for setting up schedules and for getting the writers to abide the schedule. You want someone who will keep the wheels in motion so that there's always fresh content coming out. We're not going to require this but it would be helpful if the community tries to organize someone for this role.

2. I know y'all have set this May 17th deadline you're using for the blog posts. What I'd like to see is the actual contents of, let's say 2 or 3 of the posts, when that May 17th deadline rolls around. Post them here, or host them someone online and link it from here - main thing is to get it past my eyes. I'd like to review and see what exactly this community is hoping to write about, by seeing what they do write about. Shortly after I review the stuff, a final decision will be made on whether or not we do make a full exception here and create the Mathematics Blog.

I look forward to seeing what people are planning to write!

Answer 3

Okay, so I think we have a pretty good stable of interested early contributors. I still think there are some things that need to be fleshed out before we formally inform the SE folks about our desire for a community blog.

1. First of all, we should figure out the "administration" of the blog: people willing to take on the task of trying to keep everything on schedule, and approving posts for "publication".

   • Goos
   • anorton - I will help out, but I cannot review/approve articles too far above mid-undergrad.
   • Karl Kronenfeld
   • Sanath Devalapurkar
   • [insert your display name if you're willing to help out with this task]

2. Think of some "recurring features" we might want to have. These should enable us to add new posts on a fairly regular basis (though the features themselves do not have to appear regularly).

   • Some other community blogs have "Question of the Week" posts, which in some manner highlight a question or answer voted on by the community. I think something like this could be useful in bringing more attention to some of our best content, but the "of the Week" portion is certainly mutable.

   • As mentioned in Alex Becker's original post, posts giving some information about recent major math award winners (Fields' Medal, Abel Prize, etc).

   • When major math competitions end (and problems are available to the public), it might be nice to have posts that outline their solutions.

   • Reviews of new or old math books.

   • [insert an idea here]

3. [Anything I've missed?]

To perhaps speed things along, I have created a new chat room devoted to discussions about this project. Stop by and share your ideas, thoughts and concerns. (I'm also taking suggestions for a witty yet descriptive name for the room.)

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Without the involvement of the community, the blog will not happen.

I don't think we can rely on only a small number of people to help out and keep the blog going. Our community blog should be a community effort. We've got a start, but I'm afraid that the steam has already run out. Prove me wrong!

Answer 4

Once a week as posting frequency is too ambitious. I would recommend once per month as a start, with a goal of every other week. That way, you won't, well, let's say likelihood of perceived failure is lessened.

* Possibly silly suggestion: Every other week publishing frequency would be good for distinctive branding, using fortnightly in the blog header or meta-description.