The Unapologetic Mathematician

Mathematics for the interested outsider

About this weblog

This is mainly an expository blath, with occasional high-level excursions, humorous observations, rants, and musings. The main-line exposition should be accessible to the “Generally Interested Lay Audience”, as long as you trace the links back towards the basics. Check the sidebar for specific topics (under “Categories”).

I’m in the process of tweaking some aspects of the site to make it easier to refer back to older topics, so try to make the best of it for now.


  1. You asked if I found an OS written in Lisp that I should mention it, sadly it’s not Unix-like but it is interesting nonetheless: FunOS.

    Comment by AngryPhysicist | September 12, 2007 | Reply

  2. I really enjoy reading your site however your formulas are not parsing correctly at the moment.

    its probably a problem with the external way you parse them but just in case you hadn’t noticed yet.

    Comment by Joel | September 19, 2007 | Reply

  3. Joel, yeah, I’ve noticed the embedded LaTeX going screwey at a bunch of WordPress sites recently. I hope it’ll pass, but there’s nothing I can really do at the moment.

    Comment by John Armstrong | September 19, 2007 | Reply

  4. I found you saying (in another post) that the ETS regraded the SAT and hence a static average in maths score is actually a drop of 50/1000 points – or something like that. Can you please email me some reference so I can understand what you mean by this? I am trying to understand the issue. Thanks.

    Comment by alan kwan | December 26, 2007 | Reply

  5. Some of us are starting up a blog as we enter graduate school, and (as the LaTeX-guy) how you embed LaTeX symbols into your wordpress posts? Is there a reference for how to do this?


    Comment by felicis | January 3, 2008 | Reply

  6. felicis, I commend the effort. As for using LaTeX in posts and comments on WordPress-hosted weblogs, the details on that are here.

    Comment by John Armstrong | January 3, 2008 | Reply

  7. Ah ha! Thank you very much! It’s easy, and we can even use \LaTeX in comments! Hurray!

    Eric (aka Felicis)

    Comment by felicis | January 4, 2008 | Reply

  8. Hi, I came across your site and thought it would be great for one of our clients. If interested in an advertising venture please feel free to contact me.

    Comment by Andre Buxey | December 10, 2008 | Reply

  9. […] mathematicians value communicating their ideas to non-specialists (what John Armstrong calls the Generally Interested Lay Audience (GILA)), I should probably be putting my money where my mouth […]

    Pingback by GILA I: Group actions and equivalence relations « Annoying Precision | June 14, 2009 | Reply

  10. It’s in fact pretty easy to search through your blog if it’s added to Google Reader. For instance, I typed in “group theory” in the GR’s search, and it showed all your entries where you ever mentioned it. If you don’t use it already, I highly recommend it. Thank you for all the work you’ve put into your blog.

    Comment by Sara | June 28, 2009 | Reply

  11. That’s a good point, Sara. I hope to keep it going for a good while yet.

    Comment by John Armstrong | June 28, 2009 | Reply

  12. I just have to know: is the title of this blog related to G.H. Hardy’s essay “A Mathematician’s Apology”? If so, kudos. If not, kudos.

    Comment by AndrewB | July 6, 2009 | Reply

  13. Yes, specifically that I’m not acting as an apologist, defending mathematics as a field from detractors.

    Comment by John Armstrong | July 6, 2009 | Reply

  14. Hi, it would be very pleasant (to me) to see if you could say something about automorphisms of the \mathbb{Z}-module \mathbb{Z}\oplus\mathbb{Z}\oplus\mathbb{Z}_2 for which the answer is know: as a set is GL_2(\mathbb{z}). Please.

    Comment by juanmarqz | September 17, 2009 | Reply

  15. it would say GL_2(\mathbb{Z})

    Comment by juanmarqz | September 17, 2009 | Reply

  16. juan, that sounds suspiciously like a request that I do your homework.

    Comment by John Armstrong | September 17, 2009 | Reply

    • not exactly i only want to seek interaction on a very pretty subject. Did you know that the MCG of the torus and the genus-three-non-orientable surface are equal? Anyway thanks and kudos for yer work 🙂

      Comment by juanmarqz | September 17, 2009 | Reply

  17. Hey John, the ‘unapologetic mathematician.’ So I’m currently searching for my 3rd and final interviewee, and returned to John B’s webpage to check out the blog roll, see if there were any sites I forgot to hit up.

    Then I saw the blog entry, ‘Sex Advice from Mathematicians’…
    Nice. I loved it. And of course, I read your enthusiastic response. I’d love to have you down as the 3rd one (and most definitely, be as ‘unapologetic’ and fun with the questionnaire as you can! I highly encourage that!) Contact me as soon as you can, Much regards.

    Comment by Nelson A. | October 2, 2009 | Reply

  18. hi man, i saw that a year ago or so WP had a trouble with backslashes when editing matrices in latex… so the quizz is: How did they solve the problem then?
    do you have now this very same problem now, how i have today? please

    Comment by juanmarqz | October 4, 2009 | Reply

  19. Best I can tell, Juan, the problem arose for me about a week ago. Since then, double backslashes have been replaced by single ones. The stopgap solution I’m using is to type triple backslashes where I mean to have double backslashes, but you have to replace these every single time you edit the post because triple backslashes get replaced by doubles, and then doubles will be replaced by singles when you save the post again.

    Comment by John Armstrong | October 4, 2009 | Reply

    • good grief!, well i suspect that the trouble gonna solve alone i.e. under the good will of WP. I already complained at WP-support and someone dubbed Sheri Automattic told me that they are fixing this annoying extra-feature. Thanx and Saludos from Guadalajara…

      Comment by juanmarqz | October 5, 2009 | Reply

  20. Test (product of two matrices)

    \begin{pmatrix} 1 & 4 & 0 \\ -2 & 4 & 3\end{pmatrix} \times \begin{pmatrix} 1 \\ 0 \\ -3\end{pmatrix} = \begin{pmatrix} 1 \\ -11\end{pmatrix}

    Comment by Américo Tavares | January 12, 2010 | Reply

  21. Hello,

    could I ask some more clarifications regarding the Riemann-Stieltjes integral?


    Comment by Marco | January 26, 2010 | Reply

  22. Like what?

    Comment by John Armstrong | January 26, 2010 | Reply

    • Well, I see how a Riemman integral is the summation of dproducts of the function f at an arbitrary value t, f(t) where x_i-1<t<x_i, times dx=x_i – x_i-1….

      The R-S integral instead relates a function f to another function, g using dg(x) instead of to the infinitesimal dx….

      the two integrals coincides if dg/dx is defined…..

      When that is not defined, could we not just use the Cauchy principal value of the integral to deal with points where the function is not defined at some points in the interval of integration…..


      Comment by Marco | January 27, 2010 | Reply

  23. I’m not sure really what you’re looking for in terms of “dealing with” points where g isn’t differentiable. It’s just not expressible as a Riemann integral. Why is this a problem?

    Comment by John Armstrong | January 27, 2010 | Reply

  24. […] Unapologetic Mathematician – John Armstrong’s high-level educational math blog. You can pick some topic you want to learn and track back […]

    Pingback by Math 2.0 – Konrad Voelkel's Blog | February 7, 2010 | Reply

  25. Dr. Armstrong,

    I came across your blog while searching for “mathematics” in the wordpress search bar. I was one of your students at WKU. Ellen Boswell and I met with you to do various math problems. I’m not sure if you remember it, but I wanted to say that I appreciate it. I am glad to have found your blog and I look forward to reading it.

    Comment by Tyler Clark | July 4, 2010 | Reply

  26. Sure I remember, Tyler. Glad you’re enjoying it, and I hope your master’s work goes well.

    Comment by John Armstrong | July 4, 2010 | Reply

  27. Dr. Armstrong,

    I have installed the WP LaTeX plugin and when you go to my main blog page the LaTeX works. However, when you go to the specific post, the LaTeX gets lost. Do you know how I can fix this?

    Tyler Clark

    Comment by Tyler Clark | August 18, 2010 | Reply

    • I don’t know, Tyler; I use the WordPress-hosted version, which does that for me.

      One guess might be that it’s using a relative URL to find the \LaTeX-rendering script, which gives the right absolute URL for the main page but doesn’t for the individual posts.

      Comment by John Armstrong | August 18, 2010 | Reply

  28. Nice blog.
    I hope to see more interesting posts in 2011.
    Science is interesting 🙂

    Comment by science and math | January 2, 2011 | Reply

  29. Please post more if you get time! Any recommendations for other blogs of this nature?


    Comment by Eric Auld | April 30, 2011 | Reply


    Comment by Derek Studholme | January 12, 2012 | Reply

  31. Thank you so much for your effort in creating this invaluable work. I’m an undergraduate student in mathematics, and I’ve learned so much from your blog.

    Comment by math | April 5, 2012 | Reply

  32. I often find this blog explains specific topics really well. However, I can’t easily browse through the whole blog and determine what other topics are discussed. I know you’ve mentioned you’re trying to make navigation easier, but I was wondering if there was simply an index page with all the posts you’ve made? Cheers

    Comment by hopeful | August 21, 2012 | Reply

  33. If you are the unapologetic mathematician, then why do you start this page off with an apology?

    Comment by Kerry White | December 5, 2012 | Reply

  34. What is a blath?

    Comment by isomorphismes | February 23, 2014 | Reply

  35. Thanks for following my posts. Will try to follow yours!

    Comment by Candia | July 7, 2014 | Reply

  36. Notify me of new posts via email.

    Comment by Steven Meyerson | September 7, 2014 | Reply

  37. Nice blog, keep it up 🙂

    Comment by artusartos | October 25, 2014 | Reply

  38. I am curious about a blogger who seems to be quite a competent mathematician. He also produces YouTube videos. However, I can find nothing about him. His name appears to be M L Baker and he had spent some time at the Univ of Waterloo. Any clue as to his identity?

    Comment by oldrubbie | May 30, 2016 | Reply

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