### So what is this blog all about, anyway?

Quite simply, this blog is dedicated to exploring beautiful mathematics.

### Math? Beautiful? Yeah, right.

No fair, that’s not a question. But anyway, if you can’t understand how anyone could use the words “math” and “beautiful” in the same sentence, then I dare you to stick around a bit and see if you don’t change your mind. Math is about much more than figuring out when two trains will meet or calculating compound interest. Mathematics — like the hard sciences, but even more so — seeks to discover and understand the deep, elegant structure built into the very fabric of the universe. And it’s no surprise, really, that the deep mathematical structure of a universe featuring such things as clouds, crystal lattices, rainbows, galaxies, and atoms turns out to be beautiful. Personally, I see mathematics — and all beautiful structure in the universe — as evidence of a Creator at its source, but of course you can still appreciate it without sharing that belief.

### I like it but I will never remember to come back here every now and then to check for new entries.

You don’t have to! See that box in the upper right with the button under it that says “Subscribe”? Just type your e-mail address in the box, click the Subscribe button, follow some instructions, and you will get an e-mail each time there is a new post. If you use a newsreader, you can also subscribe via RSS.

### What level of mathematics do I need in order to understand the stuff you write about?

My posts are targeted mostly at the high school level — if you’ve taken (or are taking) Algebra II, you’ll probably have most of the tools you need to understand most of what I write. But there will probably be lots of stuff at many different levels, so don’t let that scare you away (or conversely, don’t let that convince you that you will be bored). And if there’s something you don’t understand, let me know, and I’ll try to explain it to you.

### Why the high school level?

There is tons of beautiful mathematics out there which is accessible without an advanced degree in mathematics — but not much of it is taught in high school, either because teachers do not have a good grasp of the mathematics outside their set curriculum, or because it is deemed “irrelevant” or “not useful”. While I agree that one goal of education is to make sure students acquire useful skills, certainly another goal is to arouse students’ wonder and curiosity — and this is where current mathematical education (at least in the U.S.) seems to fail so miserably. I doubt this little blog can ever really make up for such a big hole in modern math curricula, but at least I hope that a few students might read it and be inspired to consider that maybe — just maybe — math isn’t quite so boring as they thought…

*The Math Less Traveled*? Huh?

It’s a punning reference to the famous Robert Frost poem “The Path Less Traveled”. *Two paths diverged in a yellow wood…* You’ve probably heard of it.

Well, actually, you probably haven’t, since it doesn’t exist; the astute student of English literature will at this point jump in to object that the real title of the poem is “The *Road* Less Traveled”, not *Path*, and it actually goes *Two roads diverged in a yellow wood…* Right, sorry about that. Hopefully you can forgive my artistic license.

At this point the *very* astute student of English literature will jump in to object that the poem is *actually* entitled “The Road *Not Taken*“, and that furthermore it does not even use the phrase “the road less traveled”, much less “path”. Well… hrmph. At any rate you can read it here.

### So, how does this blog actually work? How do you get those cool-looking formulas in your posts?

*The Math Less Traveled* is hosted by WordPress.com, which supports using for inline mathematics. is a powerful mathematics typesetting system which is the accepted standard in mathematics and science publishing, and allows you to quickly and easily typeset complicated mathematical equations (and whole papers including them). It is completely free and there are versions which run on Windows, Macs, and Unix/Linux. If you’re interested in learning more about it, visit the Comprehensive TeX Archive Network at ctan.org.

### Can I use something you wrote on my own blog/in a math competition/to make copies to give to my students/as the basis of a short story/in a chapter of the book I’m writing in order to become filthy rich?

Yes, yes, yes, yes, and no. For details, see the license.

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I hope you’re working toward writing a book based on your blog!

patti: Thanks for the encouragement! I

havethought about that, actually, but am not sure what exactly that might look like or when that might happen.Think “Martin Gardner”. He has gone and left behind a vacancy.

BTW I find no “Subscribe” functionality.

Indeed he has.

Your web browser probably has a “Subscribe” button you can use. If not, try scrolling down until you find the link on the right side labeled “Entries RSS” under the “Meta” heading, and click on that.

Your blog is wonderful. I am a 52 year old retired mgmt consultant now teaching HS math. I have a BA and MS in math and feel a kinship to all those who view math as art, textbooks as boring, math history as critical, and numbers as mysterious and wonderous. I am fighting the battle of mixing in math with the “math” curriculum. But just got approval for a course called “Life in Numbers”, an elective that celebrates numbers and has no text or worksheets. Your blog will come in handy as I prepare topics for this course.

Charles: Thanks for leaving a comment, and good luck teaching your course, it sounds wonderful! Please let me know how it goes.

Brent: A reference that you might enjoy, which I didn’t see posted on your blog: MIT’s math for computer scientists (http://courses.csail.mit.edu/6.042/spring12/class-material.shtml ). There is a great pdf here: http://courses.csail.mit.edu/6.042/spring12/mcsfull.pdf .

It has a great “how to construct a proof” section. For those needing or wanting to constructs proofs, this is one of the best references I’ve found.

Ah, that’s a fantastic reference, thanks!

I like this blog, and like you I think math is beautiful. I do not think, however, that all its beauty and structure imply the existence of a Creator. Let’s say rather that the existence of a Creator is formally undecidable (because implications are provable). Many people have tried to prove the existence of a Creator, and failed. As they should, otherwise our religions would be religions no longer, but science instead. I’m aware, of course, that not believing that there’s a Creator, is a belief also. Anyhow, the matter is irrelevant to this blog. Keep up the good work!

I agree that the existence of a Creator cannot be formally proved—note that I said the beauty and structure of math *provide evidence for*, not *imply*, the existence of a Creator, which is quite different! Glad you enjoy the blog.

Many thanks for your kind comments about my web site. Ideas for additions, changes or corrections would be most welcome.

Notify me of new posts via email.

Hi Steven, if you want to be notified of new posts via email, go to the main page (http://mathlesstraveled.com/) and find where it says “Follow Blog via Email” on the right-hand side, near the top. Enter your email address in the box there and click “Follow”.

I wantednto ask about the methods currently in use in factorization of repunits? Whats the mathematics being used the steps

I don’t know! I am not aware of any methods for factoring repunits which is any faster or better than other general factoring methods.

What do u mean by other factoring methods?could you elaborate a little kindly

For example, elliptic curve factorization (https://en.wikipedia.org/wiki/Lenstra_elliptic_curve_factorization) or the general number field sieve (https://en.wikipedia.org/wiki/General_number_field_sieve).

thanks a lot, that was really helpful.

if u don’t mind me asking, is there any primality testing algorithm out there that u know of which uses repunits in factoring primes?

I don’t know.