Marin Mersenne (1588 – 1648) was a French theologician, philosopher, and music theorist. One of his works, *Cogitata Physico-Mathematica*, investigates both acoustic and physical phenomena. Here’s a sample picture:

In the introduction to the work he discusses perfect numbers. Perfect numbers are the sum of the proper divisors of the same number; 28 is perfect because 1 + 2 + 4 + 7 + 14 = 28. Mersenne knew Euclid’s proof that gives an even perfect number whenever is prime. Theorizing what other values of are prime, Mersenne decided on values of *n* = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, and 257, and that these were the only values up to 257 where is prime.

His list did have errors: he missed *n* = 61, 89, and 107 (which also make prime), but he also named two values of *n* which shouldn’t have been on the list at all.

The first mistaken value (*n* = 67) was discovered in 1876 by Edouard Lucas. However, the actual factors weren’t known until 1903. In what may be the most bizarre lecture ever presented, Frank Cole stood up at meeting of the American Mathematical Society to deliver a talk entitled *On the factorisation of large numbers*. Cole never spoke; he simply wrote

and then followed with the numbers 761838257287 and 193707721 and performed long multiplication, obtaining to the acclaim of a standing ovation.

The second error (*n* = 257) was found by Maurice Kraitchik (of the two envelopes problem) in 1922. If is generalized for any base, using the formula

then the smallest base *b* for which the number is prime is …

… 52! And with that, we start the Carnival of Mathematics.

Kate Nowak presents an example designed to fool her students of a pattern that breaks down.

Edmund Harriss writes about (with lovely pictures!) the making of a mathematical sculpture.

David Richeson celebrates May Day by devising and investigating the maypole braid group. (Nice pictures on this one too!)

Let’s Play Math has been making fantastic math calendars. Perhaps your students would like to contribute to the next one?

Dick Lipton has been making gobs of good posts lately, but to start I recommend his explanation of Cantor’s Non-Diagonal Proof.

Terry Tao has rescaled the United States federal budget to the scale of 100 million:3, to give a better perspective of the impact of spending. (I’ve already stolen this concept for a new lesson plan.)

Sam Shah asks which books would make good awards for students.

My fellow conspirators at 360 in boosting the math history content of the blogosphere discuss Mayan math and the Dresden Codex, which now has full-color pictures available on the Internet.

David Eppstein poses an intriguing problem involving half-integer triangles and Pick’s theorem.

While that last post is well commented on, try Nick Hamblet’s question on Riemann sums that nobody has (as of this writing) answered.

Here’s a series asking a simple question with complex ramifications: how many quadratic equations with real roots are there? (Part one, Part two)

John Conway is a genius when it comes to devising notation. Exhibit A: neverendingbooks explains Conway’s big picture.

Pat Ballew points out an mathematical error in a science magazine. I recommend reading the post as a puzzle and just looking at the picture and the opening joke to try to figure out what’s wrong before checking the rest of the text.

A tricky probability problem presents itself as Praveen Puri asks: what’s the chance the patient has the disease?

Nathan Bloomfield just finished his first research paper! To celebrate he has written about his experience.

A late submission to sneak in, but a really good one: Maria Anderson has done surveys to summarize mathematical instructional practices.

And finally, a smattering of logic: Andrew Bacon discusses Restall’s Paradox, Kenny Easwaran endorses a particular kind of probabilistic proof, and I consider a slight variation on an old classic.

That’s a wrap! If you’re wanting more math carnival goodness, be sure to check the Math Teachers at Play carnival which alternates Fridays with this one.

Filed under: Mathematics

Matt E, on May 8, 2009 at 4:37 am said:I’ll leave this comment here, since Praveen Puri’s site has neither comments nor any contact information!

The problem he states is a classic in counter-intuitive probability, but I think the counter-intuitive-ness is amplified by the way the question is phrased.

His problem states that a test for a disease has “5% false positives”. I think a lot of people would read that and think (quite reasonably) that 5% of the tests that come back positive are false. Thus the belief that the answer to the question is 95%. I think it takes a little bit of extra knowledge to know that “5% false positives” means “5% of the tests given to those who do not have the disease come back positive.”

Praveen Puri, on May 8, 2009 at 7:41 am said:Hi Matt,

I’m sorry you couldn’t leave a comment. I thought comments on the blog were on. I reactivated them again.

Thanks for your comment. I just edited the post. It now reads:

A test for a disease has 5% false positives (This means that 5% of the tests given to those who do not have the disease come back positive – so if 100 people test positive, only 95 actually have the disease)…

Praveen

Matt E, on May 8, 2009 at 7:44 am said:“100 people”… who

don’thave the disease, right? :-)Carnival of Mathematics #52 « 360, on May 8, 2009 at 5:00 am said:[...] of Mathematics #52 By Ξ YES! It’s Carnival of Mathematics #52, hosted by The Number Warrior. He starts with a great math problem that had me wondering, [...]

Jason Dyer, on May 8, 2009 at 7:21 am said:Matt, I forwarded the comment to Praveen.

I also fixed the Sam Shah link above which was broken.

I’m in the Carnival! « Sumidiot’s Blog, on May 8, 2009 at 9:13 am said:[...] I’m in the Carnival! By sumidiot My post on a Riemann sum made the 52nd Carnival of Mathematics! [...]

Let’s go to the carnival « Division by Zero, on May 8, 2009 at 11:04 am said:[...] go to the carnival The 52nd Carnival of Mathematics is underway over at The Number Warrior. I’m glad it was resurrected. Check it [...]

Math Bloggers at Play « Let’s Play Math!, on May 8, 2009 at 1:27 pm said:[...] Carnival of Mathematics #52 is up and running at The Number Warrior, with tidbits about perfect numbers and Mersenne primes as [...]

samjshah, on May 9, 2009 at 6:24 pm said:Thanks for putting together a *great* carnival. I esp. loved the posts about the quadratic equation/real v. complex roots. I’ve asked myself that question and came up with a few solutions that all made sense. I am definitely going to be using that question in my MV calc class next year, fo’ sho’.

Sam

Jason Dyer, on May 10, 2009 at 10:31 pm said:That’s a new blog (last I checked I was the only subscriber on Google Reader) but the quality bodes well for future posts by the same author.

Carnival of Math 52 at Number Warrior « JD2718, on May 10, 2009 at 6:37 am said:[...] comes the actual carnival: almost 20 sharp links. I don’t know if Jason tilted it on purpose, but his carnival has a [...]

Math Teachers at Play #7 « Let’s Play Math!, on May 15, 2009 at 7:08 am said:[...] while you’re playing around with math, don’t forget the Carnival of Mathematics #52, which went up last week at The Number Warrior. Plenty of fun there, too. Does anyone know where [...]

Tracy, on May 27, 2009 at 12:05 pm said:Great math carnivale! How about some math carnivals for younger students, though?

Jason Dyer, on May 27, 2009 at 2:06 pm said:Does Math Teachers at Play (which I have plugged on this blog, but haven’t hosted yet) match what you are describing?

Math Teachers at Play

If you mean not just with links to things teachers can use for younger students, but a carnival *for* younger students … that seems like it’d need to be hand-curated, but it’s possible. Worth a thought. Maybe a compilation of material from the last 5 carnivals of Mathematics and Math Teachers at Play presented in an appropriate way could do the trick.

Badal Joshi, on May 28, 2009 at 7:57 pm said:Does anyone know where and when the next carnival (number 53) is?

Why You Want to Host the Carnival of Mathematics « The Number Warrior, on June 17, 2009 at 4:30 pm said:[...] 4. Your blog traffic will shoot up like a rocket. You may be familiar with the WordPress fastest growing blogs list. I might bring your attention to #17 on May 9, which happened to be the same day I posted the Carnival of Mathematics #52. [...]

Next Math Teachers at Play Hosted Here « The Number Warrior, on July 21, 2009 at 7:42 am said:[...] Next Math Teachers at Play Hosted Here Posted on July 21, 2009 by Jason Dyer I have hosted the Carnival of Mathematics three times before: Carnival of Mathematics #30 Carnival of Mathematics #43 Carnival of Mathematics #52 [...]

Math Teachers at Play #7 |, on August 2, 2009 at 8:06 am said:[...] while you’re playing around with math, don’t forget the Carnival of Mathematics #52, which went up last week at The Number Warrior. Plenty of fun there, too. Does anyone know where [...]