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The following piece of news, in my humble opinion, deserves more mention in the math blogosphere than it has garnered so far. At the center of the story is an Iranian student of mathematics, Mahmoud Vahidnia, who was invited to a meeting between Iran’s Supreme Leader Ayatollah Ali Khamenei and the country’s scientific elite on Oct 28, 2009. An excerpt from a Guardian report on what transpired during a (perhaps, routine) question and answer session:

“I don’t know why in this country it’s not allowed to make any kind of criticism of you,” he told Iran’s most powerful cleric, who has the final say in all state matters. “In the past three to five years that I have been reading newspapers, I have seen no criticism of you, not even by the assembly of experts [a clerical body with the theoretical power to sack the leader]. I feel that if this doesn’t happen this situation will lead to discord and grudge.”

Vahidnia, who achieved nationwide recognition two years ago by winning Iran’s annual mathematics Olympiad, made his remarks at a meeting between Khamenei and the country’s scientific elite. They came after the supreme leader asked at the end of a question-and-answer session if anyone else wanted to speak. He chose Vahidnia after seeing him being pushed down by officials when he stood to ask a question.

Referring to the post-election crackdown sanctioned by Khamenei, he asked: “Wouldn’t our system have a better chance of preserving itself if we were using more satisfactory methods and limited the use of violence only to essential circumstances?”

I discovered the above piece of news “accidentally” via the Colbert Nation.  The Associated Press also did a report. I wonder if our Iranian readers (if there is any!) could furnish more information on this.

Welcome to the 54th Carnival of Mathematics, and Happy Fourth of July to our American readers! Indeed, the carnival should have been hosted yesterday, and I apologize for being a day late.

Trivia: Today, we have the 234th Independence Day celebrations in the  US, and ours is the 54th carnival. 2+3+4 = 5+4, see? Boy, do I feel so clever!

Ok, let’s begin, now!

We start off with a post, submitted by Shai Deshe, that presents a collection of YouTube videos explaining different kinds of infinities in set theory, causality vs conditionality in probability and some topology. The videos are the kind of ones that “math people” could use to explain a few mathematical concepts to their friends, family members and colleagues who may not be enamored of math very much but may still possess a lingering interest in it.

Experimental philosophy, according to the Experimental Philosophy Society, “involves the collection of empirical data to shed light on philosophical issues“. As such, a careful quantitative analyses of results of experiments are used to shed light on many philosophical issues/debates. Anthony Chemero wrote a post titled, ‘What Situationist Experiments Show‘, that links to a paper with the same title that he coauthored with John Campbell and Sarah Meerschaert. In the paper, the authors, through quantitative analyses of actual experimental data, argue that virtue ethics has not lost to the siuationist side, whose critiques of virtue theory are far from convincing.

Next, I would like to bring the readers’ attention to two math blogs that came into existence somewhat recently and which I think have a lot of really good mathematical content. They are Annoying Precision and A Portion of the Book. In my opinion, their blog posts contain a wealth of mathematical knowledge, especially for undergraduates (and graduate students too!), who, if inclined toward problem-solving, will enjoy the posts even more. Go ahead and dive into them!

At Annoying Precision, a project aimed at the “Generally Interested Lay Audience” that Qiaochu Yuan started aims “to build up to a discussion of the Polya enumeration theorem without assuming any prerequisites other than a passing familiarity with group theory.” It begins with GILA I: Group Actions and Equivalence Relations, the last post of the series being GILA VI: The cycle index polynomials of the symmetric groups.

Usually, undergrads hardly think integrals have much to do with combinatorics. At A Portion of the Book, Masoud Zargar has a very nice post that deals with the intersection of Integrals, Combinatorics and Geometry.

Tom Escent submitted a link to an article titled, “Introduction to Nerds on Wall Street“, which actually provides a very small snapshot of the book named, Nerds on Wall Street: Math, Machines and Wired Markets whose author is David J. Leinweber. I haven’t read the book yet, but based on generally good reviews, it seems like it chronicles the contribution of Quant guys to Wall Street over the past several decades. Should be interesting to Math and CS majors, I think.

Let’s have a post on philosophy and logic, shall we? At Skeptic’s Play, there is a discussion on Gödel’s modal ontological argument regarding the possibility of existence of God. As someone who has just begun a self-study of modal logic, I will recommend Brian K. Chellas’ excellent introduction to the subject, titled Modal Logic: An Introduction.

Then, there is the Daily Integral, a blog dealing with solving elementary integrals and which I think may be particularly useful for high-school students.

Let me close this carnival by asking the reader, “What do you think is the world’s oldest mathematical artifact?” There are several candidates, and according to The Number Warrior, candidate #1 is The Lebombo Bone, found in the Lebombo Mountains of South Africa and Swaziland, that dates back to 35,000 BC!

That’s all for now! Thanks to everyone who made submissons.

I attended the CURM Conference & MAA Intermountain Section Meeting yesterday at BYU, Provo, and had the chance to attend quite a few presentations that I found interesting. There were four presentations in particular that were of special interest to me, and though, right now, I don’t have enough material to blog on ’em, I think I will eventually find the required material to post some stuff here.

These four presentations were titled

1. Exploration of G-graphs of Non-Abelian Groups: Andrea L. DeWitt & Alys M. Rodriguez (Lamar University)

2. Re-invent the Wheel: can it be done?: Christa Bauer & Jillian Hamilton (Lamar University)

3. Proving Integer Sequence Identities with Paths on Graphs: Megan Craven (St. Peters College)

4. Restricted Rado Numbers: Katrina Luckenbach & Matthew Vieira (St. Peters College)

Here is some career advice by Terry Tao on his blog. I think it has tons of useful information and wisdom.

This one, by Oleg Golberg, appeared in the 6^{th} issue of Mathematical Reflections (MR) 2007. I don’t have a solution yet, but I think I should be able to solve it sooner or later. If you find a solution, you should send it to MR by Jan 19. Here is the problem anyway.

For all integers k, n \geq 2, prove that \\ \displaystyle \sqrt[n]{1 + \frac{n}{k}} \leq \frac1{n} \log \big( 1+\frac{n}{k-1} \big) + 1.

I became interested in mathematical blogging after visiting Terence Tao’s and Timothy Gower’s blogs on numerous occasions. It seems there is a sizable number of mathematicians disseminating valuable information through their blogs, and I see this as a healthy sign. Such blogs provide a wealth of information to students like me, and dare I say, I learn most of my math from such blogs!

I intend to write about math mostly as an exercise in exposition. I am assuming this will be of great help to me later on. I also will be posting some problems in the “Problem Corner” section every now and then.

Let’s see how this goes. I am hoping my enthusiasm for blogging will not wear off too soon!

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March 2023