Passenger Delays Flight After Mistaking Math Equations for Terrorist Code

I wish I could say that this came from The Onion, but sadly this really happened:

http://www.slate.com/blogs/the_slatest/2016/05/07/passenger_delays_flight_after_mistaking_professor_s_math_equations_for_terrorist.html?wpsrc=sh_all_mob_em_ru

A flight from Philadelphia to Syracuse, New York, was delayed for two hours on Thursday after a woman expressed fears to the cabin crew that the man sitting next to her was a terrorist scribbling some sort of terrorist code into a notepad. In reality, he was a 40-year-old tenured professor at the University of Pennsylvania who was working on a differential equation…

Menzio insists he was “treated respectfully throughout” but says the whole incident served to illustrate a “broken system that does not collect information efficiently” and that anyone can end up causing a flight to be delayed for hours, no matter how ridiculous the suspicion.

A Long-Sought Proof, Found and Almost Lost

I enjoyed this article from Quanta Magazine, both for its mathematical content as well as the human interest story.

A Long-Sought Proof, Found and Almost Lost

From the opening paragraphs:

Known as the Gaussian correlation inequality (GCI), the conjecture originated in the 1950s, was posed in its most elegant form in 1972 and has held mathematicians in its thrall ever since. “I know of people who worked on it for 40 years,” said Donald Richards, a statistician at Pennsylvania State University. “I myself worked on it for 30 years.”

[Thomas] Royen hadn’t given the Gaussian correlation inequality much thought before the “raw idea” for how to prove it came to him over the bathroom sink… In July 2014, still at work on his formulas as a 67-year-old retiree, Royen found that the GCI could be extended into a statement about statistical distributions he had long specialized in. On the morning of the 17th, he saw how to calculate a key derivative for this extended GCI that unlocked the proof. “The evening of this day, my first draft of the proof was written,” he said.

Not knowing LaTeX, the word processer of choice in mathematics, he typed up his calculations in Microsoft Word, and the following month he posted his paper to the academic preprint site arxiv.org. He also sent it to Richards, who had briefly circulated his own failed attempt at a proof of the GCI a year and a half earlier. “I got this article by email from him,” Richards said. “And when I looked at it I knew instantly that it was solved” …

Proofs of obscure provenance are sometimes overlooked at first, but usually not for long: A major paper like Royen’s would normally get submitted and published somewhere like the Annals of Statistics, experts said, and then everybody would hear about it. But Royen, not having a career to advance, chose to skip the slow and often demanding peer-review process typical of top journals. He opted instead for quick publication in the Far East Journal of Theoretical Statistics, a periodical based in Allahabad, India, that was largely unknown to experts and which, on its website, rather suspiciously listed Royen as an editor. (He had agreed to join the editorial board the year before.)

With this red flag emblazoned on it, the proof continued to be ignored… No one is quite sure how, in the 21st century, news of Royen’s proof managed to travel so slowly. “It was clearly a lack of communication in an age where it’s very easy to communicate,” Klartag said.

Netflix was born out of this grad-school math problem

From Quartz magazine: Netflix was born out of this grad-school math problem

While studying computer science at Stanford University in the 1980s, Hastings said there was an exercise by computer scientist Andrew Tanenbaum in which he had to work out the bandwidth of a station wagon carrying tapes across the US. “It turns out that’s a very high-speed network,” Hastings said, speaking at a Mobile World Congress session in Barcelona. “From that original exercise, it made me think we can build Netflix first on DVD and then eventually the internet would catch up with the postal system and pass it.”

This is how Tanenbaum and co-writer David Wetherall described the problem in their book Computer Networks (fifth edition, pdf):

One of the most common ways to transport data from one computer to another is to write them onto magnetic tape or removable media (e.g., recordable DVDs), physically transport the tape or disks to the destination machine, and read them back in again. Although this method is not as sophisticated as using a geosynchronous communication satellite, it is often more cost effective, especially for applications in which high bandwidth or cost per bit transported is the key factor.

A simple calculation will make this point clear. An industry-standard Ultrium tape can hold 800 gigabytes. A box 60 × 60 × 60 cm can hold about 1000 of these tapes, for a total capacity of 800 terabytes, or 6400 terabits (6.4 petabits). A box of tapes can be delivered anywhere in the United States in 24 hours by Federal Express and other companies. The effective bandwidth of this transmission is 6400 terabits/86,400 sec, or a bit over 70 Gbps. If the destination is only an hour away by road, the bandwidth is increased to over 1700 Gbps. No computer network can even approach this. Of course, networks are getting faster, but tape densities are increasing, too.

If we now look at cost, we get a similar picture. The cost of an Ultrium tape is around $40 when bought in bulk. A tape can be reused at least 10 times, so the tape cost is maybe $4000 per box per usage. Add to this another $1000 for shipping (probably much less), and we have a cost of roughly $5000 to ship 800 TB. This amounts to shipping a gigabyte for a little over half a cent. No network can beat that. The moral of the story is:

Never underestimate the bandwidth of a station wagon full of tapes hurtling down the highway.

Meet the Math Professor Who’s Fighting Gerrymandering With Geometry

From the Chronicle of Higher Education: Meet the Math Professor Who’s Fighting Gerrymandering With Geometry, an interview with Dr. Moon Duchin, an associate professor of math and director of the Science, Technology and Society program at Tufts.

Q. What is the Metric Geometry and Gerrymandering Group’s aim?

A. In redistricting, one of the principles that’s taken seriously by courts is that districts should be compact. The U.S. Constitution does not say that, but many state constitutions do, and it’s taken as a kind of general principle of how districts ought to look.

But nobody knows exactly what compactness means. People just have the idea that it means the shape shouldn’t be too weird, shouldn’t be too eccentric; it should be a kind of reasonable shape. Lots of people have taken a swing at that over the years. Which definition you choose actually has stakes. It changes what maps are acceptable and what maps aren’t. If you look at the Supreme Court history, what you’ll see is that a lot of times, especially in the ’90s, the court would say, Look, some shapes are obviously too bizarre but we don’t know how to describe the cutoff. How bizarre is too bizarre? We don’t know; that sounds hard.

Q. It’s like how they define obscenity.

A. Exactly. When I started thinking about this, I was surprised to see that even though there were different mathematical attempts at a definition, you don’t ever see mathematicians testifying in court about it. So our first aim was to think like mathematicians about compactness and look at all the definitions that already exist, and compare them and try to prove theorems about the relationships between the definitions.

What courts have been looking for is one definition of compactness that they can understand, that we can compute, and that they can use as a kind of go-to standard. I don’t have any illusions that we’re going to settle that debate forever, but I think we can make a contribution to the debate.

See also her lecture for the Mathematical Association of America’s Distinguished Lecture Series:

How to Draw with Math

Scientific American had a nice guest article about the intersection of math and art.

 

UCLA mathematicians bring ocean to life for Disney’s ‘Moana’

From the UCLA news service:

UCLA mathematicians bring ocean to life for Disney’s ‘Moana’

From the second paragraph:

“In general, the animators and artists at the studios want as little to do with mathematics and physics as possible, but the demands for realism in animated movies are so high,” [UCLA mathematician Joseph] Teran said. “Things are going to look fake if you don’t at least start with the correct physics and mathematics for many materials, such as water and snow. If the physics and mathematics are not simulated accurately, it will be very glaring that something is wrong with the animation of the material.”

I recommend the whole article.

Five Simple Math Problems No One Can Solve

From Popular Mechanics: 5 Simple Math Problems No One Can Solve. The list:

  1. The Collatz conjecture.
  2. The moving sofa problem.
  3. The perfect cuboid problem.
  4. The inscribed square problem.
  5. The happy ending problem.

Dabbing and the Pythagorean Theorem

I enjoyed this article from Fox Sports. Apparently, a French Precalculus textbook created a homework problem asking if football (soccer) superstar Paul Pogba is doing the perfect dab by creating two right triangles.

 

Engaging students: Solving two-step algebra problems

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Jessica Bonney. Her topic, from Pre-Algebra: solving two-step algebra problems.

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How could you as a teacher create an activity or project that involves your topic?

A great activity to use in the classroom with students for this topic would have to be algebra tiles. The tiles are a good manipulative that can be used to improve the students’ understanding and offer contact to representative manipulation for students that are more kinesthetic learners. The algebra tiles can be used to help justify and explain the process of solving two-step equations. They were developed on the basis of two ideas: (1) we can isolate variables by using “zero pairs” and (2) equations don’t change when equal amounts of tiles are used on both sides of the equation. Algebra tiles come in different colors and sizes, which can be used to represent different parts of an equation that can help students solve two-step algebra problems.  I think this would be a fun and interactive activity to help students learn and understand how to go about solving these types of problems.

 

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How can this topic be used in your students’ future courses in mathematics or science?

Once a student gets to a certain grade level, they constantly start building upon what they learn. This material can be carried into high school and even college level courses.  Before a student learns two-step equations, they must master one-step equations, and even before that they need to understand basic arithmetical operations. Once mastery has been achieved, students will move onto solving larger polynomials, which can later be used in future algebra, geometry, and calculus courses. Another interesting use for two-step algebra problems is for future science and even computer science courses. In science, let’s say physics or chemistry, the students can use the two-step method for solving how fast a ball fell from a rooftop or for solving how fast a chemical evaporated at a certain temperature. Now in computer science students can learn how to develop algebraic functions in a computerized setting.

 

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What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

Rene’ Descartes, born in March of 1596, was a French mathematician, philosopher, and scientist. He is widely known for the statement, “I think, therefore I am,” deriving it from the foundation of intuition that, when he thinks, he exists. After obtaining a degree in law, his father wanted him to join Parliament, but sadly he was only 20 and the minimum age to join was 27. In turn, he moved to the Netherlands where he was influenced to study science and mathematics. During this time he formulated a common method of logical reasoning, centered on mathematics, which can be related to all sciences. This method is discussed in Discourse on Method, and is comprised of four rules: “(1) accept nothing as true that is not self-evident, (2) divide problems into their simplest parts, (3) solve problems by proceeding from simple to complex, and (4) recheck the reasoning.” We use these rules everyday when directly apply them to mathematical procedures.

 

References:

“Rene Descartes”. Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia

Britannica Inc., 2016. Web. 07 Sep. 2016 <https://www.britannica.com/biography/Rene-

Descartes>.

 

 

 

 

 

College Basketball’s Numbers Game

This is a very interesting (and readable) article about the blending of mathematics and coaching college basketball: http://www.fanragsports.com/cbb/college-basketballs-numbers-game/