Steven Strogatz possesses a special ability to see into the unseen. How does he do it? Steve is a world class mathematician, who sees through the window of math. But, lucky for us, he’s also a world class communicator. An award-winning professor, researcher, author, and creative thinker, Steve can help anyone (even Alan Alda) understand some of the unseen world of numbers. In this episode, Alan and Steven start from zero, not the number, but from a place of not knowing anything. He emerges from the darkness for a moment as Steve actually gets Alan to understand something that’s always mystified him. Steven's latest book, "Infinite Powers: How Calculus Reveals the Secrets of the Universe," is now available online and at all major book sellers.
While doing a good job of warming people up to math there was still a little bit too much “math is hard” or “math is impenetrable” discussion in the opening here. We need to get away from continuing the myth that math is “hard”. The stories we tell are crucially important here. I do like the fact that Alan Alda talks about how he’s been fascinated with it and has never given up. I’m also intrigued at Strogatz’ discussion of puzzling things out as a means of teaching math–a viewpoint I’ve always felt was important. It’s this sense of exploration that has driven math discovery for centuries and not the theorem-proof, theorem-proof structure of math text books that moves us forward.
I’ve always thought that Euler and Cauchy have their names on so many theorems simply because they did a lot of simple, basic exploration at a time when there was a lot of low hanging mathematical fruit to be gathered. Too many math books and teachers mythologize these men for what seems like magic, yet when taught to explore the same way even young children can figure out many of these same theorems for themselves.
If we could only teach the “how to do math” while children are young and then only move to the theorem-proof business later on as a means of quickly advancing through a lot of history and background so that students can get to the frontiers of math to begin doing their own explorations on their own again we would be far better off. Though along that path we should always have at least some emphasis on the doing of math and discovery to keep it at the fore.
QUINCY, MA—Confirming that they have no intention of modifying the traditional uniform of their profession at any point in the foreseeable future, mathematics professors from across the country joined their voices Monday to reaffirm their commitment to wearing chinos with running shoes. “We believe that this singular look has really been working for us for the past few decades, allowing as always for slight variations such as the presence or absence of pleats and the availability of slightly different varieties of white Reebok footwear, and we have decided to formally recommit to this outfit for as long as our profession continues to exist,” said Boston University vector analysis professor Paul Slavish, explaining that the pairing of khakis with cross trainers had become the symbol of his profession, as it offered a perfect combination of professionalism, approachability, and the comfort vital for on-campus life. “We acknowledge that our sneakers, while technically advanced, will never be used for actual running; our pants, while relatively clean, will never actually be ironed; and that this lower ensemble will always be paired with either a dress shirt two sizes too large or a sweat-wicking polo shirt that has never—and will never—wick away the sweat of exercise. Never shall we stray from this sacred combination, which proclaims at a glance that we are casual, unfussy people who happen to be very serious about mathematics. Plus, check out all these side pockets!” Slavish also confirmed that certain professors would occasionally wear a wacky necktie printed with mathematical symbols, but that this would occur at a maximum of three days per semester.
As it happens, he’d already done some work on coding theory—in the area of biology. The digital nature of DNA had been discovered by Jim Watson and Francis Crick in 1953, but it wasn’t yet clear just how sequences of the four possible base pairs encoded the 20 amino acids. In 1956, Max Delbrück—Jim Watson’s former postdoc advisor at Caltech—asked around at JPL if anyone could figure it out. Sol and two colleagues analyzed an idea of Francis Crick’s and came up with “comma-free codes” in which overlapping triples of base pairs could encode amino acids. The analysis showed that exactly 20 amino acids could be encoded this way. It seemed like an amazing explanation of what was seen—but unfortunately it isn’t how biology actually works (biology uses a more straightforward encoding, where some of the 64 possible triples just don’t represent anything). ❧
I recall talking to Sol about this very thing when I sat in on a course he taught at USC on combinatorics. He gave me his paper on it and a few related issues as I was very interested at the time about the applications of information theory and biology.
I’m glad I managed to sit in on the class and still have the audio recordings and notes. While I can’t say that Newton taught me calculus, I can say I learned combinatorics from Golomb.
Hagoromo Fulltouch Chalk is highly coveted around the world by mathematicians, who say it's superior to other kinds of chalk because it has an almost buttery texture and erases easily. When Hagoromo announced it was ceasing production, many mathematicians bought lifetime supplies, like one professor who has a four-stick-a-day habit. But a Korean company bought Hagoromo and has faithfully reproduced the original recipe so there is no longer a need to stockpile it. It's sometimes available on Amazon from third-party resellers.
In my previous post, I discussed how number theory and topology relate to other areas of math. Part of that was to show a couple diagrams from Jean Dieudonné’s book Panorama of Pure Mathematics, as seen by N. Bourbaki. That book has only small star-shaped diagrams considering one area of math at a time. I’ve created a diagram that pastes these local views into one grand diagram. Along the way I’ve done a little editing because the original diagrams were not entirely consistent.
Areas of math all draw on and contribute to each other. But there’s a sort of trade imbalance between areas. Some, like analytic number theory, are net importers. Others, like topology, are net exporters.
A biologist at Harvard was chatting with a colleague about a mentor who pushed him to do harder math problems. It turns out the colleague had the same mentor — and so did many others.
George Berzsenyi is a retired math professor living in Milwaukee County. Most people have never heard of him.
But Berzsenyi has had a remarkable impact on American science and mathematics. He has mentored thousands of high school students, including some who became among the best mathematicians and scientists in the country.
What a great little story…
I also find myself thinking, yet again, what was it about the early 1900’s in Hungary that they turned out, not even so many great scientists, but so many fantastic mathematicians? What were they doing right that we seem to be missing now? Can it be replicated? Was it cultural? Was it a certain type of teaching method? Simple expectations?
New research explains how the shapes of neurons can be classified using mathematical methods from the field of algebraic topology. Neuroscientists can now start building a formal catalogue for all the types of cells in the brain. Onto this catalogue of cells, they can systematically map the function and role in disease of each type of neuron in the brain.
A while back I answered a question on Quora: Can people actually keep up with note-taking in Mathematics lectures with LaTeX . There, I explained…
This is awesome though I’ve also heard of cases in which students use shared Google docs to collaboratively take notes like this as well.
Last night saw the wrap up of Dr. Michael Miller’s excellent Winter quarter class Introduction to Category Theory. As usual he passed out a short survey to accept ideas for the Fall and Winter quarters this coming year at UCLA Extension.
If you didn’t get a chance to weigh in, feel free to email him directly, or respond here with your suggestions (in order of preference) and I’ll pass them along.
I keep a list of his past offerings (going back to 2006, but he’s been doing this since 1973) on my site for reference. He’s often willing to repeat courses that have been previously offered, particularly if there’s keen interest in those topics.
Some of the suggestions on last night’s list included:
combinatorial group theory
point set topology
Feel free to vote for any of these or suggest your own topics. Keep in mind that many of the topics in the past decade have come about specifically because of lobbying on behalf of students.