Fermat’s Enigma

18th February 2021

Cheery Friday Greetings to our Learning How to Learners!

Book of the Week

Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem, by Simon Singh. Wow, what a book!  You might expect this volume to be the next best thing to Ambien as a sleep-inducer, but instead, Fermat’s Enigma is a real page-turner, providing a dazzling overview of the growth of mathematics from Pythagoras, (whose different way of thinking led to his being burned to death by a proto-cancel culture mob), through Euclid, and on through the early mathematical giants of Euler,  Gauss, Sophie Germaine (a mathematical savant who managed to save Gauss’s life while inadvertently revealing she was a woman), the tragic geniuses Évariste Galois (who wrote as much as he could of his key mathematical discoveries the night before his death), and Yutaka Taniyama (spoiler alert—it didn’t go well for him).  You don’t need to know much more than elementary math to enjoy this book, because an enormous part of the story is the personalities and fascinating lives of the mathematicians. By the time we finally homed in on Andrew Wiles and his solution, we thought—well, the drama is done, we’re back to the humdrum modern world.  But that’s when the book really came alive. Highly recommended!

A Wonderful Article for Lay Audiences about the Beauty of Math

We have to bring your attention to this wonderful New York Times article by Gareth Cook on mathematician Terrence Tao. (As one of Tao’s students has joked ‘‘They will never make a movie about him… He doesn’t have a troubled life. He has a family, and they seem happy, and he’s usually smiling.”)

As Cook writes:

“The true work of the mathematician is not experienced until the later parts of graduate school, when the student is challenged to create knowledge in the form of a novel proof. It is common to fill page after page with an attempt, the seasons turning, only to arrive precisely where you began, empty-handed — or to realize that a subtle flaw of logic doomed the whole enterprise from its outset. The steady state of mathematical research is to be completely stuck. It is a process that Charles Fefferman of Princeton, himself a one time math prodigy turned Fields medalist, likens to ‘‘playing chess with the devil.’’ The rules of the devil’s game are special, though: The devil is vastly superior at chess, but, Fefferman explained, you may take back as many moves as you like, and the devil may not. You play a first game, and, of course, ‘‘he crushes you.’’ So you take back moves and try something different, and he crushes you again, ‘‘in much the same way.’’ If you are sufficiently wily, you will eventually discover a move that forces the devil to shift strategy; you still lose, but — aha! — you have your first clue.

That is an excellent article. It does a great (and rare) job of explaining for the lay audience the relevance and elegance and satisfaction of mathematics.”

Brain’s ‘Background Noise’ May Hold Clues to Persistent Mysteries

This prescient article in Quanta by Elizabeth Landau homes in on an area of much interest now to neuroscientists—there is fascinating information buried in seeming electrical noise in signals from the brain. As is often said nowadays “Someone’s noise is another one’s signal.” [Hat tip: LHTL Lead Mentor Steven Cooke.]

More on Attention versus “Diffuse Mode”

LHTLer Norman Rabin points out: “In my thinking about ‘default mode’ (diffuse mode), I personally find it very helpful to remember that there is physiological suppression of parts of the brain when humans pay attention—that’s why attention is often referred to as ‘selective attention.’”  Norman points toward this Scientific American article, which notes “… the harder you concentrate, the greater the suppression. One fundamental role of cognition is to select what your brain goes on to process. It does that, at least in part, by blocking irrelevant information.”

This little video from NOVA shows how selective attention is behind our perception of magic tricks. There is a related illusion called “change blindness,” which you can see here (it’s pretty cool). Terry observes “Despite all the neurons in the visual cortex, you can only fully process one object at a time.  That’s why attention is needed to choose what to process.  Other objects are suppressed.  What is amazing is that once you have noticed the change, you can’t not see it any more.”

A Twist on the Pomodoro Technique

Prof. Rajesh Tayal shares his version of the Pomodoro technique that he also teaches his students (he teaches professional courses such as those for chartered accountants).

  1. Study for 25 minutes without any distraction
  2. Use the next 5 minutes to think seriously and organise thoughts about the topic
  3. Then use the next 5 minutes I use for making bullet point or mind map notes
  4. Use the final 5 minutes to do body stretches, drink water, and a little walk.

After 3 cycles of 40 minutes each, he takes a 20 minute break. Ultimately, he finds this approach to be very powerful. You may find the same—it combines the Pomodoro with both retrieval practice and exercise, both of which are very helpful for learning.

That’s all for this week. Have a happy week in Learning How to Learn!

Barb, Terry, and the entire Learning How to Learn team

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