Foreword for Cut the Knot: Probability Riddles by Alexander B.
How do you learn a language? There are two routes; the first is to memorize imperfect verbs, grammatical rules, future vs. past tenses, recite boring context-free sentences, and pass an exam. The second approach consists in going to a bar, struggling a little bit and, out of the need to blend-in and integrate with a fun group of people, then suddenly find yourself able to communicate. In other words, by playing, by being alive as a human being. I personally have never seen anyone learn to speak a language properly by the first route. Also, I have never seen anyone fail to do so by the second one.
It is a not well-known fact that mathematics can also be learned by playing –just watch the private correspondence, discussions and pranks of the members of the august Bourbaki circle. Some of us (and it includes this author) do not perform well on tasks via “cold” approaches, unable to muster the motivation to do boring things. But, somehow we upregulate when stimulated or when there is play (or money) involved. This may disturb many people married to cookie-cutter pedagogical methods that require things to be drab, boring, and bureaucratic for them to be effective –but that’s reality.
It is thanks to Maestro Alexander B. that numerous people have learned mathematics by the second route, by playing, just for the sake of entertainment. He helped many to make it their hobby. His mathematical website cut-the-knot has trained a generation –many seemingly approached the problem as hobbyists then got stuck with it. For, if you liked mathematics just a little bit, Maestro Bogomolny made it impossible for you to not love it. Mathematics was turned into a frolic.
I discovered his riddles on social media. (Alexander B. does not like the word “problems”. I now understand why.)
Social media brings out the best and the worst in people. He was rigorous yet open-minded, allowing people like me (who did some mathematical economics and finance) to cheat with inequalities by using the various canned methods for finding minima and maxima. He even tolerated computerized mathematics, provided of course there was some rigor in the process. I initially knew nothing about him but could observe rare attributes: an extraordinary amount of patience and a remarkable sense of humor. One summer, as he was in Israel, I informed him that I was vacationing in Lebanon. His answer: “Walking distance”. He always had a short comment that makes you smile, not laugh, which is a social art.
Alexander B. created a vibrant community around his Twitter account. He would pose a question, collect answers and patiently explain to people where they were wrong.
I, for myself, started almost every day with a puzzle, with the excitement of unpredictability, as it took from 5 minutes to 4 hours to complete –and it was usually impossible to tell from the outset. For a couple of years, it was the first thing I looked at with the morning coffee. There was some mild competition, mild enough to be entertaining but not too intense to resemble an academic rat race. Once someone got a proof, we had to look for another approach so it paid to wake up early and beat those with a time zone advantage.
In the two years since he left us there has been no Saturday morning –104 of them –that I did not solve a riddle randomly selected on the web in his memory. But, without him, it is not the same.
How did Alexander Bogomolny get there?
I met him in an Italian restaurant in New Jersey. I was surprised to see a mathematician who looked much more like a maturing actor than someone in a technical specialty: tall, athletic, jovial, and with a charismatic presence. But, as he had warned me, he had a severe hearing problem, the result of a medical treatment for the flu.
This explained to me his veering away from an academic career to get involved in computer pedagogy. His hearing was worsening with time. It is hard to imagine being a professor with reduced auditory function in one ear (in spite of a hearing aid) and none in the other.
There was something fresh and entertaining about him. He was happy. One could talk and laugh with him without much communication.
He was neither interested in money nor rank –something refreshing as I was only exposed to academics who whether they admit it or not, are obsessed with both. When I asked him about commercializing his website cut-the-knot his answer was “I have two pensions. Next year I turn seventy”. He wasn’t interested in poisoning his life for more money.
Why did I start nicknaming him Maestro? Because it was pretty much literal: he played math like a master would with a musical instrument –and mostly to himself. He was physically bothered by a sloppy derivation or an error, as if he heard a jarring note in the middle of a sonata. It was a joy to see someone so much in sync with his subject matter –and totally uncorrupted by the academic system.
Now, probability. In one conversation, I mentioned to him that probability riddles would be very useful for people who want to get into the most scientifically applicable scientific subject in the world (my very, very biased opinion). What I said earlier about play is even more applicable to probability, a field that really started with gamblers, used by traders and adventurers, and perfected by finance and insurance mathematicians. Probability applies to all empirical fields: gambling, finance, medicine, engineering, social science, risk, linguistics, genetics, car accidents. Let’s play with it by adding to his feed some probability riddles.
His eyes lit up. Hence this book.
I thank Marcos Careira, Amit Itagi, Mike Lawler, Salil Mehta, and numerous others who supported us in this project.
And a special gratitude to Stephen Wolfram, Jeremy Sykes and Mads Bahrami for ensuring that Cut-the-Knot stays alive and that this book sees the day. Additional thanks to Paige Bremmer,Glenn Schloebo, and other members of Wolfram Media for editing the manuscript.
Cut the Knot: Probability Riddles, by Alexander Bogomolny, published by Wolfram Research in collaboration with STEM Academic Press, $19.95. On Amazon.