How a Public School in Florida Built America’s Greatest Math Team

“A single, otherwise unremarkable public high school in Florida has won 13 out of the most recent 14 National Math Championships, a staggeringly successful dynasty for an otherwise average school. It’s accomplished this through treating math competition as any other sport, identifying talent as early as elementary school and developing them over the course of several years through a completely redesigned curriculum. An emphasis on speed also is crucial, and the results are pretty inarguable: The margin of victory at the national title over the past 14 years has averaged 315 points, which in 2021 jumped to 920 points.”

Walt Hickey, “Lottos, ShotSpotter, Mathletes.” Numlock News. July 15, 2022

The Wall Street Journal article is pretty interesting, I particularly liked this comment:

Will Frazer popped out of his flaming red Corvette as his students were trickling into the classrooms. A bond trader on Wall Street in the 1980s, Mr. Frazer retired young and moved to Florida, where he became a scratch golfer and lived the dream for a decade. Then he got bored.

He took a job at Buchholz coaching golf, switched to teaching math, quickly formed a math team, applied the lessons of his experience in finance and turned a bunch of teenage quants into a fearsome winning machine.

“The difference between what I do now and what I did on Wall Street is that I used to get paid money,” said Mr. Frazer, 63. “Now we get trophies.”

-Ben Cohen, “How a Public School in Florida Built America’s Greatest Math Team.” The Wall Street Journal. July 4, 2022

Paying someone to find and develop talent works not only for math, but pretty much everything in life. It makes you wonder why communities do not pay people to do this kind of thing for qualities they want more of. Want more STEM majors? Want more soccer players? Want chess champions? There’s a technique for that.

László Polgár also offers an interesting example because he was not able to select for top talent, he simply helped develop it in his own children. Presumably, if he had interest, there might be genetic factors in play, but I’d guess the bulk of his daughter’s success came from development. No reason this couldn’t be replicated in a million different ways. In the age-old question of Nature vs. Nurture, it would probably lead to a lot better outcomes if we tried a lot more nurture.

Which Computational Universe Do We Live In?

“In 1995, Russell Impagliazzo of the University of California, San Diego broke down the question of hardness into a set of sub-questions that computer scientists could tackle one piece at a time. To summarize the state of knowledge in this area, he described five possible worlds — fancifully named Algorithmica, Heuristica, Pessiland, Minicrypt and Cryptomania — with ascending levels of hardness and cryptographic possibility. Any of these could be the world we live in.”

-Erica Klarreich, “Which Computational Universe Do We Live In?” Quanta Magazine. April 18 , 2022.

Quanta has some really interesting content. Let’s hope we live in Cryptomania.

Cryptography from the Ground Up

“One of the most interesting and useful things computers can do for us is cryptography. We can hide messages, validate identities, and even build entire trustless distributed systems. Cryptography not only defines our modern world, but is a big part of how we will build the world of the future.

However, unless you want to dedicate years and a PhD to studying the subject, the actual workings of cryptography can be hard to learn. It can involve a lot of pitfalls and if you dare build from scratch, you are bound to make a fool of yourself. Why?

In my opinion, it comes down to history. Cryptography has had centuries of methods that have been made, broken, and remade again. Most tutorials on cryptography focus on the what: do this, don’t do that, follow the rules. But they skip over the why: why do we do the things we do? What are we trying to avoid?

To understand the why, we need to understand how we got here in the first place. And to do that, let’s set computers to the side for the moment and delve into the world of classical cryptography.”

https://cmdli.github.io/crypto/

Math: Ambiguity & Order of Operations

“The real answer, the one I believe any mathematician, physicist, engineer, other number-cruncher would tell you is to make sure your expressions aren’t ambiguous. There’s no extra charge for another set of parentheses. Just toss them in. If you want the answer to be 16, write (8÷2)(2+2). If you want it to be 1, write 8÷(2(2+2)). Problem solved.”

—Evelyn Lamb, “The Only Way to Win Is Not to Play the Game.” Scientific American. August 3, 2019.

Quantumcomputing For The Very Curious

“This essay explains how quantum computers work. It’s not a survey essay, or a popularization based on hand-wavy analogies. We’re going to dig down deep so you understand the details of quantum computing. Along the way, we’ll also learn the basic principles of quantum mechanics, since those are required to understand quantum computation.

Learning this material is challenging. Quantum computing and quantum mechanics are famously ‘hard’ subjects, often presented as mysterious and forbidding. If this were a conventional essay, chances are that you’d rapidly forget the material. But the essay is also an experiment in the essay form. As I’ll explain in detail below the essay incorporates new user interface ideas to help you remember what you read. That may sound surprising, but uses a well-validated idea from cognitive science known as spaced-repetition testing. More detail on how it works below. The upshot is that anyone who is curious and determined can understand quantum computing deeply and for the long term.”

Andy Matuschak and Michael Nielsen. “Quantumcomputing For The Very Curious.” Quantam.country. March 18, 2019.

Looks like I’m going to have to brush up on my math.

Greg Egan and the Permutation Problem

“Then on September 26 of this year, the mathematician John Baez of the University of California, Riverside, posted on Twitter about Houston’s 2014 finding, as part of a series of tweets about apparent mathematical patterns that fail. His tweet caught the eye of Egan, who was a mathematics major decades ago, before he launched an award-winning career as a science fiction novelist (his breakthrough 1994 novel, in a happy coincidence, was called Permutation City). “I’ve never stopped being interested in ,” Egan wrote by email.

Egan wondered if it was possible to construct superpermutations even shorter than Houston’s. He scoured the literature for papers on how to construct short paths through permutation networks, and after a few weeks found exactly what he needed. Within a day or two, he had come up with a new upper bound on the length of the shortest superpermutation for n symbols: n! + (n-1)! + (n-2)! + (n-3)! + n-3. It’s similar to the old factorial formula, but with many terms removed.”

—Erica Klarreich. “Mystery Math Whiz and Novelist Advance Permutation Problem.” Quanta. November 5, 2018.

Greg Egan’s hard sci-fi novels are amazing. Axiomatic is a collection of short stories that can give you a sense of what to expect. Read Diaspora if you want to jump right into the deep end. Read Quarantine if you want to take on a series.