I’m a trained historian. At least I consider myself one, with a Master’s in History and in International Relations, I think I qualify. But, today I must confess to a dilettantish interest in the history of mathematics. Now, please understand that I am no mathematician. I struggled through college algebra. I will, however, add that when I completed college algebra my analytical faculties grew so profoundly—at least to me in hindsight—that I made the Dean’s List every semester thereafter. So, I believe there is something quite important to be said about learning how to solve for ’n’ that we should impart to our children. In the beginning the abstract nature of algebra confounded me, but once I was able to conceptualize it, I began mastering the equations and, as aforementioned, my intellectually faculties grew rapidly and intensely. Soon, my intolerance for fucktose in an history text—or any text for that matter— become keen, acute and annoying as hell to many of my fellow junior and senior history seminar classmates. But I digress. This is about math. Let me add before the next paragraph begins that I also never took calculus. But we’ll get to calculus soon.

First, my fascination began with Euclid and how he systematized and synthesized Egyptian and Babylonian ideas into a coherent structure of elements that led to modern plane geometry. The dude took the wisdom of the pyramid builders and the ziggurat builders and discovered a way of looking at the world to build in new ways. That takes a hell of a mind, one I can appreciate, even at his far of a distance in time. As I studied Euclid I learned that Babylonia used a base-sixty numerical system. While the Egyptians used a base-ten system. The Egyptians were the first to utilize fractions around 1000 BC. Then, in the 5th century BC the Indians in an attempt to square the circle calculated the square root of two correctly to five decimal places. Then around 300 BC the Indians used Brahmi numerals to further refine the true ancestor to our base-ten system. At the same time the Babylonians invented the abacus.

The poor Romans didn’t do diddly for mathematics. Imagine complex calculations with Roman numerals? Screw that. But they sure used them to build roads and survey, among other things. So, kudos to them for applied mathematics. At lot of stuff happened between the Romans and the next development. Stuff which I am skipping because I’m trying to get to a simple point without using two thousand words to do so.

Something truly remarkable happened in India in 628 AD. Brahmagupta wrote a book that clearly explains and delineates the role of zero in a proton-hind Arabic script. This was positively revolutionary. He is the clear discoverer of the modern place value system of numbers, as well. Well, natural numbers, that is.

And now stuff really begins to accelerate.

In 810 the House of Wisdom is built in Baghdad for express purpose of translating Greek and Sanskrit mathematical and philosophical texts. Ten years later, in 820 a Persian from Khwarazm—the delta of the Oxus River into the former Aral Sea discovered a way to solve linear and quadratic equations. His name was al-Khwarizmi and his book was called Al Jabr—which was Europeanized into algebra. His book, once it reached Europe three and a half centuries later introduces the Hindu-Arabic numeral system that is adopted wholesale by the nascent scientific community emerging in the earliest European universities. Universities also have a Muslim Golden Age pedigree, coming from the great Persian vizier to the Seljuk Sultan of Central Asia Malik Shah, Nizam al-Mulk. His Nizamiyyas, now known as madrassas, were built all over the Seljuk realm and were the earliest versions of universities, where men came from all over to learn many different topics. Sadly, the madrassas fell into stagnation when al-Ghazali closed the gates of ijtihad (open questioning) in 1091 with his book The Incoherence of the Philosophers. The Muslim Golden Age ended that year.

Now, between the foundation of the earliest European universities and Isaac Newton, a lot of essential groundwork was laid for Ike’s work. I seek not to diminish any of that. But Newton begat not one, not two, not three but four revolutions in science: optics, mathematics, mechanics and gravity. His discovery of infinitesimal calculus is literally the base for modern rocket science as he used it to calculate and predict with stunning accuracy movements of heavenly bodies, hitherto impossible. Newton is simply the single greatest mind in the history of human science. He stands on the shoulders of some mighty men, but his accomplishments are of the ages.

Now, I come to the point. In this essay I have used a very specific word with each mathematical advance I have discussed. That word is “discovered.” I have purposefully eschewed the use of “invented.” And I have done so for a damn good reason. I am what you call a ‘mathematical Platonist.’ Said theory is defined by Wikipedia as “the form of realism that suggests mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging.” Thus, as the Brits would say, ‘maths’ are discovered. However, the opposite of said theory is mathematical nominalism, which has its merits and is defined as, “the philosophical view that abstract mathematical objects like numbers, sets, and functions do not exist in reality, or at least do not exist as abstract entities independent of concrete things or the mind.” Thus as we Yanks say, they be invented.

So why did I write this essay? Because this discussion on the merits of the two theories is utterly fascinating to me. And if you have ten minutes and a solid high school foundation in mathematics you will most certainly understand and appreciate it. The interview engrossed me from the first question.

One final note: Ms. Jonas, the philosopher of math being interviewed says that she is 87% certain mathematical Platonism is correct, I’ll add my confidence level as about 59%. Why? Because there is some set theory ideas I simply cannot wrap my danged head around–I reckon my grey matter isn’t as big or maybe as sophisticated as Ian’s. I licked logic in college with an A+ but this set theory stuff. Good grief. The paradoxes drive me wonko! (If you get the reference add ten bonus points to your final grade.)

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I may not be “the face that launch’d a thousand ships, and burnt the topless towers of Ilium,"1 but I am the face that launched a thousand tech bros to beat the shit out of each other with inflatables, and I think that’s just as powerful.

It all started because I was craving violence, so I sort of A/B tested fighting ring ideas by making posters and putting them on the street. Idea A: a “men’s fight to the death” to fix the gender ratio in SF. Idea B: a “couple’s fighting ring” to help spice up your relationship.

A friend posted Idea A on Twitter and it immediately blew up, so I felt obliged to make it real.

For Non-San-Franciscans, "The Ratio" is a common term used by tech bros to lament that there’s more men than women in their circles, and that's the sole reason why they're struggling to get any. Used in sentence: "Damn bro The Ratio at this AI-biohacking climbing party sucks" and "I can't deal with The Ratio, I need to move to New York where I will still get rejected, but at least by many more women."

However, while many men complain about The Ratio, none are creating B2B SaaS (Boy to Boy, Slaying as a Solution) ways to fix it. So I stepped up.

I contacted the SF Transbay Joint Powers Authority Bay to see if I could actually host the fight in Salesforce Park, but they respectfully declined. (Said it would cost $6,000.)

I thought it’d be funny to have the men fight shirtless, and the natural next thought was to make them oil up before they fight. You see, as a feminist, I am sick and tired of the objectification of women, and the best solution is to objectify men just as much. That way, the baseline of “objectification” is raised and relatively no one is objectified.

I’ve already made people strip (for CHARITY, it’s altruistic) so making them fight just seemed like the natural next step. Interestingly, there was a lot of overlap between the strip show and the fighting ring: the pole kittens became the ring girl/boy, there was a strong element of performance, each contender had an alias. The fighters were actually much more sexualized because they were shirtless and oiled up, whereas the strip show was surprisingly wholesome.

Serendipitously, my friend Samuel Sliman (or as you may know him, “Thomas The Spank Engine” from Strippers for Charity) had experience running a meme fighting ring. (He challenged the frontrunner of his college’s presidential race to a boxing match, and although some claim he “lost” the fight, he won the people’s hearts and earned the presidency.) Sam suggested using inflatable boxing gloves to minimize liability.

Because I am highly dedicated to my craft, we did a trial run of the duel. After getting sloshed on $1 margs at my weekly “office hours,” we went to one of those fancy gentrified parks and beat the shit out of each other.

^Me and Greta fighting, never say I don’t practice what I preach. (Violence.)

I made a playlist of appropriate music, including Kung Fu Fighting, Eye of The Tiger, the Wii Sports Theme, and songs from Pokemon, Mario, Super Smash Bros, and Naruto. I had my friends vote on the best oil for the men, and baby oil won. I later realized this may’ve been due to the Diddy meme, but by then it was too late to change.

Sffuncheap shared the event and called me a cultural renegade (I’m blushing). I found it really funny that they added so much context to the event. Like, what’s confusing you babyboy?

Day of, as we were staking out the location for the fight, we saw a huge children’s party, so we stayed far away (responsibly). We did end up near a baby shower, but that was for adults. Their gender reveal showed it was a boy, so a bunch of oiled up boys fighting nearby was a fitting peek into their future.

Patrick brought his folding table on a bike. Everybody say thank you Patrick.

People kept coming up to me and asking what the inspiration for the fight was. And I was like, “well I thought it would be funny.” I don’t understand what’s so confusing about this. It was funny - I was literally right.

Sam refereed the match, we actually showed up wearing the exact same shirt. Sam did an incredible job, everyone say thank you Sam. He strip dances, he referees, what can’t this guy do?

Our fighters’ names included:

• Daddy Bone

• The Accountant

• The Daltic Beast

• Shareholder Value

• Nico

• B2B Ass

• Nate

• Michael

• Tisslord

• Number 1

• Big Friendly

• Slamuel L. Jackson

• Amber Sucks

• Fist of Justin

• A Challenger Approaches

• Plot Twist

To be clear, these were mostly aliases made up for the fight. I do not know what their real names were, and I guess I never will.

The fighters got oiled up, and apparently this was actually useful, as it helped punches skim off the skin. Everything got really oily though, which was not a sensation I enjoyed.

The first two rounds were with inflatable gloves.

Then we had a five-way fight with pool noodles to make it to the semi-finals.

The semi-finals were with giant inflatable hammers, which unfortunately could not withstand the sheer power of the revved-up tech bros and ripped.

To give the finalists a breather, there was a “resurrection round” where the audience picked eliminated favorites to duel.

Then the final round brought back the gloves. The winner was awarded a bedazzled belt: “Ratio Champ.”

After the fight, Nick gifted the leftover baby oil to the baby shower happening nearby. It was only right. Then we let the crowd release any frustration (whether Ratio-related or not) in a free-for all. Finally, my friends and I celebrated another successful event by getting boba and burritos.

Upon reflection, I realized moving from a three-bedroom where I’d throw unhinged parties with my roommates, to a one-bedroom where I didn’t have space for parties, and therefore had to host them in public, has truly had cosmic effects on the San Francisco Bay Area.

I’m pretty tired out, so no more parties for a while. And by “a while” I mean until I think of something else that’s kinda funny, which is probably gonna be tomorrow.

Acknowledgements:

A huge thank you to all the incredible people who helped with this event. Sam referee. Patrick table-bringer. The two Ryan photographers. Ryan and Angela, the ring boy and girl. (I do not know why we had three Ryans.) Quincy, Mary, Isla, Graydon, Peter for operational support. Kristine and Ashwin the oilers. Mackenzie for moral support. And of course, the stars of the show, all 18 aforementioned men who had the courage to step up and square up. You guys are the best, thank you for your deep commitment to the bit.

Also so grateful for my friends for coming to support my stupid shit all the time, and the hundreds of strangers who took a chance on an event they saw off a flyer. I couldn’t do it without you. Or I could, but it’d just be me alone in a park, which would be way less fun and kinda weird.

Rogue Rattlesnake Removed from Grand Isle. This is such a Vermont story — the woman who found the snake “sat for 30 minutes, until these rangers arrived, doing my loving-kindness meditation, trying to just send peace to this snake”.

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With the more and more teachers interested in BTC, I feel that it is important to point out that the only way to build thinking in the classroom is to assign thinking problems. Having students work on practice problems on the whiteboards in groups of three will increase engagement and discourse, but it will not teach students to think.

Peter Liljedahl describes 14 practices to build thinking in the book Building Thinking Classrooms in Mathematics1. While all of the practices are important to incorporate to help build thinking, Liljedahl writes that the 14 practices don’t have to be implemented all at once. However, it is best to implement the first three practices together; assign thinking tasks, have students work on non-permanent vertical surfaces (whiteboards) in random groups of three.

I believe the most important practice in thinking classroom is assigning thinking tasks. The problem with only assigning thinking tasks is that it is very difficult to motivate students who haven’t learned to think, to start thinking. Using whiteboards, random groups, and the other BTC practices help motivate students by increasing engagement and promoting discourse.

So, what is the difference between thinking problems and practice problems? Thinking problems are assigned before students are taught how to solve them. Thinking happens when students are solving problems.

Practice problems are assigned after students have been shown how to solve them and are assigned to check understanding.

While the timing of when students solve problems in a lesson seems like a small difference, for me this switch in timing was a huge change. As a student, I spent years sitting in math classes watching my teachers show me how to solve problems. I had no experience working on thinking problems myself. So asking my students to solve problems before I tell them what to do seems strange. But, if I want students to think, I need to teach them to think, and that means breaking the cycle of doing the thinking for my students.

In a thinking classroom, a traditional “practice” worksheet with several problems that increase incrementally in difficulty can be transformed into thinking problems with a process is called thin-slicing. In this process, problems are assigned one at a time to students before they know how to solve them. Students start the sequence by solving a problem that is low floor and triggers their prior knowledge. As students solve each problem, their knowledge increases because each new challenge requires them to apply previous concepts in more sophisticated ways, reinforcing and expanding their understanding.

I found great success building my students’ thinking using thin-slicing.

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After time, I noticed that as my students became better thinkers, I found myself looking for richer problems. Around the same time my school was about to adopt a new resource and we piloted Illustrative Mathematics and the CPM Education Program. Both resources are problem-based and offer meaty problems or thick-slices. In What Types of Tasks are in a Problem-Based Curriculum I write more about these types of tasks. My school ended up adopting CPM and I have had amazing results combining CPM with BTC.

The reason for this success is that the CPM lessons are full of rich problems that require students to think deeply, and lessons build on each other to tell the story of a mathematical topic. Here is an example of a rich task in CPM Education Program Core Connections Geometry2.

Notice that there is no example of how to find the area of the shapes first. Students build on their prior knowledge of the properties of triangles to find the area.

Rich thinking problems incorporate the Math Practice Standards. The table below lists the eight Math Practice Standards and an example of how each practice is incorporated in the lesson.

It is important for us as teachers to ask ourselves how and when these math practices show up in our classrooms. Not every thinking problem will incorporate all the math practices, but it should incorporate at least one. Do you see these math practices in the math problems students are doing on the boards? Are all of these math practices represented at some point during a week, month, or year in your classroom?

It is important to vary thinking problems so that students have experience with all of the math practice standards. I hung these posters around my room to help remind me of their importance. Here is the link: it is a free download on TPT.

I realize that not everyone has control over the resources they use. The good news is that thick-sliced problems are in all textbooks. You just need to know where to look for them. If you are using a traditional textbook these tasks are usually buried at the end of a set of practice problems. They are also the problems that you have may have looked at in the past and thought, “yeah my students aren’t going to be able to solve these problems on their own”. So, assign them as thinking tasks. Students can manage more complicated problems once they start building their thinking skills and are working together on the whiteboards. Here’s an example of the last few problems in Concepts and Connections Algebra 1 lesson 4.2 in Big Ideas Mathematics3.

The authors even assign a math practice to the problems, indicating that student engagement in solving them is tied to thinking.

Again, these problems should be assigned at the beginning of the lesson to be considered thinking tasks. I would use problem 12 to introduce point-slope form. When students compare the two graphs they will see that the lines are parallel, and one line contains the point (-3,1) which correlates to the h and k in point slope form. I write more about using story problems as thick-slices and thin-slicing in my article How to Build a Thinking Classroom with a Traditional Textbook.

It is important to remember that not all thinking problems inspire the same level of thinking. Class time is valuable, and we need to choose thinking tasks carefully. In the early stages of using BTC students are learning to think so the thinking problems will need to be given in smaller pieces, thin-slicing. As students become better at thinking, they can manage more challenging problems.

The rise of the stewfluencer is more than a TikTok trend. It’s a way of life.

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The threats may not be malicious, but they are more than many security teams can handle.