Jeremy Kun

∈ Mathematicians ∩ Programmers

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I often forget I’m hungry

I’ve never heard of anyone else who has this problem. When I’m working, specifically when I’m doing mathematics, I won’t notice I’m hungry until I stop.

When I was a child my mother used to joke about how I’d get hungry every two hours. During my undergrad I regularly engaged in hours-long coding sessions, but I always noticed when I was hungry. But now as a graduate student, I can eat lunch at 1pm, start thinking about math at 5, and not realize I’m hungry until midnight when I decide it’s time for bed.

I have no idea if it’s healthy or if it’s really because of mathematics, but it’s the weirdest thing.

I think it’s because, when you start to do mathematics at a graduate level, you’re trained to think about the big picture, and you can always think about the big picture. In the shower, on the train, while grocery shopping and cooking, as you’re falling asleep, and when you get lost...

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Mathematicians are chronically lost and confused (and that’s how it’s supposed to be)

A large part of my audience over at Math ∩ Programming are industry software engineers who are discovering two things about mathematics: it’s really hard and it opens the door to a world of new ideas. In that way it’s a lot like learning to read. Once you’re mildly fluent you can read books, use the ideas to solve problems, and maybe even write an original piece of your own.

Many people who are in this position, trying to learn mathematics on their own, have roughly two approaches. The first is to learn only the things that you need for the applications you’re interested in. There’s nothing wrong with it, but it’s akin to learning just enough vocabulary to fill out your tax forms. It’s often too specialized to give you a good understanding of how to apply the key ideas elsewhere. A common example is learning very specific linear algebra facts in order to understand a particular machine...

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What would math class look like if it were a fine art?

Wahoo Public High School in Wahoo, Nebraska is by all accounts a school with ample opportunities for their students. They have the standard array of English, history, and science courses, with enough money left over for band, drama, fine arts, many sports teams, and a couple of very surprising electives (zoology, web design, and fashion design to name a few, see their current curriculum guide for the whole list).

And Wahoo HS has given some truly unique opportunities for their students to do things like watch a live heart surgery and visit the video control room of the Ralston Arena event center. Wahoo seems to treat its teachers right, too: in 2008 they sent a group of teachers to DC to learn more about its history.

I don’t bring all this up just to praise Wahoo HS for its quality (though they clearly deserve praise), but also to use it as a platform for a thought experiment: what...

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On the Social Value of “Programming for All”

Bret Victor recently published an infographic, which appears to be his own creation, pointing out some aspects of an essay written by Seymour Papert (the inventor of the Logo programming language), and contrasting those points to the claims made by famous people about the value of learning programming.

The gist of it is that Papert believes programming is a useful tool for conveying ideas (specifically mathematical ideas). So if students struggle to learn a concept with pencil and paper, they might instead try to understand the concept by writing programs that elucidate it.

Apparently the whole world mistook Papert for saying, “Programming makes you smart,” and that became canon. So people who don’t know anything about programming (and a lot of people who do) are preaching that “everyone should learn to code” for the wrong reasons. This is the focal point of Victor’s contention...

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How can you tell what’s random?

Random xkcd

A handful of really deep concepts in mathematics come from the attempt to give a formal answer to a simple question: what does it mean for something to be random?

The short answer is: we have multiple ways to understand what randomness means, but nobody knows an effective way of deciding what’s random and what’s not random.

Even with the string of digits in the above comic, how can we really tell that they’re random? Certainly they aren’t. Randall Munroe deliberately chose numbers and their placements to make it appear random (unless he flipped coins or something, which I doubt), but how can we verify or refute the claim that they’re random? Without an answer, the comic becomes doubly-ironic: it’s just describing how our perception of the meaning of randomness changes, based on age or intellectual maturity or whatever.

But before we can check whether something is random, we have to...

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If you’re going to treat education like a business, then follow the right business model!

I heard a story recently on NPR where they discussed the effectiveness of job incentives. They recalled a case study that’s very familiar to anyone who pays attention to these sorts of stories. The basic idea was that a company gave rewards to their best employees based on performance (it was sales, I believe), and it caused people to be selfish and competitive. When they removed the incentives, their employees started to work together, and resulted in a drastic increase in total sales.

There are a host of other stories like this. My old team at Amazon had the policy that you choose your own hours, so long as you get your work done. Google famously gives employees 20% of their working hours to pursue their own ideas for possible innovations and improvements to the company, and these ideas have translated into some of their best products. Even Microsoft, the dinosaur of tech companies...

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Nobody needs to learn to code, but everybody can learn to code

Barack Obama recently released a video encouraging American students to learn to write programs. A lot of people have discussed this in recent years, and the general consensus seems to be that not everyone should become a software engineer.

I totally agree with this. Writing good software is hard work, requires a lot of experience, and there’s enough poorly written software out there. The world doesn’t need more halfway-trained software engineers who think they know what they’re doing causing errors that cost everyone else time and money and potentially lives.

This is even true of extremely smart and talented people. I encounter scientists all the time who share “data” in formats entirely unusable to anyone but themselves. Why is this? Because they simply haven’t struggled enough with software and others’ data to know the right and wrong ways to do it. And more importantly they don’t...

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Mathematical thinking doesn’t look anything like mathematics

I like to think a lot about mathematics education, and I often read articles about the woes of standards and testing and bad curricula. But there’s one huge problem with all the talking heads and the purported panaceas.

It’s that nobody is giving a good description of what mathematical thinking skills are.

Oh, sure, people will throw around vague and fancy words like “critical thinking” and “quantitative reasoning” and “mathematical modeling.” But as every mathematician knows it’s the content of a definition that counts. When you get down to the details about what these fancy terms really mean, almost every article or standard or curriculum I’ve ever read falls flat on its face and reverts to the same old crappy word problems and standards we have learned to hate so passionately. I could give a huge list of specific writers, pundits, and state standards that fail in this way, but it...

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Things mathematicians know but most people don’t: dimension is malleable

One of my science pet peeves is when people say, “time is the fourth dimension.” It’s like a fishy smell; when someone says it without a hint of humor I usually end up convinced that they don’t know what dimension is or how it works. Considering that nobody really knows how time works either, the statement is just utter nonsense. Even worse are those popular “science” videos with titles like, “Imagining the Tenth Dimension” and, “Who lives in the Eleventh Dimension?”

The biggest misunderstanding is in the word “the.” That is, that time has no choice but to be the fourth dimension. Why can’t time be the first dimension? Or the eleventh? What’s so mystical and supernatural about the number four that time has to go there?

In fact, the reality is that dimension is a mathematical construction designed and redesigned as necessary to suit our needs in analyzing mathematical issues. As a...

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The Myth that Math is ‘Solving for x'

I read an article in the Atlantic today, titled The Myth of ‘I’m Bad at Math’. It made some very good points, of course the main one being that all scientific evidence points to the belief that skill in mathematics (skill in anything, really) has very little to do with genetics and almost everything to do with practice. This is an important point to make and one that I wish everyone would absorb, because the popular opinion in the United States is quite to the contrary. Most of us believe that you are born with some sort of “math gene” that enables you to solve algebra problems with dazzling ease.

Of course this is ridiculous, but there’s a much deeper problem here. The authors (Miles Kimball and Noah Smith, two economists) perpetuate an even more pernicious myth about mathematics, one that lies dormant in the minds of a startling majority of education policy makers, mathematics...

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