There was a MathOverflow thread about mathematically interesting games for 5–6 year olds. A lot of the discussion revolved around how young age 5 really is, and how we should temper expectations because we don’t really remember what it’s like to be 5. In response to an enormous answer by AlexanderChervov, user LSpice quipped, “‘Daddy, daddy, let’s play another in the infinite indexed family of perfect-information draw-free cheap-to-construct two-player games!’” That being said, Martín-Blas Pérez Pinilla’s “sprouts” game piqued my interest to find optimal strategies.

Most abstract logic games that are interesting to mathy folks are only interesting when you start asking questions beyond core gameplay. For example, the game Set is interesting when you ask, “how many cards can you have with no set?” or similar tricks to determine the last un-dealt card in a deck just by viewing the remaining board. These have little to do with skill at playing the game. I started playing chess around 5–6 years old, but realistically I was probably doing it to spend time with my dad and get approval for making correct moves. …


Over the past four years I’ve been writing a book, A Programmer’s Introduction to Mathematics. It teaches someone with programming knowledge and experience how to engage with mathematics. I can achieve this goal largely because of the implicit overlap in the content and ways of thinking between math and programming. Despite that, there is no smooth bridge from one world to the other—a bridge that explains the unfamiliar parts and focuses on the important concepts, while leveraging programming to demonstrate applications.

Until now. If you’re a programmer who wants to really grok math, this book is for you.

In this article I’ll explain how I wrote and self-published the book. …


I write a blog that provides some income, and I’m going to use that blog as a platform to publish a book this Fall (mailing list). This page lists details about the different kinds of support I accept.

Transparency is good. So here is a list of my revenue from 2016, broken down by type. Snapshot was taken 2017–01–07 at 10:00 AM UTC.

tldr; Patreon wins, WordAds loses, and I can do better with Amazon referrals.

General statistics

Total funding in 2016: $2,209.91
Total page hits in 2016: 675,930 (350K unique visitors)
Total page hits since 2011: 3.3M (1.5M …


Every so often the “should programmers learn math?” question comes up in hubs on the internet. Today, as often, it’s on HackerNews. The discussion is usually the same:

Programmer: What are these weird 19th-century squiggles that I can’t find on my keyboard, and why don’t you just write a compiler for math?

Mathematician: Writing a compiler for 2k years of legacy code with rapidly evolving standards would be waste of time and probably not useful to anyone. It’s also not even clear what “compiler for math” means when anyone is free to invent their own notation and assign it arbitrary semantic meaning. And you’re telling me that it wasn’t a completely arbitrary decision to put { } and ` on a keyboard but not find space for ∞ and ∩? You use emacs/vim and have 3–4 kinds of key modifiers, and you’re telling me you can’t just write a plugin for these symbols? …


Angela Merkel wants algorithms to be more transparent.

I’m of the opinion that algorithms must be made more transparent, so that one can inform oneself as an interested citizen about questions like ‘what influences my behaviour on the internet and that of others?’

Google’s honestly excellent when you dig into the details. They let you control what ads are served to you. They tell you exactly who they think you are. You can download and delete the content that Google uses to filter for you. You can turn off filtered results.

Hear that? YOU CAN TURN OFF PERSONALIZED RESULTS.

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You can also use incognito mode in Chrome. The unfiltered internet is just a Ctrl-Shift-N away.

People make it seem like technology companies force us to carry around this huge burden of all our life’s past decisions that hide the truth (or differing opinions) from us. Maybe Facebook is actually like that, but to generalize to algorithms as a whole is illogical. …


The most common question students have about mathematics is “when will I ever use this?” Many math teachers would probably struggle to give a coherent answer, beyond being very good at following precise directions. They will say “critical thinking” but not much else concrete. Meanwhile, the same teachers must, with a straight face, tell their students that the derivative of arccosine is important. (It goes beyond calculus, in case you were wondering)

So here is my list. The concrete, unambiguous skills that students of mathematics, when properly taught, will practice and that will come in handy in their lives outside of mathematics. Some of these are technical, the techniques that mathematicians use every day to reason about complex, multi-faceted problems. Others are social, the kinds of emotional intelligence one needs to succeed in a field where you spend almost all of your time understanding nothing. All of them are studied in their purest form in mathematics. …


Hi Lulu, Alix, Hanna, and everyone else at Invisibilia,

I’m writing in regards to your recent episode, “The Problem with the Solution,” which I thought was fantastic.

However, the beginning part nagged at me a little bit. The part where you basically set the stage for the mental illness “non-solution solution” by having the hair-trap guy tell his story and say, “Every problem has a solution! Try to solve all the things!”

I know exactly why it bothered me, but before I jump into that I just want to reinforce how great I think Invisibilia is. I don’t want this to come across as a criticism, but rather as excitement to share cool ideas with you. I need this caveat because I’m a mathematician. And mathematicians tend to think and speak in a way that emphasizes consistency, precision, and nuance of language over things like, whether you come off as an arrogant prick or whether someone’s feelings are hurt. …


In 2011 Sony sued George Hotz and his friends for jailbreaking the Playstation 3. One of the main complaints was that Hotz published an encryption key online (Sony foolishly broke one of the basic rules of digital signatures).

The case was eventually settled out of court, but the question remains whether it’s illegal to publish a specific number on the internet. The law currently seems to agree with Sony, that free speech doesn’t cover Hotz’s case.

One counterargument is that if a specific number is illegal to publish, then so is anything derived from that number. …


Step 1. Don’t make basic mathematics mistakes in your blog post, as shown below. How many mistakes can you find in the quote?

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Note in Satoshi’s Bitcoin paper he was able to do standard statistics just fine, but fails at the high-school level “process known as combinatorics” in his blog post.

Step 2. Post the file you claim to be signing so others can verify. (It was nowhere to be found on Wright’s blog post)

Step 3. Make your proof interactive. Have someone you don’t know write an open-source program to pull tweets from Twitter at random, and then you sign those messages with your private key in real time. This proves you did not spend the last three years finding a lucky hash collision.

If you were Satoshi, you’d probably know something about zero-knowledge proofs and how, to the contrary of what Wright says, signing lots of messages does provide better proof that it’s your private key. …


I had a long conversation with a feminist friend of mine the other day about sexuality. People have a lot of strong feelings about this topic. But rather than form ranks and brace for impact, my mathematical inclination drove me to pin down exactly what her claim was. Precise, logical rigor was what I was trying to tease out from phrases like, “You’ve been socialized to accept heteronormativity.”

I would ask questions like, “How do you know that I’m not just normal?” Whereafter I learned that “normal” is offensive. And I agree, at the very least, that “normal” is the wrong word to use in a technical discussion because (1) it’s overloaded both in math and real life and (2) if I’m trying to tease out definitions from other people, I shouldn’t be allowed to use a word that I’m refusing to define. …

About

Jeremy Kun

Mathematics PhD, currently at Google. Author of Math ∩ Programming @MathProgramming

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