Euler was wrong!

Leonhard Euler was the Mozart of mathematics. If you’ve ever seen the number e, you know what the “e” stands for? Euler. You know the “e” in e-mail? That doesn’t stand for Euler, but it should. Look at this guy:


My friend Dave’s car is old and busted and I hate it.

He gave me a ride today, but the car’s got a faulty engine (and a crumpled hood… and a missing window… and a bizarre burning smell). It speeds up and slows down with a mind of its own…


Did the new changes work?

Alright, let’s talk about the 2021 German election. Last Sunday, over 46 million Germans voted to elect members of Germany’s parliament (the Bundestag), and within a few weeks (or maybe months) the Bundestag will appoint Germany’s new Chancellor.

These are some takeaways on Germany’s electoral system after the 2021 election…


Recommendations from me, a guy who likes books

Usually when a friend borrows a book from me, it comes back months later, unfinished and unread.

I understand. Reading takes time. And some people dislike books. A close friend of mine once memorably called books “a fuckfest.”

For a long time I had that attitude too.


Proof with trig identities

There’s a a cool Twitter bot called infseriesbot. The other day they posted this:

These are some neat identities for sin(3x), cos(3x), and tan(3x)!

I’m going to quickly break down why the sin(3x) identity is true, step-by-step, pointing out the identities I use along the way.

Angle-Sum Identities

We’ll start with…


I’m burnt out from watching numbers on screens bob up and down

“Online points mode” is a running joke among my friends.

Usually when you play a video game, the wins and losses don’t matter once the game is over. But many games have two modes: a “normal mode” and a “ranked mode.” In ranked mode, wins and losses propel you higher…


I am hungry for a chickenjoy

Inside a Jollibee, you’re hit with the irresistible smell of greasy chicken, mango peach pies hot from the oven, piles of spaghetti dappled in sweet tomato sauce and packed into thin cardboard boxes. Jollibee is the most popular fast-food chain in the Philippines for a reason.

Jollibee has over 1300…


An explanation of the Saint-Laguë/Schepers method

Germany’s election process is complex, so complex that several parts of the process involve crunching numbers with an algorithm. But the German election process is also cool, so cool I wrote an entire post explaining it in detail. In that post I mentioned the algorithm, called the Saint-Lägue method, but…


You can feel the dread in a room when students realize double integrals and triple integrals exist. Integrals, which many students solely remember as “weird looking S things,” were already hard enough. In the 5 stages of math grief, the first is denial: they beg, “That’s a mistake right? Why…


This is a super quick proof from topology. I gotta admit, this post is not as beginner-friendly as others, and I understand if you thought the title and thought it looked like a bunch of gibberish. …

Mike Beneschan

A human, writing (mostly) about math | California | If you want to reach out mikebeneschan@gmail.com | Get the newsletter here: https://bit.ly/3Ahfu98

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