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job/study update 

As of 1,5 weeks ago, I officially have a BSc degree in mathematics 😎

Now I’m doing my mandatory civilian service until October. For the past four weeks I was at a training camp (first aid, oil spill cleanup, activism, etc.), and yesterday I started the work service. I’m playing statistician at our Institute for Atmospheric Research (INAR), doing something related to ’s. This will probably be quite interesting!

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I did promise to tell about my BSc thesis topic one day. So get ready for a thread on... fractals! Along the way we'll also meet measure theory, a bit of function theory and several bad jokes.

I'll try to keep this as accessible as possible, even though I'll use some maths terminology. Feel free to ask if something is unclear! If the LaTeX equations do not render correctly for you, try opening the thread on

This is going to be a long thread, so let's get started!

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Hi! I'm a maths student at Helsinki University. For the past year or so I've been writing a popular (not as in visitors) maths blog,, in Finnish. In addition to human languages (FIN/ENG/SWE/FRE) I respond to quite a few computer ones (esp. C#).

Interested in seeing if toots > tweets!

Yesterday I gave my talk at the E-Assessment in Mathematical Sciences 2020 conference about "Inclusive e-assessment".
It's 10 minutes long, and a lot of it is applicable to all course material, not just assessment.
The video, transcript and references are online at

math as magic 

In reply to I threaded a bit of what math is like in my head. Of course, the trick of it is, math /is/ magic, so there's no conversion necessary.


The lay folk were taught 'magic' in school, everyone had to learn it. But what they were taught was only patterns of symbols on a page. It looked exactly like magic .. without the magic in it.

Some few of them would realize what the symbols described, and in realizing it speak their true meaning with intent. Those symbols would then become so deeply a part of them that it would be hard to express their interaction with the world without invoking it.

They would see links and connections and patterns all around them, in everything these symbols described.

The difference in what this permitted them to do wouldn't be so obvious with the early symbols, but when somehow they passed exams without seeming to memorize it would become clear they had what was mistaken for a talent.

It wasn't talent, it was just that they had invoked the magic behind the symbols and taken it into themselves. Slowly as they became magicians, the world described by these symbols they acquired would fill in.

It become not just a bag of tricks, but a landscape of inter-relations and places and machines that operate on them to transform them into other things. The symbolic representations on the page were often, at that level, not even accurate any more.

Just a hopeful indication trying to drag the reader into this beautiful, powerful landscape and describe the machinery of it. New symbols could be made, and new machinery with the old ones; or the landscape explored.

But the magic had a certain fragility -- one symbol out of place and you could fall through into an abyss of confusion.

So magicians often spent a lot of their time moving, not in broad direct strokes, but in cautious circuitous patterns focused on making sure the ground was solid beneath them.

It took a lot of courage to take large steps, which more often than not landed one in the drink, but the great achievements such as new symbols that expand the entire possible landscape and its potential power...

Those always require daring to make large steps; then creating the circuitous landscape of detail to keep them from vanishing again back into the fog.

Actually performing magic, its actual practical mechanism? You'd just move ordinary things into an arrangement with a surprisingly thorough effect. But that arrangement would be determined by the patterns and mechanisms unseen, except to the magicians.


The hidden part here of course is that I meant it utterly literally .. a landscape, complete with topologies and metrics; algorithmic mechanisms and proof technique machinery. Tangible objects so abstract that they aren't possible to readily describe. Yet I assert, they are tangible.

Try to clear your mind and answer this as quickly as possible:

In a certain tower block, half the flats have a single occupant, and half have two. How many flatmates does the average person in the tower have?

academic publishing, web slowness 

I’m still debating myself on which is worse:

• Reading a magazine one article – and 20-second load – at a time on Wiley’s ePDF reader;
• Reading a book on ProQuest’s implementation that has strict timeouts, no keyboard navigation and occasionally fails to load a page.

Meanwhile at Springer: ”Download book PDF”.

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academic publishing, web slowness 

Tired: Acrobat Reader plugin
Wired: built-in PDF reader
Wiley: ”enhanced PDF” page that takes 20 seconds to load every time

And to think some people have the impudence to ask what's the point of divisibility tricks!

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To my mathsy friends, colleagues, and followers ... if someone asked you for a real-life example of the use of Group Theory, what would be your reply?

Underrated advantage of LaTeX, the output document is not the same as the one you write, I've found I helps a great deal for critical reading, checking for mistakes, etc

Antidepressants or Tolkien character? More difficult than I’d have guessed.

Normalizing pronouns in email signatures... something I wish more people of all genders would do.

I've made it standard for me at work and when corresponding with NAMI. Unfortunately, I don't see (largely cis) people doing the same in those circles.

I'd feel more supported if they included their pronouns. That way I'd not be the exception. It would be validating.

I realize it's not safe for everyone in every environment, but I'd love to see those who can do so.


Q: When I was 4, my sister was 2. I am now 44. How old is my sister?

Programmer: 44 - (4 - 2) = 42



I'm looking for a PhD student and a postdoc to work in my project "Distributed Algorithms for Fundamental Graph Problems". The main goal of this project is to design new algorithms with theoretical guarantees for fundamental graph problems, like maximum flow and shortest paths, in distributed models of computation such as the CONGEST model.

The start date for both positions is negotiable. Please contact me to find out more.

cool maths 

The is great as usual, and I especially enjoyed today’s entry. Both @mscroggs (or maybe @mathslogicbot?) and @icecolbeveridge made me go ”Ooh, that’s very nice!”

It’s a tough call, but the linear algebra interpretation of Fibonacci sequence is my favourite so far.

math problems come in two flavors

1. it's actually not so bad if you remember this handy trick

2. we have determined it is analytically impossible to solve but let's examine its behavior qualitatively

Do you have similar small probability problems (or collections thereof) that you really like? Asking both for fun and as a former/future teaching assistant.

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probability puzzle 

Here’s a tiny question a friend posed some weeks ago. We had fun clearing up and solving it. I think this is a nice formulation of a classic result.

Let N be a positive integer. Sample N numbers with replacement from the set {1, ..., N}. What happens to the probability that N itself is not included in the sample, as N goes to infinity?

Trained StyleGAN2 on pictures of my cat.
StyleGAN2 had been originally trained on human faces.
This is an intermediate training stage.

Not sure whether to laugh or scream

One of my favorite math things is...

What is 40 - 32 / 2?
The answer is 4!

I hate it when I can't tell if there's some stray diacritic on a character or if my screen is just dirty. I've tried cleaning off so many à or ï off my screen and feel a bit silly every time.

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