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A small update on what I'm doing: I started this week as a doctoral researcher (PhD student) in our Mathematical Physics group at Helsinki! I'll be working on stochastic analysis and related things.

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Maybe it's time to update my pinned toot...

Hey there! I'm a MSc student at University of Helsinki, Finland. I'm specializing in , doing quite a bit of analysis alongside. I also sometimes blog about fun maths in Finnish, at

I've been a hobbyist programmer for like 2/3 of my life, presently interested in . In addition to computer languages, you can reach me in Finnish, English, Swedish and French.

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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!

I got my MSc thesis online a few weeks ago, and it covers some of the topics I'll be looking at.

What I did there was read a couple of 90's papers by Jean Bourgain and explain the basic results. Bourgain was known for omitting *a lot* of details, so this was not an easy task! The result is 80 pages of dense maths. (Goal for MSc theses is 40 to 50...)

Chapters 2 and 6 present pretty general tools and should be readable. Chapter 4 can be used to scare demons.

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A small update on what I'm doing: I started this week as a doctoral researcher (PhD student) in our Mathematical Physics group at Helsinki! I'll be working on stochastic analysis and related things.

In topology, spaces can be classified as: regular – normal – completely normal – perfectly normal.

Are we just bad (as always) at naming things, or are the topologists hiding something? ”Keep moving… this is a perfectly normal space… nothing to see here…”

What fascinates me about generating images with CLIP is that it CAN generate depth and realistic textures, but only if you know how to ask for them.

"A herd of sheep grazing on a lush green hillside" alone

vs with "amazing awesome and epic" added

research-level maths 

My note-taking/sketching high: crossed-out cross-outs, and a folded scrap of paper taped onto the page.

(I’m reading an old Bourgain paper. He was known for conciseness.)

I wonder if I could skip the head-banging phase by just working from the restroom.

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In the past year, I seem to have made a habit of head-banging at some mathematical argument for hours, feeling miserably stupid, and then solving the whole problem during a toilet visit, with the associated feeling genius.

Today’s was just 1 hour / 1 problem; my personal best is 4 hours of staring at two coursework exercises (on different courses), then cracking both in those two minutes.

This week I started a 3-month job at the mathematical physics group of UHel (directed by prof. Antti Kupiainen). Doing stuff related to nonlinear Schrödinger equation, with the goal of producing an MSc thesis!

Very excited about the work, somewhat intimidated by the amount of literature, and quite annoyed about doing this all from my living room.

academic spam 

”Dear Well-known Researcher of one published article, whose name I neglect...”

Tooting this because I want to do it but don't have time, and I want someone to pester me about it in a few weeks' time:

I'd like to start a collection of mathematical notation ambiguities, inconsistencies, and unpleasantness. It'd be a wiki, or at least collaboratively edited

Obscure-ish topic, but does anybody here have any textbook / expository paper recommendations for contact geometry?

It's been a while now since my degree, but I've had to help out a sibling with some thermodynamics homework, and it's sparked my interest in the geometric side of physics again.

My first research article is finally out! 🥂 It describes a Python package for non-linear correlation detection, based on a bit of information theory. Our killer feature is being user-friendly and integrated with Pandas.

Article (Elsevier):

Here's something you can do without thinking, assuming you've had the same realisation I've just had:

Write down a multiple of 2¹⁰⁰

A team at our university won this year’s Dance Your PhD contest with a rap on atmospheric secondary aerosol formation. (I did my civilian service at the same institute, but was nowhere as cool.)

”I’m the first author, you’re just et al.”

"Sometimes we need to establish which God wins over another," Zeus said.
"Traditionally, this meant war," Odin said.
"Which we realised is wasteful."
"Instead we ask a small child to set us a challenge."
I nodded. "Which is why you walk backwards with a tortoise on your head?"
#MicroFiction #TootFic #SmallStories

After all these years of studying, I was able to follow the proof! You can actually learn this stuff! (Still no idea how anybody could prove the result in the first place.)

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Recently learned a neat maths fact: all continuous functions from \( [0, 1]^n \to \mathbb R \) can be represented as a composition of a continuous real function with a sum of \( 2n+1 \) univariate functions. That is, addition is the only ”genuine” continuous multivariate function.

The article in AMS Bulletin (open access) has some nice examples and history before going technical:

cc @esoterica

You know, that quote, by Sofya :kovalevskaya: "It is impossible to be a mathematician without being a poet in soul." ?

I was wondering why it sounds so much like Weierstrass's own quip, "It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician."

That's because she is paraphrasing her collaborator in a letter to Madame Schabelskoy. I prefer Kovalevskaya's version.

Here is an excerpt from a memoir/biography of hers:


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