Viktor Futó · Stay human

Spatially written math & proofs with LaTeX - @thebrainec
Alumni: University of Coimbra, Charles University in Prague

[Viktor Futó · Stay human @optimistavf]

I have a dream,
that all scientific articles, journals, editorials, all written means of knowledge exchange - documents themselves, are one day going to look like this. (via @thebrainec) #diagrammatics #explorables #scicomm

[Viktor Futó · Stay human @optimistavf]

Fue un gusto presentar la práctica de escritura espacial con LaTeX y @thebrainec en @MatematicasUN , el viernes pasado.

Muchas gracias al profesor Andrés Villaveces y a la UNAL por la organización de la sesión, y a Javier por las fotos.

[Viktor Futó · Stay human @optimistavf]

A spatial story that you write on Brainec can be exported as a single .html file and opened in any web browser.

If there are no images, only math expressions and text, it runs fully offline.

Image embedding for offline use is in development.

[Brainec · Stay human @thebrainec]

Too many *.pdf, *.doc, *.ppt, online platforms and tools?

💪 Own your content.

🚀 Now it is possible to export your brain-friendly spatial stories to universal *.HTML documents #spatialwriting #maths

[Viktor Futó · Stay human @optimistavf]

It’s always a joy to witness a math professor’s reaction when showing them their own research rewritten spatially.

This time, I dived into model theory:
https://t.co/MVEaVFiRPP

[Viktor Futó · Stay human @optimistavf]

@andruyeung Spatial way of writing [not only] mathematics.

Brain-friendly format of capturing complexity and understanding - it shows author's understanding explicitly. Solves AI erosion in studying/teaching at Unis.

Building, distributing and executing: )

[Viktor Futó · Stay human @optimistavf]

One recurring theme as I speak with professors is how AI is completely eroding the studying process, verification of assignments, the understanding of concepts.

Linear text is infected with AI, but spatial text forces the author to write and to understand what they are writing.

[Viktor Futó · Stay human @optimistavf]

Adivina qué campus visité ayer!
Guess which campus did I visit yesterday!

[Viktor Futó · Stay human @optimistavf]

Adivina qué campus visité ayer!
Guess which campus did I visit yesterday!

[Viktor Futó · Stay human @optimistavf]

Such a fascinating part of the entrepreneurial experience:

In one place, you show what you do - nobody cares.
In another, you show what you do - “This is exactly what we need!”

[Viktor Futó · Stay human @optimistavf]

@Lauracsc_ @steveruizok That looks wonderful! ...✍️

I admire work behind power user note-taking tools such as Obsidian, but I often feel that complexity in design and organization is a distraction itself. This is so well done! 👏 And I love the use of the local file system!!

[Viktor Futó · Stay human @optimistavf]

@2oovy That's truly tough 😆 Curious about what are the other classes

[Viktor Futó · Stay human @optimistavf]

another creator made a video of their spatial notes written in Brainec and posted it on TikTok 😳

this certainly will be the last one for a while, surely...

Guys, I haven't even implemented exportation to video yet. It's so tedious to do these manually!

[Viktor Futó · Stay human @optimistavf]

A creator just brought their Brainec story to TikTok for the first time 🥲

[Viktor Futó · Stay human @optimistavf]

A creator just brought their Brainec story to TikTok for the first time 🥲

[Viktor Futó · Stay human @optimistavf]

@Icarussiano @eyishazyer It indeed is, but on Wednesday alphaxiv announced the integration of NotebookLM into their platform, didn't they?

Thank you kindly for the reply!

[Viktor Futó · Stay human @optimistavf]

See how Mertens’ Second Theorem enters the final stage of the proof of Lemma 4.4, a key step toward the density-one Davis–Lelièvre theorem:
https://t.co/a1iYkBbCyW

Based on: Kontorovich, A., & Zhang, X. (2024). On the local-global conjecture for combinatorial... arXiv:2409.10682

[Viktor Futó · Stay human @optimistavf]

𝐌𝐞𝐫𝐭𝐞𝐧𝐬' 𝐒𝐞𝐜𝐨𝐧𝐝 𝐓𝐡𝐞𝐨𝐫𝐞𝐦
1737 - Euler showed: Σ 1/𝑝 diverges.
1874 - Mertens’ Second Theorem estimated how quickly - rate of growth: log log 𝑥.

For 𝑥 ∈ ℝ and 𝑥 ≥ 2:
Σₚ≤𝑥 1/𝑝 = log log 𝑥 + 𝑀 + O(1/log 𝑥)

𝑀 = ... ↓ | #morningmath #numbertheory

[Viktor Futó · Stay human @optimistavf]

𝑀 - Meissel-Mertens constant
𝑀 ≈ 0.26149721…

See how can you write it spatially:
https://t.co/wAVZ5sj714

[Viktor Futó · Stay human @optimistavf]

@Golovanov_ammoc Been preparing for exams by rewriting proofs. Even when I wasn't sure about all the steps, when I returned to it in 2nd/3rd iteration with fresh mind, it already got into the brain.

I always wondered if there's more beautiful, easier-to-read and remember way of writing maths.

[Viktor Futó · Stay human @optimistavf]

@prof_g @zetascale63727 Maybe visualization isn’t the best word for what I've been excited about. This is a format I’ve been exploring:

[Viktor Futó · Stay human @optimistavf]

See how can you write it spatially:
https://t.co/8XUyLis6Jg

#morningmath #numbertheory

[Viktor Futó · Stay human @optimistavf]

𝐄𝐮𝐥𝐞𝐫'𝐬 𝐓𝐨𝐭𝐢𝐞𝐧𝐭 𝐅𝐮𝐧𝐜𝐭𝐢𝐨𝐧
φ(𝑛) = how many positive integers ≤ than 𝑛 are relatively prime to 𝑛
φ(𝑛) = |{ 𝑘 ∈ ℕ : 𝑘 ≤ 𝑛, gcd(𝑘,𝑛)=1 }|

𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝑙𝑦 𝑝𝑟𝑖𝑚𝑒 ≡ 𝑐𝑜𝑝𝑟𝑖𝑚𝑒 ≡ gcd(𝑎,𝑏)=1

𝑬𝒙𝒂𝒎𝒑𝒍𝒆:
φ(9) = 6
{1,2,4,5,7,8}