Riesz-Fischer theorem is a norm version of it, and Carleson's theorem is stronger pointwise almost everywhere version.
Note that the Riesz-Fischer theorem is weaker because the pointwise limit could not exist just according to it: norm sequence convergence does not imply pointwise convergence.
This channel contains several 2D continuous simulations and explains AI techniques used.
The engine appears to be open source: github.com/Primer-Learning/PrimerTools (previously at: github.com/Helpsypoo/primer). Models are closed source however.
They have several interesting multiagent game ideas.
Ciro became mildly jealous of this channel when he found out about it, because at 800k subscribers at the time, the creator is likely able to make a living off of it, something which Ciro thought impossible.
As of 2022 he was at 1.6M followers with only 17 videos! Of course, much of those videos is about the software and they require infinite development hours to video time ratios.
Well done!
Created by Justin Helps. Awesome name.
To make things better, the generically named channel is also the title of one of the best films of al time: Primer (2004).
Sponsor Ciro Santilli's work on OurBigBook.com Why you should give money to Ciro Santilli by
Ciro Santilli 40 Updated 2025-07-16
So that he can work full time on OurBigBook.com and revolutionize advanced university-level science, technology, engineering, and mathematics eduction for all ages.
Donating to Ciro is the most effective donation per dollar that you can make to:
- improve hardcore university-level STEM education for all ages
- help make every child into the next Nobel Prize/Fields Medal/deep tech unicorn co-founder
Ciro's goal in life is to help kids as young as possible to reach, and the push, the frontiers of natural sciences human knowledge, linking it to applications that might be the the next big thing as early as possible. Because nothing is more motivating to students than that feeling of:rather than repeating the same crap that everyone is already learning.
To do this, Ciro wants to work in parallel both on:
- the multi-user website e-learning platform of OurBigBook.com
- creating amazing teaching content that motivates that platform, and that deeply interests Ciro, notably quantum mechanics and its related applications:
- quantum computing
- molecular biology
- condensed matter physics and chemistry
- slightly more theoretical stuff in somewhat related fields of:
- continue to dump his brain/research in areas Ciro has expertise in: software engineering and open source software
Ciro believes that this rare combination of both:produces a virtuous circle, because Ciro:
- proven passion and capability to learn and teach science, technology, engineering, and mathematics subjects
- proven programming skills, including web development
- wants to learn and teach, so he starts to create content
- then he notices the teaching tools are crap
- and since he has the ability to actually improve them, he does
As explained at OurBigBook.com and high flying bird scientist, Ciro is most excited to make contributions at the "missing middle level of specialization" that lies around later undergrad and lower grad education:in a way that is:
But on that middle sweet spot, Ciro believes that something can be done, in such as way that delivers:
- beauty
- power
- in your face, without requiring you to study for a year
- but also giving enough precision to allow you to truly appreciate the beauty of the subjectCiro's programming skills can also be used to create educational, or actually more production-like, simulations and illustrations.
Ciro believes that today's society just keep saying over and over: "STEM is good", "STEM is good", "STEM is good" as a religious mantra, but fails miserably at providing free learning material and interaction opportunities for people to actually learn it at a deep enough level to truly appreciate why "STEM is good". This is what he wants to fix.
The following quote is ripped from Gwern Branwen's Patreon page, and it perfectly synthesizes how Ciro feels as well:
In addition to all of this, financial support also helps Ciro continue his general community support activities:
- writing and updating his amazing Stack Overflow answers: Section "Ciro Santilli's Stack Overflow contributions"
- saving the world from the CCP: Section "Ciro Santilli's campaign for freedom of speech in China"
Jean-Baptiste L. Romé de l'Isle was a French mineralogist and geologist, best known for his work in crystallography during the 18th century. He made significant contributions to the understanding of crystal structures and the principles of crystallography. One of his notable works is the formulation of the "law of symmetry" in crystals, which contributed to the classification of crystals based on their geometric shapes and symmetry properties.
Problem Book in Quantum Field Theory by Voja Radovanovic (2008) by
Ciro Santilli 40 Updated 2025-07-16
This didn't really deliver. It does start from the basics, but it is often hard to link those basics to more interesting or deeper points. Also like many other Quantum field theory book, it does not seem to contain a single comparison between a theoretical result and an experiment.
An Introduction To Quantum Field Theory by Peskin and Schroeder (1995) by
Ciro Santilli 40 Updated 2025-07-16
Unfortunately, this approach bores Ciro Santilli to death. Or perhaps is too just advanced for him to appreciate. Either of those.
800+ pages.
Sponsor Ciro Santilli's work on OurBigBook.com Accounting method by
Ciro Santilli 40 Updated 2025-07-16
A detailed list of all transactions is kept at: ../sponsor/budget.js.
Ciro Santilli use the following accounting for this sponsorship calculations.
For significant one time donations, he takes the final money received in one of his cash GBP accounts, then he checks how much that is in dollars on Google at the time of cash out, and then writes that amount down as the final dollar value which is what ultimately counts. This exposes Ciro to USD/GBP fluctuations, but it simplifies accounting for donors which is more important, so it is likely worth it.
Richard Epp is a physicist known for his contributions to the field of theoretical physics, particularly in areas related to quantum mechanics and condensed matter physics. His research often involves the analysis of complex physical systems and phenomena. He may also be involved in academic activities, such as teaching and mentoring students.
Quantum field theory lecture by Tobias Osborne (2017) mentions that quantization is a guess.
"Book on the Measurement of Plane and Spherical Figures" is a treatise attributed to the ancient Greek mathematician Archimedes. Although it is often referred to, the most well-known writings by Archimedes related to measurement actually come from various manuscripts and texts containing his work on geometry and calculus. In these works, Archimedes explored methods for calculating areas, volumes, and surface areas of various geometric shapes, both two-dimensional (plane figures) and three-dimensional (spherical figures).
Nia Imara is an artist and writer known for her work that often explores themes related to identity, culture, and the African diaspora. She combines various mediums, including painting and writing, to express her perspectives on race and social issues. Imara’s work frequently draws inspiration from her own background and experiences, and she aims to create narratives that amplify underrepresented voices.
An adaptive algorithm is a type of algorithm that adjusts its parameters or structure in response to changes in the environment or the data it is processing. The key characteristic of adaptive algorithms is their ability to modify their behavior based on feedback or new inputs, allowing them to optimize performance over time or under varying conditions. ### Key Features of Adaptive Algorithms: 1. **Flexibility**: They can adjust to new data patterns or dynamic environments.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.Figure 4. Visual Studio Code extension tree navigation.Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact





