Weihrauch reducibility is a concept from the field of computability theory and reverse mathematics. It arises in the study of effective functionals, particularly in the context of understanding the complexity of mathematical problems and their solutions when framed in terms of algorithmic processes. In basic terms, Weihrauch reducibility provides a way to compare the computational strength of different problems or functionals.
Fernique's theorem is a result in probability theory, particularly in the context of Gaussian processes and stochastic analysis. It deals with the continuity properties of stochastic processes, specifically the continuity of sample paths of certain classes of random functions.
A **Grothendieck space** typically refers to a specific kind of topological vector space that is particularly important in functional analysis and the theory of distributions. Named after mathematician Alexander Grothendieck, these spaces have characteristics that make them suitable for various applications, including the theory of sheaves, schemes, and toposes in algebraic geometry as well as in the study of functional spaces.
Radó's theorem is a result in complex analysis and the theory of Riemann surfaces. It states that any analytic (holomorphic) function defined on a compact Riemann surface can be extended to a function that is also holomorphic on a larger Riemann surface, provided the larger surface has the same genus as the compact surface.
Teichmüller modular forms are a class of mathematical objects that arise in the study of Teichmüller theory, which is a branch of mathematics dealing with the moduli spaces of Riemann surfaces. Specifically, these modular forms are associated with the deformation theory of complex structures on Riemann surfaces as well as with the geometry of the moduli space of stable curves and Riemann surfaces.
A weakly harmonic function is a function that satisfies the properties of harmonicity in a "weak" sense, typically using the framework of distribution theory or Sobolev spaces.
Errett Bishop (1928–2019) was a prominent American mathematician known for his significant contributions to functional analysis and mathematical pedagogy. He is particularly well-known for his work in the foundations of mathematics, especially in the field of constructive mathematics. Bishop advocated for a constructive approach to analysis, which emphasizes the importance of providing explicit examples and methods for proving the existence of mathematical objects rather than relying on non-constructive methods prevalent in classical mathematics.
Micro Machines is a brand and line of toy vehicles that are miniature in size. First introduced by Galoob in 1987, these toys consist of tiny cars, trucks, and other vehicles, often accompanied by playsets that feature intricate environments and designs. The appeal of Micro Machines lies in their small scale, allowing for a wide variety of designs and configurations. In addition to the toy line, Micro Machines gained popularity through video games, especially during the 1990s.
John Toland (born 1670, died 1722) was an Irish mathematician, philosopher, and writer known for his contributions to various fields, including mathematics and the philosophy of science. He was also associated with the early development of the concept of mathematical analysis. Toland is perhaps best known for his philosophical work rather than strictly mathematical contributions. He was a proponent of empiricism and skepticism and engaged in discussions about the nature of knowledge and the limits of human understanding.
Louis de Branges de Bourcia is a French mathematician known for his work in several areas of mathematics, particularly in the field of functional analysis and differential equations. He gained significant attention in the mathematical community for his proof of the Bieberbach conjecture in 1985, which is a famous problem in complex analysis related to the coefficients of univalent (or one-to-one) functions.
Charles Cook is an academic known for his work in the field of political science, particularly in the area of voting behavior, elections, and political analysis. He has contributed significantly to the understanding of electoral systems, political parties, and the dynamics of political competition. Cook often focuses on empirical research, applying quantitative methods to analyze electoral trends and public opinion. His work is recognized for its rigor and has been published in various academic journals.
Robin Williams is a mathematician known for his contributions to the field of mathematics, particularly in areas such as mathematical education and the application of mathematics in various contexts. He has published works and may have been involved in teaching and research, but specific details about his contributions can vary. It's important to note that there are several individuals with the name Robin Williams in various fields, including the late actor and comedian.
Mike Steel is a mathematician known for his work in the fields of combinatorics, phylogenetics, and evolutionary biology. He has made significant contributions to the study of mathematical structures related to trees and networks, often in the context of biological applications such as the reconstruction of evolutionary relationships among species. His research includes the development of methods for inferring phylogenetic trees, exploring the mathematical properties of these trees, and applying statistical techniques to improve the accuracy of evolutionary models.
The curie (symbol: Ci) is a unit of radioactivity that was originally defined as the amount of radioactivity in a sample of radium-226 that produces 37 billion disintegrations per second. It is named after Marie Curie and her husband Pierre Curie, who conducted pioneering research on radioactivity. In terms of the International System of Units (SI), 1 curie is equivalent to 3.
Roger Godement (1921–2018) was a prominent French mathematician known for his contributions to several areas of mathematics, including algebraic geometry, number theory, and particularly the theory of distributions and functional analysis. He is known for his work on the structure of mathematical objects and for his development of the Godement resolutions, which are important in the study of sheaf cohomology and derived categories.
Szolem Mandelbrojt was a notable Polish mathematician, known for his work in the fields of analysis and functional analysis. He was born on January 18, 1899, in Poland and had a significant academic career, contributing to various areas of mathematics. Mandelbrojt is perhaps best known for his contributions to the theory of functions and his work on convergence of series, as well as his involvement in the development of mathematical analysis.
"Éléments de mathématique" is a comprehensive series of mathematics books written by the French mathematician Nicolas Bourbaki. The series aims to provide a rigorous and systematic foundation for various areas of mathematics, presenting concepts in a formal and abstract manner. Bourbaki, a group of mathematicians that includes André Weil, Henri Cartan, and others, sought to unify and clarify mathematical theories and eliminate ambiguities.
Stefan Mazurkiewicz was a Polish mathematician known for his contributions to various areas of mathematics, particularly in topology and functional analysis. He is often recognized for his work in set theory and measure theory. One of his notable contributions is the development of concepts related to topology, such as the Mazurkiewicz topology, which is related to the properties of sequences and convergences.
Thomas William Körner is a mathematician known for his contributions to the fields of functional analysis and partial differential equations, as well as for his work in mathematical analysis and its applications. He has authored several influential books and papers, including works that explore mathematical concepts in a clear and accessible manner. His contributions have been significant in various areas, including harmonic analysis and the study of geometric properties of functions.

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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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