Dieter Kotschick is a mathematician known for his contributions to the fields of differential geometry and mathematical physics. He has worked on topics such as the geometry of manifolds and the interplay between mathematical physics and geometry. Specific details about his work, publications, or prominent theories may require further exploration depending on your area of interest.
Ib Madsen is not a widely recognized name in popular culture, science, or history, so it's possible that you might be referring to a specific individual who is less known or a fictional character, or perhaps a niche topic that is not broadly documented.
Marston Morse refers to a mathematical concept related to Morse theory, which was developed by the American mathematician Marston Morse in the early 20th century. Morse theory is a branch of differential topology that studies the topology of manifolds using smooth real-valued functions defined on them, known as Morse functions. A Morse function is a smooth function where its critical points (points where the gradient is zero) have distinct non-degenerate critical values.
Peter Teichner is a mathematician known for his work in the fields of topology and mathematical physics, particularly in the study of knot theory and its connections to quantum field theory. He has made significant contributions to the understanding of the relationships between various mathematical structures and their applications.
William Browder is an American mathematician known for his contributions to topology, particularly in the areas of algebraic topology and the theory of manifolds. He has made significant advances in various mathematical fields, particularly in homotopy theory and differential topology. Browder is also known for his work on the Browder surgery theory, which relates to the classification of manifolds.
Wolfgang Lück is a prominent German mathematician known for his work in various fields of mathematics, particularly in topology and algebraic topology. He has made significant contributions to the understanding of manifold theory, homotopy theory, and K-theory. In addition to his research, Lück is also recognized for his involvement in mathematical education and for authoring textbooks and papers that facilitate the teaching of complex mathematical concepts.
In the context of topology, a uniform space is a set equipped with a uniform structure that allows for the generalization of concepts such as uniform continuity and uniform convergence. A **uniformly connected space** specifically refers to a uniform space that satisfies certain path-connectedness conditions.
The Axiom of Infinity is one of the axioms of set theory, particularly in the context of Zermelo-Fraenkel set theory (ZF), which is a foundational system for mathematics. The Axiom of Infinity asserts the existence of an infinite set. Specifically, the axiom states that there exists a set \( I \) such that: 1. The empty set \( \emptyset \) is a member of \( I \).
The Copleston–Russell debate refers to a famous philosophical discussion between the British philosopher Frederick Copleston and the philosopher and logician Bertrand Russell that took place in 1948 on the BBC radio program "The Third Programme." This debate primarily centered on the existence of God and the rationality of belief in God. Copleston, a Jesuit priest, presented a classical philosophical argument for the existence of God, particularly the cosmological argument.
The Russell Tribunal, also known as the International War Crimes Tribunal, was established in 1966 by the British philosopher Bertrand Russell and other intellectuals to address and investigate war crimes, particularly those committed by the United States during the Vietnam War. The tribunal was not an official legal body but rather a forum for public opinion, aimed at raising awareness and creating pressure for legal accountability for such actions.
Alexander Radishchev (1749–1802) was a Russian writer and social critic who is best known for his controversial work "Journey from St. Petersburg to Moscow," published in 1790. This book is considered one of the earliest examples of Russian travel literature and provides a vivid description of the social, political, and economic conditions in Russia during that time.
Benito Jerónimo Feijóo y Montenegro (1676-1764) was a notable Spanish Benedictine monk, scholar, and rationalist who played a significant role in the Spanish Enlightenment. He is best known for his works that promoted scientific thought and skepticism toward superstition and traditional beliefs, which were prevalent in his time.
Emanuel Swedenborg (1688–1772) was a Swedish scientist, philosopher, theologian, and mystic best known for his writings on theology and the afterlife. Trained as an engineer and a natural philosopher, Swedenborg made significant contributions to various fields, including anatomy, physics, and astronomy, but he is most recognized for his spiritual writings.
Maximilian III Joseph was the Elector of Bavaria from 1745 until his death in 1777. Born on December 28, 1727, he was a member of the House of Wittelsbach. As Elector, Maximilian III Joseph played a significant role in the political landscape of the Holy Roman Empire during his reign. He was known for his efforts to modernize the administration of Bavaria and improve the state's economy and infrastructure.
Theoklitos Farmakidis is a notable figure in the field of medicine, particularly known for his contributions to medical education and practice. While specific details about his life and work may not be widely available, it is important to note that individuals with similar names may exist in various domains.
Implicit theories of intelligence refer to the beliefs and assumptions individuals hold about the nature of intelligence. This concept is often explored in the fields of psychology, particularly in educational contexts, and it was notably studied by psychologist Carol Dweck and her colleagues. There are generally two primary types of implicit theories of intelligence: 1. **Entity Theory** (Fixed Mindset): This perspective posits that intelligence is a stable and unchangeable trait.
In philosophy, "point of view" refers to a particular perspective or standpoint from which an individual interprets and understands experiences, concepts, beliefs, and reality itself. It encompasses various dimensions, including epistemological, ethical, and metaphysical considerations. Here are some key aspects of point of view in philosophy: 1. **Epistemology**: In the context of knowledge and belief, a point of view can influence what one perceives as true or valid.
Thought-action fusion (TAF) is a cognitive phenomenon often discussed in the context of obsessive-compulsive disorder (OCD) and other anxiety disorders. It refers to the belief that one's thoughts can directly influence real-world events or that merely thinking about an action can be morally equivalent to carrying it out. TAF can manifest in two primary ways: 1. **Likelihood TAF**: This involves the belief that having a specific thought increases the likelihood that the corresponding action will occur.
Wish fulfillment is a psychological concept referring to the process of satisfying one's desires or wishes, often seen in dreams, fantasies, and some forms of art or literature. The term is commonly associated with Sigmund Freud's psychoanalytic theory, which posits that dreams can serve as a means for individuals to fulfill their unconscious desires and wishes that may not be achievable in their waking lives.
"Continuum" is a sculpture by the artist Anish Kapoor, known for his unique and often large-scale works that explore themes of space, perception, and materiality. Created in 2007, "Continuum" is characterized by its polished surfaces and intriguing interplay with light, creating a dynamic visual experience for viewers. The sculpture is typically interpreted as an exploration of infinity and the continuous nature of form, drawing attention to the relationships between the object, its environment, and the observer.

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