# pure mathematics

> mathematics independent of application

**Wikidata**: [Q837863](https://www.wikidata.org/wiki/Q837863)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Pure_mathematics)  
**Source**: https://4ort.xyz/entity/pure-mathematics

## Summary
Pure mathematics is the study of mathematical concepts independent of any application outside of the field. It is an academic discipline and a branch of mathematics classified as basic research, focusing on theoretical work to acquire new knowledge of underlying foundations.

## Key Facts
- Defined as mathematics independent of application.
- Classified as an academic discipline and a field of study.
- Functions as an academic major, representing a focus of study leading to a degree.
- Considered a form of basic research, involving theoretical work to understand the foundations of phenomena and observable facts.
- Has a sitelink count of 60 across various knowledge bases.
- Wikipedia title is "Pure mathematics".
- Parent field is mathematics.
- Related subfields include number theory, mathematical analysis, functional analysis, and discrete mathematics.

## FAQs
**How is pure mathematics distinguished from other fields?**
It is defined specifically by its independence from application, focusing on theoretical concepts rather than practical utility.

**What type of research does pure mathematics involve?**
It is categorized as basic research, which is theoretical work undertaken primarily to acquire new knowledge of the underlying foundations of phenomena and observable facts.

**Which specific branches of mathematics fall under this category?**
Notable branches include number theory (study of integers), mathematical analysis, functional analysis (infinite-dimensional topological vector spaces), and discrete mathematics (study of discrete mathematical structures).

**Who are some notable figures associated with this field?**
Associated figures include G.H. Hardy and Percy John Daniell of the UK, as well as Russian mathematicians Alexander Friedmann, Stepan Rumovsky, Konstantin Andreev, and Lubov Zapolskaya.

## Why It Matters
Pure mathematics serves as the theoretical backbone of the entire mathematical field, providing the rigorous framework necessary for understanding abstract structures. By engaging in basic research, it expands the fundamental knowledge of phenomena and observable facts without the constraint of immediate practical application. This focus on the "underlying foundations" allows for the development of advanced concepts like infinite-dimensional topological vector spaces and the deep study of integers, which often later become critical in applied sciences.

## Notable For
- Being defined strictly by its separation from real-world application.
- Encompassing number theory, a branch devoted entirely to the study of the integers.
- Including functional analysis, which specializes in infinite-dimensional topological vector spaces.
- Serving as a primary academic discipline and major for theoretical study.
- Attracting prominent historical scholars such as G.H. Hardy (British) and Alexander Friedmann (Russian).

## Body

### Definition and Classification
Pure mathematics is fundamentally defined as mathematics that is independent of application. It operates as a distinct academic discipline and is recognized as a specific field of study. As an academic major, it represents a focus of study that leads to a degree. Furthermore, it is categorized as basic research, which is described as experimental or theoretical work undertaken to acquire new knowledge of the underlying foundations of phenomena and observable facts. The field has a significant presence in academic databases, evidenced by a sitelink count of 60 and a Wikipedia title matching the entity name.

### Branches and Subfields
The domain of pure mathematics encompasses several specialized branches. It is a parent category to functional analysis, a branch of mathematical analysis concerned with infinite-dimensional topological vector spaces, often spaces of functions. Number theory is also a key component, defined as a branch of pure mathematics devoted primarily to the study of the integers. Additionally, the field includes mathematical analysis and discrete mathematics, the latter being the study of discrete mathematical structures.

### Notable Figures
The development of pure mathematics has involved numerous contributors from various backgrounds.

**British Mathematicians**
*   **G.H. Hardy (1877–1947):** A British mathematician and mathematical historian.
*   **Percy John Daniell (1889–1946):** A British mathematician with citizenship in the United Kingdom and the United States.

**Russian Mathematicians**
*   **Alexander Friedmann (1888–1925):** A Russian mathematician, cosmologist, physicist, and geophysicist.
*   **Stepan Rumovsky:** A Russian mathematician and astronomer.
*   **Konstantin Andreev (1848–1921):** A Russian mathematician.
*   **Lubov Zapolskaya (1871–1943):** A Russian mathematician.

## References

1. Freebase Data Dumps. 2013
2. BBC Things
3. Quora
4. [Source](https://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/1297.02008?OpenDocument)
5. KBpedia
6. [Source](https://vocabs.ardc.edu.au/viewById/316)
7. [OpenAlex](https://docs.openalex.org/download-snapshot/snapshot-data-format)
8. [Best Pure Mathematics Posts - Reddit](https://www.reddit.com/t/pure_mathematics/)