Datasets:

s-kat0
/

enwikimath

id stringlengths 2 8	title stringlengths 1 130	text stringlengths 0 252k	formulas listlengths 1 823	url stringlengths 38 44
10002357	Khintchine inequality	Theorem in probability In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Latin alphabet, is a theorem from probability, and is also frequently used in analysis. Heuristically, it says that if we pick formula_0 complex numbers formula_1, and add them together e...	[ { "math_id": 0, "text": " N " }, { "math_id": 1, "text": " x_1,\\dots,x_N \\in\\mathbb{C}" }, { "math_id": 2, "text": "\\pm 1 " }, { "math_id": 3, "text": " \\sqrt{\|x_1\|^{2}+\\cdots + \|x_N\|^{2}}" }, { "math_id": 4, "text": " \\{\\varepsilon_n\\}_{n=1}^N " },...	https://en.wikipedia.org/wiki?curid=10002357
10004115	Brushed DC electric motor	Internally commutated electric motor A brushed DC electric motor is an internally commutated electric motor designed to be run from a direct current power source and utilizing an electric brush for contact. Brushed motors were the first commercially important application of electric power to driving mechanical energy,...	[ { "math_id": 0, "text": "I = \\frac{V_\\text{applied} - V_\\text{cemf}}{R_\\text{armature}}" }, { "math_id": 1, "text": "P = I \\cdot V_\\text{cemf}" }, { "math_id": 2, "text": "\\begin{align}\n T &= \\frac{1}{2\\pi} k_b I_a \\Phi \\\\\n &= k_T I_a \\Phi\n\\end{align}" }, { ...	https://en.wikipedia.org/wiki?curid=10004115
10004409	Shear strength (soil)	Magnitude of the shear stress that a soil can sustain Shear strength is a term used in soil mechanics to describe the magnitude of the shear stress that a soil can sustain. The shear resistance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding of particle contacts. Due t...	[ { "math_id": 0, "text": "\\tau" }, { "math_id": 1, "text": "\\mu" } ]	https://en.wikipedia.org/wiki?curid=10004409
1000441	Artificial chemistry	An artificial chemistry is a chemical-like system that usually consists of objects, called molecules, that interact according to rules resembling chemical reaction rules. Artificial chemistries are created and studied in order to understand fundamental properties of chemical systems, including prebiotic evolution, as w...	[ { "math_id": 0, "text": "\\subset" } ]	https://en.wikipedia.org/wiki?curid=1000441
1000450	Johann Heinrich von Thünen	German economist (1783–1850) Johann Heinrich von Thünen (24 June 1783 – 22 September 1850), sometimes spelled Thuenen, was a prominent nineteenth-century economist and a native of Mecklenburg-Strelitz, now in northern Germany. Even though he never held a professorial position, von Thunen had substantial influence on ec...	[ { "math_id": 0, "text": "R = Y(p - c) - YFm \\," } ]	https://en.wikipedia.org/wiki?curid=1000450
10005756	Sample mean and covariance	Statistics computed from a sample of data The sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables. The sample mean is the average value (or mean value) of a sample of numbers t...	[ { "math_id": 0, "text": " \\bar{X}=\\frac{1}{N}\\sum_{i=1}^{N}X_{i}." }, { "math_id": 1, "text": "\\bar{x} = (1+4+1)/3 = 2" }, { "math_id": 2, "text": "\\mu = (1+1+3+4+0+2+1+0) /8 = 12/8 = 1.5" }, { "math_id": 3, "text": "x_{ij}" }, { "math_id": 4, "text": "\\...	https://en.wikipedia.org/wiki?curid=10005756
10006830	Disk loading	Characteristic of rotors/propellers In fluid dynamics, disk loading or disc loading is the average pressure change across an actuator disk, such as an airscrew. Airscrews with a relatively low disk loading are typically called rotors, including helicopter main rotors and tail rotors; propellers typically have a higher ...	[ { "math_id": 0, "text": "A" }, { "math_id": 1, "text": "v" }, { "math_id": 2, "text": "\\rho" }, { "math_id": 3, "text": "\\dot{m}" }, { "math_id": 4, "text": "\\dot m = \\rho \\, A \\, v." }, { "math_id": 5, "text": "w" }, { "math_id": 6, ...	https://en.wikipedia.org/wiki?curid=10006830
10008	Electrode	Electrical conductor used to make contact with nonmetallic parts of a circuit An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte, a vacuum or air). Electrodes are essential parts of batteries that can consist of a variety of materials ...	[ { "math_id": 0, "text": "\\qquad \\qquad" }, { "math_id": 1, "text": "\\qquad" }, { "math_id": 2, "text": "\\Delta G^{\\dagger}" }, { "math_id": 3, "text": "\\Delta G^{0}" }, { "math_id": 4, "text": "\\Delta G^{\\dagger} = \\frac{1}{4 \\lambda} (\\Delta G^{0} ...	https://en.wikipedia.org/wiki?curid=10008
1001293	Irreducibility (mathematics)	In mathematics, the concept of irreducibility is used in several ways. <templatestyles src="Dmbox/styles.css" /> Index of articles associated with the same name This includes a list of related items that share the same name (or similar names). <br> If an [ internal link] incorrectly led you here, you may wi...	[ { "math_id": 0, "text": "\\mathbb RP^2" } ]	https://en.wikipedia.org/wiki?curid=1001293
1001329	Class function	In mathematics, especially in the fields of group theory and representation theory of groups, a class function is a function on a group "G" that is constant on the conjugacy classes of "G". In other words, it is invariant under the conjugation map on "G". Such functions play a basic role in representation theory. Chara...	[ { "math_id": 0, "text": " \\sum_{g \\in G} f(g) g" }, { "math_id": 1, "text": " \\langle \\phi , \\psi \\rangle = \\frac{1}{\|G\|} \\sum_{g \\in G} \\phi(g) \\overline{\\psi(g)} " }, { "math_id": 2, "text": " \\langle \\phi, \\psi \\rangle = \\int_G \\phi(t) \\overline{\\psi(t)}\\, dt....	https://en.wikipedia.org/wiki?curid=1001329
1001361	Semisimple module	Direct sum of irreducible modules In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring that is a semisimple module over itself is known as an Artinian semisimple ring...	[ { "math_id": 0, "text": "0 \\to A \\xrightarrow{f} B \\xrightarrow{g} C \\to 0 " }, { "math_id": 1, "text": "B \\cong A \\oplus C" }, { "math_id": 2, "text": "B \\cong f(A) \\oplus s(C)." }, { "math_id": 3, "text": " A=\\mathbf{Q}{\\left[x,y\\right]}/\\langle xy-yx-1\\ran...	https://en.wikipedia.org/wiki?curid=1001361
10013925	Multiple inert gas elimination technique	Medical technique The multiple inert gas elimination technique (MIGET) is a medical technique used mainly in pulmonology that involves measuring the concentrations of various infused, inert gases in mixed venous blood, arterial blood, and expired gas of a subject. The technique quantifies true shunt, physiological dead...	[ { "math_id": 0, "text": "V_A/Q=8.63 \\times \\frac{C_{c'}\\ce{O2} - C_v\\ce{O2}}{P_I\\ce{O2} - P_A\\ce{O2}}" }, { "math_id": 1, "text": "V_A/Q=8.63 \\times \\frac{C_v\\ce{CO2} - C_{c'}\\ce{CO2}}{P_A\\ce{CO2}}" }, { "math_id": 2, "text": "V_A/Q = 8.63 \\times \\ce{solubility} \\times ...	https://en.wikipedia.org/wiki?curid=10013925
10014466	Copper cable certification	Cable testing regimen In copper twisted pair wire networks, copper cable certification is achieved through a thorough series of tests in accordance with Telecommunications Industry Association (TIA) or International Organization for Standardization (ISO) standards. These tests are done using a certification-testing too...	[ { "math_id": 0, "text": "2" }, { "math_id": 1, "text": "\\sqrt 2" } ]	https://en.wikipedia.org/wiki?curid=10014466
1001490	Convex conjugate	Generalization of the Legendre transformation In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel transformation, Fenchel transformation, or Fenchel conjugate (afte...	[ { "math_id": 0, "text": "X" }, { "math_id": 1, "text": "X^{}" }, { "math_id": 2, "text": "\\langle \\cdot , \\cdot \\rangle : X^{} \\times X \\to \\mathbb{R}" }, { "math_id": 3, "text": "\\left( x^, x \\right) \\mapsto x^ (x)." }, { "math_id": 4, "text": "...	https://en.wikipedia.org/wiki?curid=1001490
10016360	Excellent ring	In commutative algebra, a quasi-excellent ring is a Noetherian commutative ring that behaves well with respect to the operation of completion, and is called an excellent ring if it is also universally catenary. Excellent rings are one answer to the problem of finding a natural class of "well-behaved" rings containing m...	[ { "math_id": 0, "text": "\\mathbb{Z}" }, { "math_id": 1, "text": "R" }, { "math_id": 2, "text": "k" }, { "math_id": 3, "text": "K" }, { "math_id": 4, "text": "R\\otimes_kK" }, { "math_id": 5, "text": "R \\to S" }, { "math_id": 6, "text"...	https://en.wikipedia.org/wiki?curid=10016360
1002045	Émilie du Châtelet	French mathematician, physicist, and author (1706–1749) Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (; 17 December 1706 – 10 September 1749) was a French natural philosopher and mathematician from the early 1730s until her death due to complications during childbirth in 1749. Her most recognized ach...	[ { "math_id": 0, "text": "mv^2" } ]	https://en.wikipedia.org/wiki?curid=1002045
1002128	Giant magnetoresistance	Phenomenom involving the change of conductivity in metallic layers Giant magnetoresistance (GMR) is a quantum mechanical magnetoresistance effect observed in multilayers composed of alternating ferromagnetic and non-magnetic conductive layers. The 2007 Nobel Prize in Physics was awarded to Albert Fert and Peter Grünber...	[ { "math_id": 0, "text": "\\delta_H = \\frac{R(H)-R(0)}{R(0)}" }, { "math_id": 1, "text": "w = - J (\\mathbf M_1 \\cdot \\mathbf M_2). " }, { "math_id": 2, "text": "R = R_0 + \\Delta R \\sin^2 \\frac{\\theta}{2}," }, { "math_id": 3, "text": "\\rho_{F\\pm}=\\frac{2\\rho_F}{...	https://en.wikipedia.org/wiki?curid=1002128

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Dataset Card

This dataset is created from the English Wikipedia dump file (enwiki-20240901-pages-articles-multistream.xml.bz2), available for download from Wikimedia Dumps. It includes pages containing mathematical content, extracted using the wikimathextractor tool, which is an adaptation of the wikiextractor specifically designed to extract mathematical contents.

Dataset Sources

Repository: s-kat0/wikimathextractor
Data Source: Wikipedia Dumps

Direct Use

This dataset is intended for use in tasks that require the processing and understanding of mathematical content in natural language, such as mathematical question answering and symbolic math problem solving.

Dataset Structure

Data Instances

A typical data entry in the dataset corresponds to one Wikipedia article that includes mathematical content. Here is an example:

{
  'id': '26513034',
  'title': 'Pythagorean theorem',
  'text': 'Relation between sides of a right triangle\nIn mathematics, the Pythagorean theorem or Pythagoras\' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. ...'
  'formulas': [
    {'math_id': 0, 'text': 'a^2 + b^2 = c^2 .'},
    {'math_id': 1, 'text': 'a + b'}, ...
  ],
  'url': 'https://en.wikipedia.org/wiki?curid=26513034'
}

Data Fields

id (str)
- a string representing the unique identifier of the article.
title (str)
- the title of the Wikipedia article.
text (str)
- the text content of the article, with some tags removed. Details are available in the GitHub repository.
formulas (list[dict[str, int | str]])
- a list of mathematical expressions extracted from the article, where each formula is represented as follow.
  - math_id: an index representing the position of the formula in the text.
  - text: the textual representation of the formula, without $tags.$
url (str)
- the URL of the Wikipedia article.

Data Splits

The dataset is provided in a single training split:

train: 38,661 rows

The DatasetDict structure is as follows:

DatasetDict({
    'train': Dataset({
        features: ['id', 'title', 'text', 'formulas', 'url'],
        num_rows: 38661
    })
})

Dataset Creation

Please refer to the GitHub repository for details about the dataset construction.

Source Data

Original Source: English Wikipedia available from Wikipedia Dumps

Data Collection and Processing

Please refer to the GitHub repository for details about the dataset construction.

Who are the source data producers?

Shota Kato

Bias, Risks, and Limitations

This dataset is in English and contains English Wikipedia page related to mathematical topics.

Acknowledgements

This dataset was constructed with references to several projects and tools. Acknowledgement is given to the following resources:

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