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'''Mathematics''' (from Greek μάθημα ''máthēma'', "knowledge, study, learning") is the study of topics such as ([[Number (nonfiction)|numbers (nonfiction)]]), [[structure (nonfiction)]], [[space (nonfiction)]], [[time (nonfiction)]], [[motion (nonfiction)]], [[change (nonfiction)]], and [[measurement (nonfiction)]].
[[File:Mayan_numerals.svg|thumb|Mayan numerals.]]'''Mathematics''' (from Greek μάθημα ''máthēma'', "knowledge, study, learning") is the study of topics such as numbers, structure, space, [[time]], motion, change, and [[measurement]].


== Definition ==
Mathematicians seek out patterns and use them to formulate new conjectures.


There is a range of views among [[Mathematician (nonfiction)|mathematicians  (nonfiction)]] and philosophers as to the exact scope and definition of mathematics.
Mathematicians resolve the truth or falsity of conjectures by mathematical proof.
 
== Patterns and conjectures ==
 
Mathematicians seek out patterns and use them to formulate new [[Conjecture (nonfiction)|conjectures (nonfiction)]].
 
== Mathematical proof ==
 
Mathematicians resolve the truth or falsity of conjectures by [[mathematical proof (nonfiction)]].
 
== Physics ==


When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.
When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.


See [[Physics (nonfiction)]].
There is a range of views among [[Mathematician (nonfiction)|mathematicians]] and philosophers as to the


== Fundamental principles ==
Practical mathematics has been a human activity for as far back as written records exist.


Through the use of [[Abstraction (mathematics) (nonfiction)]] and [[logic (nonfiction)]], mathematics developed from:
The research required to solve mathematical problems can take years or even centuries of sustained inquiry.


* [[Counting (nonfiction)]]
It is not to be confused with the fictional "[[mathematics]]" of the equally fictional [[Gnomon algorithm]].
* [[Calculation (nonfiction)]]
* [[Measurement (nonfiction)]]
* The systematic study of the shapes and motions of physical objects


== History ==
== In the News ==


Practical mathematics has been a human activity for as far back as written records exist.
<gallery>
File:Woman teaching geometry circa 1309.jpg|link=Geometry (nonfiction)|Women geometers first to ask [[Geometry (nonfiction)|geometry]] how it feels.
File:Voronoi-diagram-color-commentators.jpg|link=Fantasy Voronoi diagram|[[Fantasy Voronoi diagram]] color commentators discussing recent scores from hotly contested [[Voronoi diagram (nonfiction)|Voronoi diagrams]].
File:Cantor set (four iterations).png|link=Set theory (nonfiction)|Crime-fighter [[The Sigil (crime fighter)|The Sigil]]'s seen wearing new [[Sigil (nonfiction)|sigil]]. "Naturally I am pleased," said [[Georg Cantor]].
File:Euclid_Lueneburg_ms_page_8.jpg|link=Mathematical diagram (nonfiction)|Artifically intelligent manuscript of Euclid's ''Elements'' needs to upgrade itself, has [[Mathematical diagram (nonfiction)|sketch on back of envelope]] it wishes to show you.
File:John Venn computing diagram.jpg|link=John Venn|[[John Venn]] computes a [[Venn diagram|Demon-repelling diagram]] for [[Roger Zelazny]] and [[William Blake]].
File:Benoit Mandelbrot.jpg|link=Benoit Mandelbrot (nonfiction)|[[Benoit Mandelbrot (nonfiction)]] survived by [[Benoit Mandelbrot]].
</gallery>


== Effort required ==
== Fiction cross-references ==


The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
* [[Audible (mathematics)]] - a mathematical [[Abuse of notation (nonfiction)|abuse of notation]] expressed as an impromptu verbal deviation from an established plan.  
* [[Axiom Antics]]
* [[Crimes against mathematical constants]]
* [[Gnomon Algorithm]]
* [[Pi disaster]]
* [[Mathematician]]
* [[Mathematics]]
* [[Poem]]
* [[Three is the Color of My True Love's Hair (analysis)]]


== Nonfiction cross-reference ==
== Nonfiction cross-reference ==


* [[Abstract syntax (nonfiction)]]
* [[Algebraic geometry (nonfiction)]]
* [[Abstract syntax tree (nonfiction)]]
* [[Abstraction (mathematics) (nonfiction)]]
* [[Algebra (nonfiction)]]
* [[Algorithm (nonfiction)]]
* [[Algorithm (nonfiction)]]
* [[Analysis (nonfiction)]]
* [[Argument of a function (nonfiction)]]
* [[Arithmetic (nonfiction)]]
* [[Axiom (nonfiction)]]
* [[Binomial (nonfiction)]]
* [[Calculus (nonfiction)]]
* [[Cellular automaton (nonfiction)]]
* [[Cellular automaton (nonfiction)]]
* [[Complex dynamics (nonfiction)]]
* [[Complex number (nonfiction)]]
* [[Computation (nonfiction)]]
* [[Computation (nonfiction)]]
* [[Conjecture (nonfiction)]]
* [[Constant (mathematics) (nonfiction)]]
* [[Covering space (nonfiction)]]
* [[Discrete mathematics (nonfiction)]]
* [[Dynamical systems (nonfiction)]]
* [[Equation (nonfiction)]]
* [[Equation (nonfiction)]]
* [[Euler angles (nonfiction)]]
* [[Existence theorem (nonfiction)]]
* [[Fibonacci coding (nonfiction)]]
* [[Fibonacci sequence (nonfiction)]]
* [[Fixed-point theorem (nonfiction)]]
* [[Formal language (nonfiction)]]
* [[Formal grammar (nonfiction)]]
* [[Foundations of mathematics (nonfiction)]]
* [[Fractal (nonfiction)]]
* [[Fractal (nonfiction)]]
* [[Function (mathematics) (nonfiction)]]
* [[Differential equation (nonfiction)]]
* [[Expression (nonfiction)]]
* [[Geometry (nonfiction)]]
* [[Geometry (nonfiction)]]
* [[Gnomon (nonfiction)]]
* [[Gnomon (nonfiction)]]
* [[Graph theory (nonfiction)]]
* [[Inverse problem (nonfiction)]]
* [[Hexadecimal (nonfiction)]]
* [[Killed process (nonfiction)]]
* [[How to Solve It]]
* [[Language of mathematics (nonfiction)]] - the system used by [[Mathematician (nonfiction)|mathematicians]] to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language (for example English) using technical terms and grammatical conventions that are peculiar to mathematical discourse (see Mathematical jargon), supplemented by a highly specialized [[Mathematical notation (nonfiction)|symbolic notation for mathematical formulas]].
* [[Idempotence (nonfiction)]]
* [[Integer (nonfiction)]]
* [[Julia set (nonfiction)]]
* [[Lambda calculus (nonfiction)]]
* [[Large cardinal (nonfiction)]]
* [[Logic (nonfiction)]]
* [[Logic (nonfiction)]]
* [[Mandelbrot set (nonfiction)]]
* [[Mandelbrot set (nonfiction)]]
* [[Mathematical analysis (nonfiction)]]
* [[Mathematical beauty (nonfiction)]]
* [[Mathematical logic (nonfiction)]]
* [[Mathematical humor (nonfiction)]]
* [[Mathematical notation (nonfiction)]]
* [[Mathematical notation (nonfiction)]]
* [[Mathematical object (nonfiction)]]
* [[Mathematical proof (nonfiction)]]
* [[Mathematician (nonfiction)]]
* [[Mathematician (nonfiction)]]
* [[Morse theory (nonfiction)]]
* [[Metamathematics (nonfiction)]]
* [[Morse–Smale system (nonfiction)]]
* [[Music theory (nonfiction)]]
* [[Natural number (nonfiction)]]
* [[Newton's method (nonfiction)]]
* [[Number (nonfiction)]]
* [[Number (nonfiction)]]
* [[Number theory (nonfiction)]]
* [[Numeral system (nonfiction)]]
* [[Outsider mathematician (nonfiction)]]
* [[Outsider mathematician (nonfiction)]]
* [[Permutation (nonfiction)]]
* [[Pi (nonfiction)]]
* [[Pi (nonfiction)]]
* [[Polar coordinate system (nonfiction)]]
* [[Positional notation (nonfiction)]]
* [[Prenex normal form (nonfiction)]]
* [[Prenex normal form (nonfiction)]]
* [[Power of two (nonfiction)]]
* [[Proof theory (nonfiction)]]
* [[Real number (nonfiction)]]
* [[QED manifesto (nonfiction)]]
* [[Recursion (nonfiction)]]
* [[Rounding (nonfiction)]]
* [[Round-off error (nonfiction)]]
* [[Scaling (geometry) (nonfiction)]]
* [[Self-reference (nonfiction)]]
* [[Signal (nonfiction)]]
* [[Signal processing (nonfiction)]]
* [[Simplicial complex (nonfiction)]]
* [[The Unreasonable Effectiveness of Mathematics in the Natural Sciences (nonfiction)]]
* [[Tuple (nonfiction)]]
* [[Turing machine (nonfiction)]]
* [[Turing machine (nonfiction)]]
* [[Variable (mathematics) (nonfiction)]]
* [[Witch of Agnesi (nonfiction)]]
* [[Undecidable problem (nonfiction)]]
 
By category:


== Fiction cross-references ==
* [[:Category:Mathematicians_(nonfiction)]]
* [[:Category:Mathematics_(nonfiction)]]
 
External links:
 
Math blogs:


* [[Axiom Antics]]
* [https://divisbyzero.com/blog-division-by-zero/ Division by Zero] - David Richeson, Professor of Mathematics at Dickinson College.
* [[Gnomon Algorithm]]
* [[Pi disaster]]
* [[Mathematician]]
* [[Mathematics]]
* [[Poem]]
* [[Three is the Color of My True Love's Hair (nonfiction)]]


== External links ==
General:


* [http://en.wikipedia.org/wiki/Mathematics Mathematics] @ Wikipedia
* [http://en.wikipedia.org/wiki/Mathematics Mathematics] @ Wikipedia
* [https://www.quantamagazine.org/20170202-math-and-the-best-life-francis-su-interview/ To Live Your Best Life, Do Mathematics]
* [https://kpknudson.com/my-favorite-theorem/ My Favorite Theorem]
* [http://kasmana.people.cofc.edu/MATHFICT/printable.php A Printable List of Mathematical Fiction]
* [http://www.josleys.com/index.php Mathematical imagery by Jos Leys]
* [https://newrepublic.com/article/148150/math-kill-god Did Math Kill God?]
* [https://mathigon.org Mathigon] - Mathematics education platform
* [http://maxbittker.github.io/Mojulo/#eCAqIHkgKiB0aW1l Animations of equations] - web app by Max Bittker
* [https://www.maa.org/news/on-this-day On This Day] @ Mathematical Association of America
* [http://math.ucr.edu/home/baez/books.html How to learn math and physics] by John Baez - list of books and other resources, along with practical advice.
* [https://soundcloud.com/stephenwolfram/a-very-brief-history-of-mathematics A Very Brief History of Mathematics] by Stephen Wolfram
YouTube:


* [https://www.youtube.com/watch?v=kZTKuMBJP7Y How Not to Be Wrong: The Power of Mathematical Thinking] @ YouTube
* [https://www.youtube.com/watch?v=kZTKuMBJP7Y How Not to Be Wrong: The Power of Mathematical Thinking] @ YouTube

Latest revision as of 04:53, 7 April 2020

Mayan numerals.

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of topics such as numbers, structure, space, time, motion, change, and measurement.

Mathematicians seek out patterns and use them to formulate new conjectures.

Mathematicians resolve the truth or falsity of conjectures by mathematical proof.

When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.

There is a range of views among mathematicians and philosophers as to the

Practical mathematics has been a human activity for as far back as written records exist.

The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

It is not to be confused with the fictional "mathematics" of the equally fictional Gnomon algorithm.

In the News

Fiction cross-references

Nonfiction cross-reference

By category:

External links:

Math blogs:

  • Division by Zero - David Richeson, Professor of Mathematics at Dickinson College.

General:

YouTube:

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