的施莱格尔图]]
數學物件（Mathematical object）是数学中的抽象概念。用數學的普通語言來說，對象是任何可以或已經用演绎推理和数学证明正式定義的物件。一般地，一個數學物件可以是一個能代入变数的值，從而可以用於公式裡。 經常遇到的數學物件包括数、集合、函数、表示式、几何形状、其他數學物件的变换和空间。數學物件可以非常複雜。比如說，定理、证明甚至理论在证明论中被視為數學物件。
數學物件的存在是數學哲學家進行大量研究和討論的對象。
按分支分類的數學物件列表
- 数论
** 数、运算
- 组合数学
**置换、错排、组合
- 集合论
**集合、集合划分
**函数、关系
- 几何学
**点、线、线段
**多边形（三角形、正方形、五边形、六边形……)、圆、椭圆、抛物线、双曲线
**多面体（四面体、立方体、八面体、十二面体、二十面体）、球体、椭球、抛物面、双曲面、圆柱体、圆锥体
- 图论
**图、树、顶点、边
- 拓扑学
**拓扑空间、流形
- 线性代数
**标量、向量、矩阵、张量
- 抽象代数
**群
**环、模
**域、向量空间
**群论格、序论格
參見
- 抽象对象
- 数学结构
參考文獻
- Azzouni, J., 1994. Metaphysical Myths, Mathematical Practice. Cambridge University Press.
- Burgess, John, and Rosen, Gideon, 1997. A Subject with No Object. Oxford Univ. Press.
- Davis, Philip and Reuben Hersh, 1999 [1981]. The Mathematical Experience. Mariner Books: 156–62.
- Gold, Bonnie, and Simons, Roger A., 2011. [https://books.google.com/books?id=wPhwJdjI-dIC&printsec=frontcover#v=onepage&q=%22mathematical%20object%22&f=false Proof and Other Dilemmas: Mathematics and Philosophy] . Mathematical Association of America.
- Hersh, Reuben, 1997. What is Mathematics, Really? Oxford University Press.
- Sfard, A., 2000, "Symbolizing mathematical reality into being, Or how mathematical discourse and mathematical objects create each other," in Cobb, P., et al., Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools and instructional design. Lawrence Erlbaum.
- Stewart Shapiro, 2000. Thinking about mathematics: The philosophy of mathematics. Oxford University Press.
外部鏈接
- Stanford Encyclopedia of Philosophy: "[http://plato.stanford.edu/entries/abstract-objects Abstract Objects] "—by Gideon Rosen.
- Wells, Charles, "[https://web.archive.org/web/20081014205857/http://www.abstractmath.org/MM//MMMathObj.htm Mathematical Objects.]"
- [https://web.archive.org/web/20100717234001/http://theory.cs.uvic.ca/amof/ AMOF: The Amazing Mathematical Object Factory]
- [https://web.archive.org/web/20100611203942/http://www.math.cuhk.edu.hk/exhibit/ Mathematical Object Exhibit]
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