Schlegel wireframe 8-cell
mathematical object is an
abstract concept arising in
In the usual language of mathematics, an object is anything that has been (or could be) formally defined, and with which one may do
deductive reasoning and
mathematical proofs. Typically, a mathematical object can be a value that can be assigned to a
variable, and therefore can be involved in
formulas. Commonly encountered mathematical objects include
transformations of other mathematical objects, and
spaces. Mathematical objects can be very complex; for example,
proofs, and even
theories are considered as mathematical objects in
ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics.
List of mathematical objects by branch
Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In
proof theory, proofs and
theorems are also mathematical objects.
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A Subject with No Object. Oxford Univ. Press.
Davis, Philip and
Reuben Hersh, 1999 . The Mathematical Experience. Mariner Books: 156–62.
Gold, Bonnie, and Simons, Roger A., 2011.
. Mathematical Association of America. Proof and Other Dilemmas: Mathematics and Philosophy 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.