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File:Godfrey Harold Hardy.jpgG. H. Hardy
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

File:Rubik float.pngRubik's Cube
The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra.An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra.

Group theory
The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra.

Lattice
An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra.

Structure

Image:Elliptic curve simple.png|Many mathematical objects, such as sets of numbers and functions, exhibit internal structure. Image:Rubik float.png|The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra. Image:Group diagdram D6.svg|Group theory Image:Lattice of the divisibility of 60.svg|An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra.

Image:Elliptic curve simple.png|Many mathematical objects, such as sets of numbers and functions, exhibit internal structure. Image:Rubik float.png|The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra. Image:Group diagdram D6.svg|Group theory Image:Lattice of the divisibility of 60.svg|An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra.

Space

Image:Elliptic curve simple.png|Many mathematical objects, such as sets of numbers and functions, exhibit internal structure. Image:Rubik float.png|The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra. Image:Group diagdram D6.svg|Group theory Image:Lattice of the divisibility of 60.svg|An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra.

Image:Elliptic curve simple.png|Many mathematical objects, such as sets of numbers and functions, exhibit internal structure. Image:Rubik float.png|The structural properties of these objects are investigated in the study of groups, rings, fields and other abstract systems, which are themselves such objects. This is the field of abstract algebra. Image:Group diagdram D6.svg|Group theory Image:Lattice of the divisibility of 60.svg|An important concept here is that of vectors, generalized to vector spaces, and studied in linear algebra.