abstract algebra
noun
: a branch of mathematics in which algebraic concepts are generalized by using symbols to represent basic arithmetical operations
Abstract algebra courses introduce students to advanced mathematical concepts such as group theory and lattices.
Examples of abstract algebra in a Sentence
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Questions on straightforward topics, like high school history, produced up to six times fewer emissions than subjects like abstract algebra or philosophy, which required lengthy reasoning processes.
—
Simmone Shah, Time, 19 June 2025
This is part of a field of abstract algebra called group theory, which studies symmetry.
—Eugenia Cheng, WSJ, 4 Aug. 2022
One of these topics, Elliptic Curves, was completely undiscovered in Fermat’s time, leading many to believe Fermat never really had a proof of his Last Theorem. From solving Rubik’s Cube to proving a fact about body-swapping on Futurama, abstract algebra has a wide range of applications.
—Dave Linkletter, Popular Mechanics, 28 Jan. 2022
Getting the most popular programs to work may approach abstract algebra.
—Sonja Sharp Staff Writer, Los Angeles Times, 12 Apr. 2021
The mathematician who follows the ice queen often dislikes concrete applications or specific cases — Alexander Grothendieck, one of the high priests of abstract algebra, once famously picked 57 as an example of a prime number.
—Quanta Magazine, 16 June 2020
Five of them will be taking college courses in differential equations, abstract algebra and discrete mathematics as 10th-graders at Pasadena High School this fall.
—Jay Mathews, Washington Post, 6 July 2019
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Simmone Shah, Time, 19 June 2025
This is part of a field of abstract algebra called group theory, which studies symmetry.
—Eugenia Cheng, WSJ, 4 Aug. 2022
One of these topics, Elliptic Curves, was completely undiscovered in Fermat’s time, leading many to believe Fermat never really had a proof of his Last Theorem. From solving Rubik’s Cube to proving a fact about body-swapping on Futurama, abstract algebra has a wide range of applications.
—Dave Linkletter, Popular Mechanics, 28 Jan. 2022
Getting the most popular programs to work may approach abstract algebra.
—Sonja Sharp Staff Writer, Los Angeles Times, 12 Apr. 2021
The mathematician who follows the ice queen often dislikes concrete applications or specific cases — Alexander Grothendieck, one of the high priests of abstract algebra, once famously picked 57 as an example of a prime number.
—Quanta Magazine, 16 June 2020
Five of them will be taking college courses in differential equations, abstract algebra and discrete mathematics as 10th-graders at Pasadena High School this fall.
—Jay Mathews, Washington Post, 6 July 2019
Cite this Entry
“Abstract algebra.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/abstract%20algebra. Accessed 4 Sep. 2025.
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