Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A mathematician who specializes in algebra.
from the GNU version of the Collaborative International Dictionary of English
 n. One versed in algebra.
from The Century Dictionary and Cyclopedia
 n. One who is versed in the science of algebra. Also algebrist.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a mathematician whose specialty is algebra
Etymologies
Sorry, no etymologies found.
Examples

My father was an algebraist, taught college math all his life.

In the judgment of many, she is the greatest algebraist of the twentieth century.

Her ideas revolutionized current understanding of algebra and laid the groundwork for further work by her "children" and "grandchildren" in the mathematical world, who consider her the greatest algebraist of the last hundred years.

Come to think of it the villain in "The algebraist" really seems out of place in an Iain M Banks Sci fi ...

Peirce was primarily an algebraist in his mathematical style; for example, he was enthusiastic for the cause of quaternions in mechanics after their introduction by W.R. Hamilton in the mid 1840s, and of the various traditions in mechanics he showed some favour for the

The problem is of course (as any algebraist sees at once) a case of “simultaneous simple equations” It is, however, easily soluble by arithmetic only; and, when this is the case, I hold that it is bad workmanship to use the more complex method.

If it is all his own, he will make a good algebraist in the time to come.

Luminous members whom I recall with special vividness were the algebraist Richard Brauer, the nonEuclidean geometer, H.S.M. Coxeter, the aforementioned

Busy calculation and restless labor appear at first to be the grand elements of American life; mirth is apparently excluded, as the superfluous members of his equations are eliminated by the algebraist.

To this task, so clearly defined by Fresnel, Cauchy devoted the most powerful efforts of his genius as an algebraist and, thanks to this pupil of Laplace, the Newtonian physics of molecular attraction became an active factor in the propagation of the theory of undulatory optics.
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