Sylvester to twórca szeregu terminów naukowych, zwłaszcza z algebry. Wśród nich są: graf (ang. graph) Jeff Miller, graph [w:] Earliest Known Uses of Some of the Words of Mathematics (G) , MacTutor History of Mathematics archive, University of St Andrews, mathshistory.st-andrews.ac.uk [dostęp 2022-02-18].; wyróżnik (ang. discriminant) Jeff Miller, discriminant [w:] Earliest Known Uses of Some of the Words of Mathematics (D) , MacTutor History of Mathematics archive, University of St Andrews, mathshistory.st-andrews.ac.uk [dostęp 2022-02-18]., macierz (ang. matrix) Jeff Miller, Matrix [w:] Earliest Known Uses of Some of the Words of Mathematics (M) , MacTutor History of Mathematics archive, University of St Andrews, mathshistory.st-andrews.ac.uk [dostęp 2022-02-18]., jakobian (ang. Jacobian) Jeff Miller, Jacobian [w:] Earliest Known Uses of Some of the Words of Mathematics (J) , MacTutor History of Mathematics archive, University of St Andrews, mathshistory.st-andrews.ac.uk [dostęp 2022-02-18]., hesjan (ang. Hessian) Jeff Miller, Hessian [w:] Earliest Known Uses of Some of the Words of Mathematics (H) , MacTutor History of Mathematics archive, University of St Andrews, mathshistory.st-andrews.ac.uk [dostęp 2022-02-18]., kowariancja (ang.