At age 14 he moved to Constantinople to study painting. In 1844 his schooling was in Euclidean geometry, he studied with Tahir Pasha. He graduated in 1860. Upon the death of his teacher, Tevfik took over his classes and began to instruct students in algebra, analytic geometry, calculus, mechanics and astronomy. Tevfik was sent to Paris and became associated with the Young Ottomans there: Tevfik's expertise in small arms led to assignments to the United States: In 1878 he taught military engineering in Constantinople, and published Linear Algebra in 1882. He continued in diplomatic and military service: According to Sinan Kuneralp, Tawfik was "A mathematician of great talent, he assembled during his long stay a valuable library of scientific works and regularly lectured on a variety of subjects in clubs and institutes on the East coast". Tevfik was also offended by what he considered to be excess liberty and license among the lower classes in the United States.
Linear Algebra
In Constantinople in 1882 Tevfik published Linear Algebra with the presses of A. Y. Boyajain. He begins with the concept of equipollence: The book has five chapters and an appendix "Complex quantities and quaternions" in 68 pages with contents listed on page 69. Tevfik's book refers on page 11 to Introduction to Quaternions by Kelland and Tait which came out with a second edition in 1882. But complex numbers and quaternions are missing. Rather a three-dimensional treatment of geometry uses vectors extensively. A space algebra is introduced with Products are given: : Chapter three treats the cross product of vectors, calling it the "special perpendicular" and writing for the cross product of α and β. The special perpendicular is employed to compute the volume of a pyramid, an equation on skew lines that reduces to zero when they are coplanar, a property of a spherical triangle, and the coincidence of the perpendiculars in a tetrahedron. Chapter four describes equations of geometric figures: line, plane, circle, sphere. The definition of a conic section is taken from Kelland and Tait: "the locus of a point which move so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line." Ellipse, hyperbola, and parabola are then illustrated. Chapter five, "Some additional applications" introduces the instantaneous velocity of a point moving along a curve as a limit, a reference to calculus. The second rate of change is related to the reciprocal of the radius of curvature of the curve
