A Brief History & Development of Geometry

Greek mathematician who studied conic sections.

Greek mathematician, often referred to as the "Father of Geometry." Best known for his book "The Elements" that collected the theorems of previous mathematicians. He also had works on conic sections, spherical geometry, and number theory.

Greek Mathematician who analyzed the area of a circle and discovered how to calculate volumes and surface areas of spheres and cylinders.A famous result that is inscribed on his tomb stone is that "the volume of a sphere is two/thirds the volume of its circumscribed cylinders."

Greek mathematician who discovered the Conchoid Curve, which can be used to trisect angles.

Greek mathematician, geographer, astronomer, and historian. His major accomplishment was his creation of a sieve that determines prime numbers up to any given limit.

Greek mathematician known as 'The Great Geometer'. Famous book, Conics that introduced terms such as ellipse, parabola, and hyperbola.

Greek astronomer, geographer,and mathematician considered to be one of the greatest astronomers if his time. He made advances in geography and math, specifically trigonometry.One of his major contribution, included the division of a circle into 360 degrees and the creation of one of the first trigonometric tables for solving triangles.

Greek mathematician, scientist, inventor and engineer. The vending machine was one of his ideas mentioned in his book. He was also the first to make a machine that operated with a windwheel. To geometry he approximated square roots and formulated the area of a triangle.
A = √(s(s−a)(s−b)(s−c))

Greek mathematician and astronomer who first defined a spherical triangle. His most important work was on the geometry of the sphere.

Greek mathematician known for Papus's Theorem in projective geometry. "Projective geometry is the branch of geometry dealing with the properties and invariants of geometric figures under projection from a point."

First woman to make a substantial contribution to the development of math. Her father was a professor at a University. She would later teach "Arithmetica". She wrote a commentary on Apllonius' "Conics".

A Greek philosopher who wrote a commentary on The Elements where he commented on attempting to have a proof to the 5th postulate using the other four.

Chinese mathematician. His greatest accomplishment was to calculate the diameter of a sphere of a given volume.

Brahmagupta was the foremost Indian mathematician of his time. He made advances in astronomy and most importantly in number systems including algorithms for square roots and the solution of quadratic equations.

An Iraqi Muslim mathematician, physician, astronomer, and translator who lived in Baghdad. He made important discoveries in algebra, geometry, and astronomy. In math, he discoverd an equation for determining amicable numbers. He also wrote on the theory of numbers, and extended their use to describe the ratios between geometrical quantities. He is also known for having calculated the solution to a chessboard problem involving an exponential series.

Persian mathematician and astronomer who worked in Baghdad. He made important innovations in spherical trignometry. He was the first to use negative numbers in an Islamic text. He is also credited with compiling the tables of sines and tangents at 15 degree intervals. He also introduced the secant and cosecant functions.He established several trigonometric identities in their modern form.He discovered the law of sines for spherical triangles.

Italian mathematician considered by some "the most talented western mathematician of the Middle Ages." He is best known for the spreading of the Hindu-Arabic numeral system in Europe, and for the Fibonacci numbers.

German mathematician, astronomer,and astrologer. A key figure in the 17th century scientific revolution, best known for his laws of planetary motion. He published the first description of the hexagonal symmetry of snowflakes, what would later become known as the Kepler conjecture. He was one of the pioneers of the mathematical applications of infinitesimals.

French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' famous 'perspective theorem' - that when two triangles are in perspective the meets of corresponding sides are collinear.

French philosopher, writer, and mathematician. Best known for the Cartesian coordinate system. He is credited as the father of analytical geometry.

French lawyer and and mathematician who is given credit for early developments that led to calculus. He is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines. He made notable contributions to analytic geometry, probability, and optics. Best known for Fermat's Last Theorem.

French mathematician, physicist, inventor, writer, and philosopher. Known for Pascal's triangle.

German mathematician and philosopher. He developed calculus independently of Newton. Leibniz was the first to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular.

Italian priest, philosopher, and mathematician. He is known for his work in non-Euclidean geometry. He wanted to develop a proof for Euclid's 5th postulate by contradiction, but failed.

Swiss mathematician and physicist who made important discoveries in calculus and graph theory. He introduced the concept of a function and was the fist to write f(x) to denote the function f applied to the argument x. He also introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm, the Greek letter Σ for summations and the letter i to denote the imaginary unit.The use of the Greek letter pi to denote the ratio of a circle's circumference was also popularized by Euler.

French mathematician, the inventor of descriptive geometry and the father of differential geometry.

Scottish scientist and mathematician, and a professor of philosophy. He wrote a famous commentary on Euclid's 5th postulate which he proposed replacing it by an axiom, "Given a line and a point not on the line, it is possible to draw exactly one line through the given point parallel to the line".

Gauss developed the Gauss method for adding large amounts of consecutive numbers when he was six. However, his most important creation is that of non-Euclidean geometry.

French mathematician whose most notable work was in projective geometry, in particular, his work on Feuerbach's theorem. He also made discoveries about projective harmonic conjugates; among these were the poles and polar lines associated with conic sections. These discoveries led to the principle of duality, and also aided in the development of complex numbers and projective geometry.

Russian mathematician and geometer, known for his work on hyperbolic geometry, also known as Lobachevskian geometry. He was the founder of non-Euclidean geometry, which he developed independently of János Bolyai and Carl Gauss.

Hungarian mathematician, one of the founders of non-Euclidean geometry. He also developed a geometric concept of complex numbers as ordered pairs of real numbers.

German polymath who is remembered for his development of the basic calculus for vectors. Grassmann also initiated the representation of subspaces of a given space by coordinates; this leads to a point mapping of an algebraic manifold, called the Grassmannian

British mathematician. He defined the concept of a group-as a set with a binary operation satisfying certain laws. In group theory, Cayley's theorem,states that every group G is isomorphic to a subgroup of the symmetric group acting on G.

Riemann was one of the foremost geometers in the development of Non-Euclidean Geometry. He also made contributions to analysis, number theory, and differential geometry.

German mathematician known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. At the Erlangen Program Klein proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory.

German mathematician who developed many ideas in many areas, such as invariant theory and the axiomatization of geometry. Hilbert is known as one of the founders of proof theory and mathematical logic.

Swedish mathematician who is most famous for the Koch snowflake, one of the earliest fractal curves to be described.

German physicist who made many contributions to the field of calculus and geometry. Einstein contributed many equations to geometry and calculus, ten of them known as Einstein Field Equations.

American mathematician, geometer and topologist. His work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905. There is an award named after him granted by the American Mathematical Society. He made important contributions to differential geometry and the early development of topology.

A Dutch graphic artist. He is known for intertwining art and mathematics. In his art he used repeating patterns of interlocking motifs, tessellations of the Euclidean and the hyperbolic plane and his drawings represented impossible figures.

Polish mathematician of Jewish origin known for his work in functional analysis, partial differential equations, and mathematical physics. Most of his work is in the field of functional analysis. He is best known for the Schauder fixed point theorem which is a major tool to prove the existence of solutions in various problems, the Schauder bases, and the Leray-Schauder principle.

French mathematician known for his foundational work was discovering the connections between algebraic geometry and number theory. This began his doctoral work that led to the Mordell-Weil theorem. Another accomplishment was Weil conjectures.

French mathematician who worked on algebraic topology and differential equations. Together with Juliussz Schauder, discovered a topological invarient, known as the Leray-Schauder degree. His main work in toplogy was done with he was a prisoner of war at Edelbach, Austria from 1940-1945. He hid the fact that he was an expert in differential equations, because he feared that would led him to be asked to do war work.

British-born Canadian geometer. He is known as the "Man who saved Geometry". He made contributions of major importance in the theory of Coxeter groups which gave rise to tesselations, non-euclidean geometry, group theory and combinatorics.

American mathematician and meteorologist. He is a pioneer of chaos theory. He introduced the butterfly effect.

An American mathematician known for the first general results on the Weil conjectures.

Polish-born, French and American mathematician who is largely responsible for the present interest in fractal geometry. He showed how fractals can occur in many different places in both math and elsewhere. He discovered the Mandelbrot set, of intricate, never-ending fractal shapes.

French mathematician. Serre applied spectral sequences to the study of the relations between the homology groups of fibre, total space and base space in a fibration. This allowed him to discover fundamental connections between the homology groups and homotopy groups of a space and to prove important results on the homotopy groups of spheres. His theorem led to increased progress in algebraic topology and homological algebra.

French mathematician, born in Germany. He is the central figure behind the creation of the modern theory of algebraic geometry. In algebraic geometry, he worked on sheaf theory and homological algebra, where he introduced Abelian categories.

American mathematician known for contributions to algebraic geometry.

German mathematician known for his work in number theory. His Frey curve, was central to Wiles' proof of Fermat's Last Theorem. His research is applied to coding theory and cryptography.

American mathematician who paved the way towards Andrew Wiles's proof of Fermat's last theorem. He proved the epsilon conjecture by Jean-Pierre Serre was true and the Herbrand-Ribel theorem helped proof Fermat's Last Theorem.

British mathematician who specializes in number theory. He is most known for proving Fermat's Last Theorem.

was a Polish mathematician. He was known for outstanding contributions to set theory, number theory, theory of functions and topology. hree well-known fractals are named after him (the Sierpinski triangle, the Sierpinski carpet, and the Sierpinski curve), as are Sierpinski numbers and the associated Sierpiński problem.

She "believes that Mathematics is the most elegant branch of learning in which I could engage and I intend to pass that attitude to my students."