- Evariste Galois (1811-1832)
- Born in France.
- He suggested the theory of groups of substitutions, later pursued by others.
- Carl Friedrich Gauss (1777-1855)
- Born in Germany.
- He discovered that a regular 17-sided polygon can be constructed with compass and straightedge.
- He was able as a child to add all the numbers from 1 to 100 in his head by using a simple procedure.
- He provided a proof of the theorem that every integral rational algebraic function can be decomposed into real factors of the first and second degree.
- Sophie Germain (1776-1831)
- Born in France.
- In pure mathematics, she did work in number theory.
- In applied mathematics, she solved problems in acoustics and elasticity.
- Albert Girard (1595-1631)
- Born in France.
- He introduced such things as the use of brackets; a geometrical interpretation of the negative sign; the statement that the number of roots of an algebraic equation is equal to its degrees; and the recognition of imaginary roots.
- Kurt Gödel (1906-1978)
- Born in Czech Republic.
- Using the axiomatized version of the set theory, proved that the continuum hypothesis is logically consistent with the other axioms of the theory.
- Christian Goldbach (1690-1764)
- Born in Kaliningrad.
- His conjecture, which has yet to be proved, states that any even number greater than 3 can be written as the sum of two primes.
- Hermann Günther Grassmann (1809-1877)
- Born in Germany.
- He did research on non-commutative algebra.
- James Gregory (1638-1675)
- Born in Scotland.
- He showed how the areas of the circle and the hyperbola can be obtained in the form of infinite convergent series.
