**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.