10. Pythagoras

Since at least the first century BC, Pythagoras has
commonly been given credit for discovering the Pythagorean
theorem ,a theorem in geometry that states that
"in a right-angled triangle the square of the hypotenuse is
equal to the sum of the squares of the two other
sides".

9. Andrew Wiles

Wiles was born on 11 April 1953 in Cambridge , England,
the son of Maurice Frank Wiles (1923–2005), the Regius
Professor of Divinity at the University of Oxford , and
Patricia Wiles (née Mowll). His father worked as the
Chaplain at Ridley Hall, Cambridge , for the years 1952–55.
Wiles attended King's College School, Cambridge, and The
Leys School, Cambridge .

Wiles states that he came across Fermat's Last Theorem
on his way home from school when he was 10 years old.
He stopped at his local library where he found a book about
the theorem. Fascinated by the existence of a theorem
that was so easy to state that he, a ten-year-old, could
understand it, but that no one had proven, he decided to be
the first person to prove it.

However, he soon realised that
his knowledge was too limited, so he abandoned his
childhood dream, until it was brought back to his attention
at the age of 33 by Ken Ribet 's 1986 proof of the epsilon
Fermat's famous equation.

8. Isaac Newton and Wilhelm Leibniz

Sir Isaac Newton and Gottfried Wilhelm Leibniz are two of
the most supreme intellects of the 17th century. They are
both considered to be the inventors of Calculus. However,
after a terrible dispute, Sir Isaac Newton took most of the
credit.

Gottfried Wilhelm Leibniz (1646-1716) was a
German philosopher, mathematician, and statesman born
in the country of Leipzig. He received his education at the
universities of Leipzig, Jena, and Altdorf. He received a
doctorate in law. He devoted much of his time to the
principle studies of mathematics, science, and philosophy.

Leibniz’s contribution in mathematics was in the year
1675, when he discovered the fundamental principles of
infinitesimal calculus. He arrived at this discovery
independently at the same time along with the English
scientist Sir Isaac Newton in 1666.

However, Leibniz’s
system was published in 1684, three years before Newton
published his. Also at this time Leibniz’s method of
notation, known as mathematical symbols, were adopted
universally.

7. Alan Turing

Turing was an English computer scientist,
mathematician, logician , cryptanalyst, philosopher, and
theoretical biologist. He was highly influential in the
development of theoretical computer science, providing a
formalisation of the concepts of algorithm and computation
with the Turing machine, which can be considered a model
of a general purpose computer.

Turing is widely considered to be the father of theoretical computer science and artificial intelligence .

6. Leonardo Pisano Bigollo

Leonardo popularized the Hindu–Arabic numeral system in
the Western World primarily through his composition in
1202 of Liber Abaci (Book of Calculation). He also
introduced Europe to the sequence of Fibonacci numbers,
which he used as an example in Liber Abaci.

5. René Descartes

French Philosopher, Physicist and Mathematician, Rene
Descartes is best known for his ‘Cogito Ergo Sum’
philosophy. Despite this, the Frenchman, who lived 1596 to
1650, made ground breaking contributions to mathematics.
Alongside Newton and Leibniz, Descartes helped provide the
foundations of modern calculus (which Newton and Leibniz
later built upon), which in itself had great bearing on the
modern day field.

Alongside this, and perhaps more familiar
to the reader, is his development of Cartesian Geometry,
known to most as the standard graph (Square grid lines, x
and y axis, etc.) and its use of algebra to describe the
various locations on such. Before this most geometers used
plain paper (or another material or surface) to preform their
art.

Previously, such distances had to be measured literally,
or scaled. With the introduction of Cartesian Geometry this
changed dramatically, points could now be expressed as
points on a graph, and as such, graphs could be drawn to
any scale, also these points did not necessarily have to be
numbers.

The final contribution to the field was his
introduction of superscripts within algebra to express
powers. And thus, like many others in this list, contributed
to the development of modern mathematical notation.

4. Euclid of Alexandria

Euclid was a Greek mathematician , often
referred to as the "founder of geometry" or the "father of
geometry". He was active in Alexandria during the reign of
Ptolemy I (323–283 BC).

His Elements is one of the most
influential works in the history of mathematics , serving as
the main textbook for teaching mathematics (especially
geometry ) from the time of its publication until the late 19th
or early 20th century.

In the Elements, Euclid
deduced the theorems of what is now called Euclidean
geometry from a small set of axioms. Euclid also wrote
works on perspective, conic sections , spherical geometry,
number theory, and rigor.

3. G. F. Bernhard Riemann

Riemann was a German
mathematician who made contributions to analysis, number
theory , and differential geometry. In the field of real analysis,
he is mostly known for the first rigorous formulation of the
integral, the Riemann integral, and his work on Fourier
series.

His contributions to complex analysis include most
notably the introduction of Riemann surfaces , breaking new
ground in a natural, geometric treatment of complex
analysis.

His famous 1859 paper on the prime-counting
function , containing the original statement of the Riemann
hypothesis , is regarded as one of the most influential papers
in analytic number theory. Through his pioneering
contributions to differential geometry ,

Riemann laid the
foundations of the mathematics of general relativity

2. Carl Friedrich Gauss

Carl was a German mathematician
and physicist who made significant contributions to many
fields, including algebra, analysis , astronomy , differential
geometry , electrostatics , geodesy , geophysics, magnetic
fields , matrix theory, mechanics , number theory , optics and
statistics.
Sometimes referred to as the Princeps mathematicorum
( Latin for "the foremost of mathematicians") and "the
greatest mathematician since antiquity",

exceptional influence in many fields of mathematics and
science, and is ranked among history's most influential
mathematicians.

1. Leonhard Euler

Leonhard was a Swiss
mathematician , physicist , astronomer , logician and
engineer , who made important and influential discoveries in
many branches of mathematics, such as infinitesimal
calculus and graph theory, while also making pioneering
contributions to several branches such as topology and
analytic number theory.

He also introduced much of the
modern mathematical terminology and notation , particularly
for mathematical analysis , such as the notion of a
mathematical function.

He is well known for his work in
mechanics , fluid dynamics , optics , astronomy , and music
theory. Euler was one of the most eminent mathematicians of the
18th century and is held to be one of the greatest in history.

He is also widely considered to be the most prolific
mathematician of all time. His collected works fill 60 to 80
quarto volumes, more than anybody in the field.