Often called the language of the universe, mathematics is
fundamental to our understanding of the world and, as such, is vitally
important in a modern society such as ours. Everywhere you look it is
likely mathematics has made an impact, from the faucet in your kitchen
to the satellite that beams your television programs to your home. As
such, great mathematicians are undoubtedly going to rise above the rest
and have their name embedded within history. This list documents some
such people. I have rated them based on contributions and how they
effected mathematics at the time, as well as their lasting effect. I
also suggest one looks deeper into the lives of these men, as they are
truly fascinating people and their discoveries are astonishing – too
much to include here. As always, such lists are highly subjective, and
as such please include your own additions in the comments!

Greek Mathematician Pythagoras is considered by some to be one of the
first great mathematicians. Living around 570 to 495 BC, in modern day
Greece, he is known to have founded the Pythagorean cult, who were noted
by Aristotle to be one of the first groups to actively study and
advance mathematics. He is also commonly credited with the Pythagorean
Theorem within trigonometry. However, some sources doubt that is was him
who constructed the proof (Some attribute it to his students, or
Baudhayana, who lived some 300 years earlier in India). Nonetheless, the
effect of such, as with large portions of fundamental mathematics, is
commonly felt today, with the theorem playing a large part in modern
measurements and technological equipment, as well as being the base of a
large portion of other areas and theorems in mathematics. But, unlike
most ancient theories, it played a bearing on the development of
geometry, as well as opening the door to the study of mathematics as a
worthwhile endeavor. Thus, he could be called the founding father of
modern mathematics.

The only currently living mathematician on this list, Andrew Wiles is
most well known for his proof of Fermat’s Last Theorem: That no
positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n
greater then 2. (If n=2 it is the Pythagoras Formula). Although the
contributions to math are not, perhaps, as grand as other on this list,
he did ‘invent’ large portions of new mathematics for his proof of the
theorem. Besides, his dedication is often admired by most, as he quite
literally shut himself away for 7 years to formulate a solution. When it
was found that the solution contained an error, he returned to solitude
for a further year before the solution was accepted. To put in
perspective how ground breaking and new the math was, it had been said
that you could count the number of mathematicians in the world on one
hand who, at the time, could understand and validate his proof.
Nonetheless, the effects of such are likely to only increase as time
passes (and more and more people can understand it).

8
Isaac Newton and Wilhelm Leibniz

I have placed these two together as they are both often given the
honor of being the ‘inventor’ of modern infinitesimal calculus, and as
such have both made monolithic contributions to the field. To start,
Leibniz is often given the credit for introducing modern standard
notation, notably the integral sign. He made large contributions to the
field of Topology. Whereas all round genius Isaac Newton has, because of
the grand scientific epic Principia, generally become the primary man
hailed by most to be the actual inventor of calculus. Nonetheless, what
can be said is that both men made considerable vast contributions in
their own manner.

7
Leonardo Pisano Blgollo

Blgollo, also known as Leonardo Fibonacci, is perhaps one of the
middle ages greatest mathematicians. Living from 1170 to 1250, he is
best known for introducing the infamous Fibonacci Series to the western
world. Although known to Indian mathematicians since approximately 200
BC, it was, nonetheless, a truly insightful sequence, appearing in
biological systems frequently. In addition, from this Fibonacci also
contributed greatly to the introduction of the Arabic numbering system.
Something he is often forgotten for.

Haven spent a large portion of his childhood within North Africa he
learned the Arabic numbering system, and upon realizing it was far
simpler and more efficient then the bulky Roman numerals, decided to
travel the Arab world learning from the leading mathematicians of the
day. Upon returning to Italy in 1202, he published his Liber Abaci,
whereupon the Arabic numbers were introduced and applied to many world
situations to further advocate their use. As a result of his work the
system was gradually adopted and today he is considered a major player
in the development of modern mathematics.

Computer Scientist and Cryptanalyst Alan Turing is regarded my many,
if not most, to be one of the greatest minds of the 20th Century. Having
worked in the Government Code and Cypher School in Britain during the
second world war, he made significant discoveries and created ground
breaking methods of code breaking that would eventually aid in cracking
the German Enigma Encryptions. Undoubtedly affecting the outcome of the
war, or at least the time-scale.

After the end of the war he invested his time in computing. Having
come up with idea of a computing style machine before the war, he is
considered one of the first true computer scientists. Furthermore, he
wrote a range of brilliant papers on the subject of computing that are
still relevant today, notably on Artificial Intelligence, on which he
developed the Turing test which is still used to evaluate a computers
‘intelligence’. Remarkably, he began in 1948 working with D. G.
Champernowne, an undergraduate acquaintance on a computer chess program
for a machine not yet in existence. He would play the ‘part’ of the
machine in testing such programs.

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.

Living around 300BC, he is considered the Father of Geometry and his
magnum opus: Elements, is one the greatest mathematical works in
history, with its being in use in education up until the 20th century.
Unfortunately, very little is known about his life, and what exists was
written long after his presumed death. Nonetheless, Euclid is credited
with the instruction of the rigorous, logical proof for theorems and
conjectures. Such a framework is still used to this day, and thus,
arguably, he has had the greatest influence of all mathematicians on
this list. Alongside his Elements were five other surviving works,
thought to have been written by him, all generally on the topic of
Geometry or Number theory. There are also another five works that have,
sadly, been lost throughout history.

Bernhard Riemann, born to a poor family in 1826, would rise to become
one of the worlds prominent mathematicians in the 19th Century. The
list of contributions to geometry are large, and he has a wide range of
theorems bearing his name. To name just a few: Riemannian Geometry,
Riemannian Surfaces and the Riemann Integral. However, he is perhaps
most famous (or infamous) for his legendarily difficult Riemann
Hypothesis; an extremely complex problem on the matter of the
distributions of prime numbers. Largely ignored for the first 50 years
following its appearance, due to few other mathematicians actually
understanding his work at the time, it has quickly risen to become one
of the greatest open questions in modern science, baffling and
confounding even the greatest mathematicians. Although progress has been
made, its has been incredibly slow. However, a prize of $1 million has
been offered from the Clay Maths Institute for a proof, and one would
almost undoubtedly receive a Fields medal if under 40 (The Nobel prize
of mathematics). The fallout from such a proof is hypothesized to be
large: Major encryption systems are thought to be breakable with such a
proof, and all that rely on them would collapse. As well as this, a
proof of the hypothesis is expected to use ‘new mathematics’. It would
seem that, even in death, Riemann’s work may still pave the way for new
contributions to the field, just as he did in life.

Child prodigy Gauss, the ‘Prince of Mathematics’, made his first
major discovery whilst still a teenager, and wrote the incredible
Disquisitiones Arithmeticae, his magnum opus, by the time he was 21.
Many know Gauss for his outstanding mental ability – quoted to have
added the numbers 1 to 100 within seconds whilst attending primary
school (with the aid of a clever trick). The local Duke, recognizing his
talent, sent him to Collegium Carolinum before he left for Gottingen
(at the time it was the most prestigious mathematical university in the
world, with many of the best attending). After graduating in 1798 (at
the age of 22), he began to make several important contributions in
major areas of mathematics, most notably number theory (especially on
Prime numbers). He went on to prove the fundamental theorem of algebra,
and introduced the Gaussian gravitational constant in physics, as well
as much more – all this before he was 24! Needless to say, he continued
his work up until his death at the age of 77, and had made major
advances in the field which have echoed down through time.

If Gauss is the Prince, Euler is the King. Living from 1707 to 1783,
he is regarded as the greatest mathematician to have ever walked this
planet. It is said that all mathematical formulas are named after the
next person after Euler to discover them. In his day he was ground
breaking and on par with Einstein in genius. His primary (if that’s
possible) contribution to the field is with the introduction of
mathematical notation including the concept of a function (and how it is
written as f(x)), shorthand trigonometric functions, the ‘e’ for the
base of the natural logarithm (The Euler Constant), the Greek letter
Sigma for summation and the letter ‘/i’ for imaginary units, as well as
the symbol pi for the ratio of a circles circumference to its diameter.
All of which play a huge bearing on modern mathematics, from the every
day to the incredibly complex.

As well as this, he also solved the Seven Bridges of Koenigsberg
problem in graph theory, found the Euler Characteristic for connecting
the number of vertices, edges and faces of an object, and (dis)proved
many well known theories, too many to list. Furthermore, he continued to
develop calculus, topology, number theory, analysis and graph theory as
well as much, much more – and ultimately he paved the way for modern
mathematics and all its revelations. It is probably no coincidence that
industry and technological developments rapidly increased around this
time.