Mathematics often referred to as the language of the universe, is crucial to our world understanding and is therefore vital in a modern society like ourselves. Mathematics, from the hack in your kitchen to the satellite, from your televisions to your home, will affect everywhere you look. Therefore, great mathematicians will unquestionably rise above the rest and have their names embedded in history.

Few of them are documented in this list. I rated them based on their contributions and how they performed and their lasting effect in mathematics at that time. I rated them based on their contributions and how they performed and their lasting impact in mathematics at that time. I also suggest that you examine the lives of these men more deeply, as their discoveries and fascinating people are amazing – too far to include here. These lists are, as always, highly subjective.

Table of Contents

#### Here’s the list of Top 10 Greatest Mathematicians.

#### 10. Pythagoras of Samos

Greek Mathematician Pythagoras is considered by some to be one of the first extraordinary mathematicians. Living around 570 to 495 BC, in Greece, he is acknowledged to have established the Pythagorean church, which Aristotle marked as the first groups to study and promote mathematics actively. He is also usually attributed with the Pythagorean Theorem within trigonometry.

Nevertheless, some experts question that is was him who constructed the grounds (Some credit it to his pupils, or Baudhayana, who belongs to India).

Nonetheless, the influence of this, as with large portions of fundamental mathematics, is widely felt today, with the theorem playing a major part in modern measurements and technical devices, as well as being the foundation of a large portion of other fields and theorems of mathematics. Yet, unlike most ancient theories, it played a role in geometry development as well as opening the door as a worthwhile pursuit to the study of mathematics. He may thus be considered the founding father of modern mathematics.

#### 9. Isaac Newton and Wilhelm Leibniz

I put these two together because both are often given the glory of being the ‘inventor’ of contemporary infinitesimal calculus, and therefore each has made monolithic contributions to the development.

To commence with, Leibniz often gets the credit to introduce modern standard notation, prominently the integral sign. He made great benefactions to topology field.

Whereas all-round genius Isaac Newton has become the primary man hailed by most to be the actual inventor of calculus, due to the great scientific epic Principia. Nevertheless, what can be said is that in their way, both men made significant huge contributions.

#### 8. Leonardo Pisano Blgollo

Blgollo, also known as Leonardo Fibonacci, may well be one of the greatest mathematicians of the Middle Ages. Living from 1170 to 1250, he is best known for introduction to the western world of the infamous Fibonacci Series. Though known to Indian mathematicians since about 200 BC, it was, nonetheless, an insightful series that frequently appears in biological systems. Moreover, from this Fibonacci also considerably contributed to the introduction of the Arabic numbering system. Something he is regularly overlooked for.

He spent a good part of his childhood in North Africa studying the Arabic numerical system, so when he discovered it was both easier and more effective than the cumbersome Roman numerals, he wanted to visit the Arab world studying from the leading mathematicians of the day. On his return to Italy in 1202, he wrote his Liber Abaci, which incorporated Arabic numbers and extended to other world conditions to further promote their use. As a consequence of his research, the method was slowly accepted and today he is considered to be a significant player in the growth of modern mathematics.

#### 7. Alan Turing

Computer Scientist and Cryptanalyst Alan Turing found by many, if not most, to be one of the best minds of the 20th century. Having served in the British Government Code and Cypher School during the Second World War, he made significant advances and created innovative code-breaking techniques that would ultimately help solve the German Enigma Encryptions. Doubtlessly influencing the result of the battle, or at least the period.

He dedicated his time in computing after the end of the world war. Having come up with a concept of a computer-style system before the war, he is considered one of the first real computer scientists. Also, he published a variety of excellent articles on the topic of computation that are still important today, especially on Artificial Intelligence, in which he created the Turing test, which is now used to determine the intellect of computers. Remarkably, in 1948 he started working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in permanence. He would play the ‘role’ of the machine in examining such programs.

#### 6. René Descartes

Rene Descartes, the French philosopher, physicist, and mathematician is best known for his philosophy of “Cogito Ergo Sum.” Notwithstanding, The Frenchman, who lived from 1596 to 1650, made groundbreaking contributions to mathematics. Alongside Newton and Leibniz, Descartes helped to establish the groundwork for modern calculus (built on later by Newton and Leibniz), which in itself had a great significance on the modern-day domain.

In addition to this, and perhaps more familiar to the reader, is his development of Cartesian Geometry, most commonly known as the standard graph (Square grid lines, x-axis and y-axis, etc.) and his use of algebra to describe the different locations on it. Until this, most geometers employed plain paper (or different material or surface) to perform their work. Earlier, such distances had to be measured precisely or scaled.

Since the advent of Cartesian Geometry, things shifted significantly, points could now be represented as points on a line and, as such, maps could be constructed of any dimension, so such points did not always have to be numbers. The last contribution to the area was his implementation of superscripts for describing powers within algebra. And hence, like many others in this list, contributed to the advancement of modern mathematical notation.

#### 5. Srinivasa Ramanujan

Srinivasa Ramanujan (1887-1920) was an Indian mathematician who made significant and unique contributions to many mathematical areas, number theory, complex analysis, continued fractions and infinite series. He’s been “discovered” by G. H. Hardy, J. E. Littlewood, two remarkable mathematicians at Cambridge, shared an exceptionally productive time of cooperation between 1914 and 1919.

Ramanujan’s intellect was known from the sequence of letters which he submitted to the Mathematics of Cambridge (1913) by Hardy, who was a prominent mathematician by himself. Unlike much of his works, the letters included a dizzying collection of unprecedented and complex results, stated without much explanation or evidence. The contradiction between Hardy, who was above all worried with mathematical precision and sincerity, and Ramanujan, whose writing was challenging to read and peppered with mistakes but bespoke an almost miraculous insight, provided a rich partnership.

Ramanujan ‘s writings have been studied comprehensively since his death (many in his esteemed notebooks). Some of his claims and conjectures have contributed to the formulation of new fields of study. Many of his speculations are found credible but untested.

#### 4. Euclid

Born about 300BC, he is called the founder of Geometry and his chef-d’oeuvre: Elements remains one of the best scientific works of history to be included in the curriculum before the 20th century. Unfortunately, his story is not well known, and what remains was published long after his presumed demise. Nevertheless, Euclid is attributed to the teaching of a meticulous, rational proof of theorems and conjectures.

Such a framework remains in use until now, and thus, arguably, he has had the greatest influence of all mathematicians on this list. Five other surviving works alongside his Elements were thought to have been written by him, all usually on the subject of Geometry or Number theory. There are also five more works which, unfortunately, have been lost in history.

#### 3. G. F. Bernhard Riemann

Bernhard Riemann, born in an underprivileged family in 1826, would ascend to become one of the worlds leading mathematicians in the 19th Century. The list of contributions to geometry are huge, and he has a wide array of theorems that bear his name. Riemannian Geometry, Riemannian Surfaces and the Riemann Integral, to name only a few: He is probably most renowned (or infamous) for his legendarily complicated Riemann hypothesis, though; an incredibly complex problem in the matter of prime number distributions.

For the first 50 years after its appearance, largely ignored, because few other mathematicians understood his work at the time, it has quickly risen to become one of the biggest open questions in modern science, confusing even the greatest mathematicians. Albeit progress has been made, it has been astonishingly slow. However, the Clay Maths Institute has offered a prize of $1 million for proof, and one would almost undoubtedly receive a Fields medal if under 40 (Mathematics Nobel Prize).

The fallout from such a proof is hypothesized to be large: with such proof, major encryption systems are thought to be breachable, and everything that relies on them would collapse. Besides this, it is anticipated that a proof of the hypothesis will use ‘new mathematics.’ It would appear that Riemann ‘s work may indeed open the path for new contributions to the field, even in death, just as he did in life.

#### 2. Carl Friedrich Gauss

Young genius Carl Friedrich Gauss, the ‘Prince of Mathematics,’ made his first significant breakthrough as a teenager and published his piece de resistance, the brilliant Disquisitions Arithmeticae, at around 21. Many know Gauss for his exceptional mental ability – cited to have added the numbers 1 to 100 within seconds while attending primary school (with the help of an ingenious trick).

The local Duke, recognising his ability, sent him to Collegium Carolinum before he went for Gottingen (at that time the world’s most prestigious mathematical university, with many of the best students). After graduating at the age of 22 in 1798, he commenced making numerous contributions in significant fields of mathematics, most prominently number theory (notably on Prime numbers).

He proved the fundamental theorem of algebra, and brought in the Gaussian gravitational constant in physics, besides much more – before he was 24! Admittedly, until his death, at the age of 77, he continued work in this field and made significant progress that echoed over the years.

#### 1. Leonhard Euler

Euler was the greatest mathematician ever to grace this earth from 1707 to 1783. All mathematical formulas are said to be named after Euler’s next person to discover them. He was groundbreaking in his day and genius equal to Einstein.

His main (if possible) contribution to the area is the invention of mathematical terminology, namely the definition of function (and how it is represented as f(x)), the simplified 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 the imaginary units, as well as the symbol pi for the ratio of the equation. All of which play a major role in contemporary mathematics, from the extremely abstract to the regular.

Along with this, he also solved the problem of the Seven Bridges of Koenigsberg in graph theory, found the Euler Characteristic to link the number of vertices, edges and faces of the object, and (dis)proved many well-known theories, too many to list. Also, he helped to establish calculus, topology, number theory, classification and graph theory as well as much, much more–and eventually led the way for modern mathematics with all its discoveries. It is certainly no coincidence that industry and technological advances have grown exponentially during this time. He is first in the list of top 10 greatest mathematicians.