Top 20 Most Famous Mathematicians in the World

Isaac Newton is not only a mathematician but also a physicist, philosopher, astronomer,... a luminary of humanity. In mathematics, he, along with Gottfried Leibniz, researched and developed differential and integral calculus. He also introduced Newton's general binomial theorem.

Differential and integral calculus were created to address the 4 scientific problems of the 17th century:

• Problem 1: Solve physics problems; objects move according to a formula as a function of time.
• Problem 2: Find the tangent of a curve. This problem belongs to geometry, but it has important applications in science.
• Problem 3: Problem of finding the maximum and minimum values of a function
• Problem 4: Find the length of a curve, such as the distance traveled by a planet in a certain period; the area of the region bounded by curves; the volume of solids bounded by surfaces,…

Isaac Newton was born into a poor farming family in Lincolnshire, United Kingdom. Thanks to his passion for scientific numbers, he has produced valuable scientific theories and research for all of humanity up to now and the future, such as Newton's laws, the law of universal gravitation,...

Fibonacci was a brilliant Italian mathematician. Although not an inventor, he played a crucial role in popularizing the Hindu-Arabic numeral system throughout Europe. His eponymous Fibonacci sequence is still widely used today.

Applications of the Hindu-Arabic numeral system: Apply it to bookkeeping, unit conversion, length measurement, profit calculation, currency exchange, and other applications.

• A random coincidence where the Fibonacci sequence matches the number of petals in most flowers. In the sequence: 3, 5, 8, 13, 21, 34, 55, or 89. Lilies have 3 petals, buttercups have 5 petals, goldenrods usually have 8 petals, daisies have 13 petals, asters have 21 petals, sunflowers have 34, or 55, or 89 petals.
• The Fibonacci sequence is considered the golden ratio for the standard of beauty in art, architecture, and finance.

Blaise Pascal was a talented French mathematician, physicist, inventor, and Christian philosopher. He was the first to research and invent a mechanical calculator known as the Pascaline. In 1653, he wrote Traité du triangle arithmétique (Treatise on the Arithmetical Triangle) describing a pattern known as Pascal's Triangle. Despite passing away at the age of 39 due to frail health, he left behind a rich legacy and contributions to the global field of mathematics.

Applications of the Pascal programming language in real life:

• Application programming, software development,...
• Programming motion for robots.

• Foundation for deriving 7 memorable mathematical identities.
• Used to prove Newton's binomial theorem.
• Applied in algorithms in the field of computer science.

Greece, the land of convergence for some of the most brilliant minds in the world, presents Pythagoras, a notable figure. Pythagoras was a Greek philosopher and the founder of the Pythagoreanism religious movement. He is often remembered as a great scientist and mathematician. In Vietnamese, his name is commonly transliterated from French as Pi-ta-go.

Pythagoras, a renowned Greek mathematician, philosopher, and scientist of ancient times. His name and fundamental mathematical theorems are ever-present in textbooks. With the famous theorem bearing his name, 'In a right-angled triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two sides,' he is celebrated worldwide.

Applications of the Pythagorean Theorem to solve geometric problems:

• Finding the sides of a right-angled triangle.
• Calculating the distance between two points in the X-Y plane.
  

Thales of Miletus, or in Vietnamese pronunciation, Ta-lét, was a philosopher and mathematician from ancient Greece who lived before Socrates and led the seven sages of Greece. He is also considered one of the first philosophers in ancient Greek philosophy, known as the 'father of science.'

Thales was a mathematician and one of the seven famous philosophers of ancient Greece. He made significant contributions to mathematics by inventing a mathematical theorem named after himself, known as Thales' theorem.

Applications of Thales' theorem in daily life:

• Measuring the height of the Great Pyramid of Khufu.
• Measuring distances when direct measurement is not feasible: distance across a river, height of a mountain,...

Andrew Wiles is a British mathematician, renowned for being the first to prove Fermat's Last Theorem. His exact birth and death years are still uncertain. Andrew John Wiles is a British mathematician, known as the first person to prove Fermat's Last Theorem.

Wiles was introduced to Fermat's Last Theorem when he was just 10 years old. In the following years, he attempted to prove the theorem using traditional methods found in textbooks. However, during his graduate studies, he shifted his focus to the study of elliptic curves under the guidance of Professor John Coates.

During his time as a research student at Clare College, Cambridge, Wiles also served as an assistant professor at Harvard University. By 1980, when he earned his Ph.D., Wiles spent some time working in Bonn before coming to the United States. In 1981, he became a professor at Princeton University.

Alan Turing was a British mathematician, cryptanalyst, and logician, often hailed as the father of computer science. Turing's Test is one of the contributions he left for humanity.

Alan Mathison Turing was a British mathematician, logician, and cryptanalyst widely regarded as the father of computer science. Turing's Test is one of his contributions to artificial intelligence: this challenge raises the question of whether machines can achieve consciousness and thinking abilities.

Applications of Turing's Test:

• Inspiration for scientists researching supercomputers and artificial intelligence in the future.
• In 1952, he published a paper on this issue, titled 'The Chemical Basis of Morphogenesis.' The focal point that drew his attention was studying the arrangement of leaves in Fibonacci sequences, the existence of Fibonacci sequences in plant structures. He used reaction-diffusion equations, which are now at the core of the field of pattern formation.

Euclid, sometimes known as Euclid of Alexandria, lived in the 3rd century BCE and was an eminent ancient Greek mathematician. He is famously called the 'father of geometry.' Most of the geometry knowledge taught in basic high school is systematically and precisely covered in Euclid's 13-book series known as 'Elements,' which has been the most influential mathematical work since its publication in the late 19th and early 20th centuries.

By selectively choosing, distinguishing existing geometric knowledge, supplementing, abstracting, and organizing them into a coherent system, using properties beforehand to deduce subsequent properties, Euclid's extensive 'Elements' laid the foundation for both geometry and the entire ancient mathematics. The series consists of 13 books: the first six cover plane geometry, the next three present number theory in geometric form, the tenth book contains constructions related to algebra, and the final three books discuss solid geometry.

In the first book, Euclid presents five postulates: Through any two points, a straight line can be drawn, A straight line can be extended infinitely, With any center and radius, a circle can always be drawn, All right angles are equal, If two lines form angles with a third line, and the sum of the inner angles is less than 180 degrees, they will intersect on that side. Additionally, there are five common notions: Things that are equal to the same thing are equal to each other, If equals are added to equals, the wholes are equal, If equals are subtracted from equals, the remainders are equal, Things that coincide with one another are equal, The whole is greater than the part.

With those postulates and common notions, Euclid rigorously proved all the geometric properties.

René Descartes, a French mathematician, scientist, and philosopher, is often considered the father of modern philosophy. Born in 1596 and passing away in 1650, Descartes made significant contributions to mathematics. He systematized analytic geometry, described exponents, and developed theories on equations. He pioneered modern mathematics by introducing variables x, y, z as unknowns.

Descartes' most crucial contribution to mathematics was the systematic formulation of analytic geometry, with the Cartesian coordinate system named after him. He was the first mathematician to classify curves based on the properties of the equations defining them. He also contributed to the theory of equations. Descartes was the first to use the last letters of the alphabet (x, y, z) to represent unknowns and the first letters for known values. He created a system of symbols to represent the exponentiation of numbers (e.g., x² in expressions). Additionally, he established the method, known as Descartes' rule of signs, to determine the number of positive and negative roots of any algebraic equation.

Among all great mathematicians, Cantor is the epitome of the intertwining of mathematical genius and mental illness. As a renowned mathematician and the father of set theory, the foundation of this discipline, Cantor initiated a mathematical revolution, shaking the very core of the subject with a simple question: 'How large is infinity?'

Before Cantor, the concept of infinity was not fully understood or systematized, giving rise to numerous paradoxes and confusion. Theologians often used the idea of infinity in metaphorical expressions. Cantor was the first to provide a rational, precise, and systematic explanation of this concept. However, his contributions terrified and criticized many mathematicians who perceived mathematics as a solid foundation, while Cantor's ideas seemed vague, counterintuitive, and filled with paradoxes. These elements posed a threat to the certainty of mathematics.

In 1894, Cantor relentlessly worked on the 'Continuum Hypothesis' for over two years. During this time, his life took a downturn. In May of that year, he suffered a severe mental breakdown and fell into depression. Ultimately, he was admitted to Nervenklinik, a psychiatric hospital in Halle.

Carl Friedrich Gauss, the talented German mathematician, is hailed as the prince of mathematicians. His contributions span various mathematical domains, including number theory, analysis, and differential geometry. Gauss is renowned for proving that every regular polygon with a Fermat prime number of sides can be constructed with a compass and straightedge.

Carl Friedrich Gauss, a brilliant German mathematician and scientist, made significant contributions to various scientific fields such as number theory, analysis, differential geometry, geodesy, magnetism, electricity, astronomy, and optics.

Known as the 'prince of mathematicians,' Gauss, with profound influence on the development of mathematics and science, is often ranked alongside Leonhard Euler, Isaac Newton, and Archimedes as one of the greatest mathematicians in history. Gauss's vital contributions include advancements in algebra and number theory. Additionally, he introduced the Gauss constant, conducted research on magnetism, and is honored with the naming of the unit of magnetic flux after him.

Considered the most prolific mathematician of all time, Euler published nearly 900 books. Despite losing his sight in his late 50s, his capabilities across various domains only increased. Euler introduced a famous mathematical expression, a profound connection between complex exponential functions and trigonometric functions, known as Euler's identity: eiπ + 1 = 0. He also pioneered many mathematical symbols still in use today, including the symbol 'pi' representing the ratio of a circle's circumference to its diameter, sin, cos, tan, cot, Δx (differential), Σ (sum), f(x) (function f of x), and more.

Euler made significant contributions to mechanics and physics, particularly in studying Isaac Newton's laws of motion. Beyond physics, Euler explored astronomy, the theory of curves, cartography, construction, music theory, theology, and philosophy. Recognized for his scientific contributions, Euler was honored as a member of eight academies worldwide, including those in the United Kingdom, France, Russia, Germany, and more. He is regarded as the most important mathematician of the 18th century.

Paul Erdős was a Hungarian mathematician who pursued problems in combinatorics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Regarded as one of the most outstanding mathematicians of the 20th century, Erdős was also known for his eccentric personality.

Without a permanent home or family, he lived in various mathematical institutes, staying with colleagues or residing in hotels during conferences. All his possessions fit into a single suitcase. Additionally, Erdős rarely published alone; he enjoyed collaboration and authored around 1,500 papers with 511 different collaborators. Erdős became the second most prolific mathematician after Euler in terms of productivity. On September 20, 1996, Erdős passed away due to a heart attack while attending a mathematical conference in Warsaw, Poland, leaving behind significant contributions to the field of mathematics worldwide.

Hypatia was the world's first female mathematician, as well as an astronomer, philosopher, and physicist. She was the only daughter of mathematician Theon of Alexandria and absorbed her education from her father. Hypatia later became a scholar at the library in Alexandria in the 4th century AD.

Her most valuable scientific legacy is the edited version of Euclid's The Elements, the most important Greek mathematical text and a standard version for many centuries. Despite her talent, Hypatia met a tragically gruesome end. She was brutally tortured and murdered by a fanatical Christian mob, followed by being set ablaze.

Girolamo Cardano was an Italian mathematician, physician, and astrologer of the Renaissance. Although he studied medicine, his somewhat difficult personality and eccentric lifestyle made it challenging for him to find employment. However, due to his passion, he persevered and became the first to provide explanations for typhoid fever.

Cardano encountered mathematics by chance, driven by necessity, he immersed himself in gambling. In his book on probability in games, 'Liber de ludo aleae,' written in 1560 and published in 1663 after his death, Cardano's systematic explanations of probabilities led to the development of statistics, marketing, insurance, and weather forecasting. Today, Cardano is best known for his achievements in algebra. He published solutions to cubic and quartic equations in his work, 'The Rules of Algebra.'

Archimedes (around 287 BCE – around 212 BCE) was a mathematician, physicist, engineer, inventor, and astronomer from Ancient Greece. Though few details about his life are known, he is considered one of the leading scientists of the ancient world.

Often regarded as the greatest mathematician of antiquity and one of the greatest mathematicians of all time, he anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to rigorously derive and prove a range of geometric theorems, including theorems about the area of a circle, the surface area and volume of a sphere, as well as the area under a parabola.

Other mathematical achievements include approximating the value of pi, defining a type of spiral known as the Archimedean spiral, and developing a system using exponents to represent large numbers. He was also among the first to apply mathematics to physical problems, establishing the fields of hydrostatics and statics, including an explanation of the principle of the lever. He is also known for designing various machines, such as the Archimedean screw pump, complex pulley systems, and war machines to defend his hometown, Syracuse.

Gottfried Wilhelm Leibniz was a German polymath whose works were primarily written in Latin and French. Educated in law and philosophy, and serving as a factotum for two prominent German noble families, Leibniz played a significant role in European politics and diplomatic affairs in his time.

He holds a prominent place in both the history of philosophy and mathematics. He independently discovered calculus along with Isaac Newton, and his notation is widely used since then. He also explored the binary number system, the foundation of most modern computer architectures.

Georg Friedrich Bernhard Riemann was a German mathematician who made significant contributions to mathematical analysis and differential geometry, laying the foundation for the development of later theories of relativity.

Riemann is one of the most influential mathematicians in the mid-19th century. Though he didn't publish extensively, his works opened new avenues of research combining analysis and geometry, including the theory of Riemann surfaces, algebraic geometry, and the theory of complex manifolds. The Riemannian geometry was extended by Felix Klein and, notably, Adolf Hurwitz. This field in mathematics serves as the foundation in topology and is still applied in novel ways in mathematical physics in the 21st century.

Riemann worked in real analysis, where he was a prominent figure. In addition to defining Riemann integration using Riemann sums, he developed the theory of non-Fourier trigonometric series, the first steps in the theory of general summation, and researched the Riemann-Liouville integral. He made famous contributions to modern analytic number theory. In a short paper (his only paper on the subject), he introduced the Riemann zeta function and established its significance in understanding the distribution of prime numbers. He had a series of conjectures about the properties of the zeta function, one of which is the famous Riemann hypothesis.

Jules Henri Poincaré (April 29, 1854 – June 17, 1912) was a French mathematician, theoretical physicist, and philosopher. He was a polymath and is regarded as having profound insights across various scientific domains, particularly in mathematics.

As a mathematician and physicist, he made fundamental contributions to pure mathematics, applied mathematics, mathematical physics, and celestial mechanics. He posed the famous Poincaré conjecture in mathematics. While studying the three-body problem, he was the first to discover a system with deterministic chaotic behavior, later foundational to modern chaos theory. He is considered one of the founding fathers of topology.

Muhammad ibn Musa al-Khwarizmi was a mathematician, astronomer, astrologer, and geographer from Persia. He was born around the year 780 in Khwārizm, then part of the Persian Empire (now Khiva, Uzbekistan), and passed away around 850. Throughout most of his life, he served as a scholar at the House of Wisdom in Baghdad.

The book 'Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala' is the first systematic exposition of solving quadratic and linear equations. Thanks to this work, he is regarded as the father of algebra, a title shared with Diophantus. Latin translations of his book on arithmetic, which dealt with Indian numerals, introduced the decimal positional number system to the Western world in the 12th century. He also surveyed and updated Ptolemy's Geography and wrote several works on astronomy and astrology.

His contributions not only had a profound impact on mathematics but also on language. The term algebra originates from al-jabr, one of the two operations he used to solve quadratic equations, as described in his book.