Top Ten Mathematicians Who Made Maths Awesome

Mathematics is the language of the universe. It allows for predicting the unknown and has provided many answers to human problems. However, mathematics didn’t become an overnight sensation; instead, many mathematicians made it a universal medium for explaining the events of our universe. In this blog, we will try to discover the works of the top ten mathematicians whose works shaped modern mathematics.

1. Euclid (325BC – 265BC)

Euclid
Euclidean geometry was the only type known till the 19th century. Credits: WIkimedia/Mark A. Wilson

Euclid’s most outstanding work, the Elements, is a pillar of geometry. The theorems and axioms are simple yet so groundbreaking that a whole field of geometry is dedicated to theories laid down by Euclid, known as Euclidean geometry. In fact, it wasn’t until the 19th century that N. Lobachevsky discovered non-Euclidean geometry. One of his most famous works is the golden section, which is a parameter of artistic beauty. Let’s inspire ourselves with some of his most remarkable contributions:

 

  • Euclid’s ten axioms presented in the Elements provide the basis for many geometric concepts.
  • Euclid introduced us to congruent triangles. A pair of triangles are considered congruent if they can be superimposed on one another.
  • He proved the presence of similar shapes, which are figures similar in shape but different in size. For example, the shape of an object appears similar under a magnifying glass, but the size is enlarged.
  • Euclid’s fifth postulate introduced us to parallel lines and has been used to prove that the sum of all the angles of a triangle is 180°.

2. Aryabhata (476CE – 550CE)

Aryabhata
Aryabhata added zero to the number system. Credits: Wikimedia/1940368 Hemateja

Most mathematicians overlooked the need to quantify an empty value. Aryabhata discovered and gave null a value of 0 or zero. Zero is necessary in some algebraic systems and important in place value systems. Apart from mathematics, Aryabhata also took an interest in astronomy. He was a pioneer in combining math with astronomy and has done so in his book, Aryabhatiya. Let’s check out a few of his contributions to mathematics.

 

  • Aryabhata invented the decimal system and even found methods for calculating square and cubic roots.
  • He estimated the value of pi at 62,832/20,000, which is the closest estimation of the value made by any ancient mathematicians.
  • He derived a formula for finding the area of a triangle using the perpendicular and half-side (1/2*b*h)

3. Girolamo Cardano (1501-1576)

Girolamo Cardano was the pioneer of probability theory
Girolamo Cardano was the pioneer of probability theory. Credits: Wikimedia

Girolamo Cardano was an Italian doctor and mathematician. The quote above was the last line in his book of algebra called Ars Magna, which certainly stood the test of time. It had the solution of the cubic equation (the solution of x has either one or three values) and the quartic equation (the solution of x has four values). Let’s look at his other works:

 

  • He was the first person to explain chance mathematically. In his book Liber de ludo aleae, he gave the idea of probability. It is the study of the chance of an event that might or might not happen.
  • Cardano was the first to recognize imaginary numbers (based on √-1).

4. Pierre de Fermat (1601-1665)

Pierre de Fermat was one of the forerunners in developing calculus alongside Newton and Leibniz. Credits: Wikimedia

Pierre de Fermat is known as the father of the modern theory of numbers. Fermat’s lesser theorem concludes that ap-a is divisible by p, where p is a prime number. And a is an integer. Fermat was one of the best mathematicians of his day, but his reluctance to publish marred his impact on the subject. However, his works have shaped modern maths:

  • Fermat was one of the founding figures in developing analytic geometry. He studied geometric shapes along axes and through points plotted on graphs from solutions to equations.
  • He is regarded as the inventor of differential calculus, which is the study of the rate of change of one quantity to another.
  • He helped advance probability theory and optics.

5. Gottfried Wilhelm Leibniz (1646-1716)

Christoph_Bernhard_Francke
Leibniz developed a calculator called the stepped reckoner. Credits: Wikimedia/Claus Cordes

At a time when Sir Isaac Newton was revolutionizing physics, Leibniz worked his way up the ladder in maths. Along with Isaac Newton, Pierre de Fermat, and many others, Leibniz is heralded as a torch-bearer of calculus. He even built a calculator, which he called the stepped reckoner. His famous contributions to the world of maths are:

  • Leibniz developed the modern notations for calculus.
  • He invented the binary number system, which is used in computers. It is a way of writing numbers in 0s and 1s.
  • Leibniz is also credited with discovering the use of matrices or arrays to solve math problems.
Stepped reckoner
Stepped reckoner. Credits: Wikimedia/Plenuska

6. Sir Isaac Newton (1643-1727)

Sir Isaac Newton (1643-1727)
Sir Isaac Newton did not only work on physics but also upheld the development of mathematics. Credits: Wikimedia/Godfrey Kneller

There isn’t a scientist who has given us so much to ponder about. Throughout his remarkable life, he has given us the laws of gravity and the laws of force. However, one of his celebrated works is the Principia Mathematica, which is considered a treasure in maths. A few of his notable works are:

  • Isaac Newton introduced us to the binomial theorem, in which a binomial (an expression with two terms) can be expanded to any power.
  • He is said to be the inventor of calculus.

7. Leonhard Euler (1707-1783)

Leonhard Euler
Although blind at a later stage of life, Euler continued working out math problems in his head. Credits: Wikimedia/Jakob Emanuel Handmann

Leonhard Euler has touched upon multiple fields within maths. His books and memoirs added precision to calculus. Lagrange succeeded him, whose contributions paved the way for the famous Euler-Lagrange equation used in calculus today. Euler lost sight due to a cataract over time but kept working on math problems in his head. His other works significantly improved the world of maths:

  • Leonhard Euler developed theories on trigonometric and logarithmic functions
  • He developed various elementary geometric constructions, including the Euler line, which helped find a triangle’s balance point or center of gravity.
  • Provided a lot of modern-day notations for various operations in mathematics

8. Carl Friedrich Gauss (1777-1855)

Carl_Friedrich_Gauss
Gauss is known for his work in geometry, and he almost laid the foundation of non-Euclidean geometry. Credits: Wikimedia/Gottlieb Biermann

Carl Friedrich Gauss could do complex calculations in his head, an ability he retained forever. Born to poor parents, the Duke of Brunswick quickly discovered his talent and funded his studies. His work on number theory and geometry has changed how we view these fields. Other contributions of his are:

  • Gauss proved that the number of solutions a polynomial equation has is equal to the highest power of the variable.
  • He developed the method of least squares to eliminate errors from observation.
  • Formulated the theory that the curvature of a surface is not always altered even if the surface is bent without being stretched.

9. Georg Cantor (1845-1918)

Georg Cantor gave an idea about transfinite numbers. Credits: Wikimedia

Georg Cantor is a visionary in modern math. His attempt to gauge how infinity works is an example of his genius. His diagonal argument proved that some infinities are countable while others are not. His other beautiful works are:

  • Cantor developed the set theory, which helps us to organize data and numbers.
  • He combined the concept of real numbers with the theory of trigonometric series.
  • He developed the concept of transfinite, a number greater than finite numbers but not quite infinite.

10. John Horton Conway (1937-2020)

John_Conway_browses_Genius_at_Play
Georg Cantor going through the book Genius at Play. Credits: Wikimedia/Tanyakh

John Horton Conway is known for finding math in the nooks of puzzles and games. When interviewed at eleven, he wished to be a mathematician at Cambridge, a feat he would later achieve. He was heavily invested in Backgammon and developed an algorithm of his own. His game, called Game of Life, fascinated early computer scientists. His other discoveries and work include:

  • He brought the concept of surreal numbers to light.
  • A very fundamental discovery on triangles is the Conway circle. When a triangle is extended through its three vertices so that the length of the extension is the same as the length of the opposite side, the points fall onto a circle.
  • Developed the thrackle conjecture, which is still an unsolved problem.

Here’s a link to a website where you can play the Game of Life: https://playgameoflife.com/. Check https://playgameoflife.com/info for the rules of the game

To know more about Cantor’s proof and Conway’s Game of Life, watch this video

References

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