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November 5, 2019

Who was the best mathematician in the initial era?

Alright! So there are a number of Mathematicians who have enriched the field of Mathematics like Pythagoras,Leonardo Pisano, Srinivasa Ramanujan, Euler.

Not really pointing at the best but one of the best Mathematicians till date we have is Johann Carl Friedrich Gauss. Johann Carl Friedrich Gauss, born on 30th April 1777 and died on 23rd February 1855 at the age of 77 was a German Mathematician, He was a brilliant Mathematician and is considered to be the most influential Mathematicians in History.He is often regarded as the “Prince of Mathematics” and “Foremost of Mathematicians”.

Gauss was born on Brunswick and he belonged to a poor family. His supreme intelligence captured the attention of the Duke of Brunswick who sent him to the Collegium Carolinum (now, known as the Braunschweig University of Technology and to University of Gottingen. He attended the Collegium Carnolium from the year 1792-1795 and Gottingen from 1795-1798. Gauss had child prodigy, means a person under ten age of ten having exceptional knowledge and outputs on a particular domain like that of an adult. In 1796, Gauss came up with the discovery that if the number of sides of a polygon occurs as the product of distinct Fermat primes and a power of 2, then a regular polygon can be constructed using a compass and straightedge. Fermat number is referred to as a positive integer of the form

\(F_n\) = \(2^{2n}\)+1, where n is an integer. Some Known Fermat Numbers are 3,5,17,257,....... The Fermat numbers which are primes are known as Fermat primes.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root (includes polynomial having real coefficients).

In his book ‘Disquisitiones Arithmeticae ‘,meaning Arithmetical Investigations in Latin,Gauss worked a lot on number theory and found the symbol of congruence used in modular arithmetic.

Gauss proved a number of theorems like

  1. Fermat’s polygonal number theorem for n=3
  2. Descarte’s rule of signs.
  3. Algorithm for determining date of ester
  4. Fermat’s last theorem for n=5.

Fermat’s polygonal number theorem for n=3

This theorem states that every positive integer can be expressed as the sum of three or more triangular numbers, three or more square numbers or three or more pentagonal numbers.

Triangular number-p is called a triangular number if it is the number of dots that can be arranged in a triangle having p dots on a side and equals to the sum of p natural numbers from 1 to p. example- 31,3,6,10,15,21……(here p is any natural number)

Square numbers refers to those numbers which are a perfect square of an integer. Example '9', as it is a square of 3*3.

Pentagonal numbers are just an extension of square and triangular numbers but the arrangement of dots is different in this case. Let p_n be nth pentagonal number where n is the number of dots \(n>=1\) Then \(p_n\) is given by the formula

\(p_n\) = \(\frac{3(n^2)-n}{2}\)

The triangular concept was proved by Gauss in 1796. Gauss's results are often referred to as the Eureka Theorem.

Descarte’s Rule of Signs

This is a method to find the number of positive real roots of a polynomial. It states that the number of positive roots of a polynomial is the number of sign changes in the polynomial sequence excluding the zero coefficients and the difference between the numbers is always even.


\(f(x)\) = + \((x^3)\) + \((x^2)\) - \((x)\) -2

Here sign change is occurring jut one time between the second and third term. Therefore this polynomial has one positive root.

Fermat's last theorem for n=5

Fermat’s last theorem by Pierre de Fermat states that no three integers can satisfy the equation

\(a^n\)+ \(b^n\)=\(c^n\) , where a,b,c, are positive integers and n is any integer greater than 2

This above theorems were proved by Gauss.

Now there were several Mathematicians of the initial era as mentioned above but among them according to me Gauss was the best because of his ravishing outlook towards Mathematics. The famous Easter calculation concept was also provided by him. Easter is a festival which was celebrated first three days after Crucifixion of Jesus Christ. Initially it was believed that there were no fixed dates for Easter in the calendar every year. Gauss obtained this calculation using modular Arithmetic. Thus his way of connecting each and every saga of life with Mathematics is extremely unique.

Some other famous Mathematicians are

  1. Thales of Miletus (considered as the first true Mathematician).
  2. Pythagoras of Samos, creator of famous Pythagoras theorem.
  3. Leonardo Pisano, inventor of Fibonacci series.
  4. Euclid, famously mentioned as the Father of Geometry.
  5. Leonhard Euler, one of the greatest Mathematicians ever existed.
  6. Srinivasa Ramanujan, had huge contributions towards Mathematical Analysis, Continued Fractions, Number Theory.
  7. Pierre de Fermat, best known for Fermat’s principle of light and Fermat’s last theorem.
  8. Christian Goldbach, famous for his still unsolved Goldbach conjecture.
  9. Georg Ferdinand Ludwig Philipp Cantor , creator of set theory.
  10. Sir Issac Newton, developer of infinitesimal calculus.
  11. Jules Henri Poincaré ,described as the "The Last Universalist,"
  12. Georg Friedrich Bernhard Riemann, one of the greatest contributors of differential geometry.
  13. Augustin-Louis Cauchy,had great contributions in the line of Mathematical analysis.
  14. Diophantus of Alexandria,famous for his study on Diophantine equations.
  15. Pierre-Simon, marquis de Laplace ,formulator of Laplace equation and Laplace transformation.
  16. Lodovico Ferrari. solver of quarter equations.
  17. Gerolamo Cardano,well known in the field of Algebra and solver of cubic equations.

One of Gauss’s popular quotes

“It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.”

which i truly believe.

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