1. Euclid

He was also known as Euclid of Alexandria and referred as the father of geometry deduced the Euclidean geometry. The name has it all, which in Greek means “renowned, glorious”. He worked his entire life in the field of mathematics and made revolutionary contributions to geometry.

2. Pythagoras

The famous ‘Pythagoras theorem’, yes the same one we have struggled through in our childhood during our challenging math classes. This genius achieved in his contributions in mathematics and become the father of the theorem of Pythagoras. Born is Samos, Greece and fled off to Egypt and maybe India. This great mathematician is most prominently known for, what else but, for his Pythagoras theorem.

3. Archimedes

Archimedes is yet another great talent from the land of the Greek. He thrived for gaining knowledge in mathematical education and made various contributions. He is best known for antiquity and the invention of compound pulleys and screw pump.

4. Thales of Miletus

He was the first individual to whom a mathematical discovery was attributed. He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry.

5. Aristotle

Aristotle had a diverse knowledge over various areas including mathematics, geology, physics, metaphysics, biology, medicine and psychology. He was a pupil of Plato therefore it’s not a surprise that he had a vast knowledge and made contributions towards Platonism. Tutored Alexander the Great and established a library which aided in the production of hundred of books.

6. Diophantus

He was a Hellenistic Greek mathematician and was best known as the father of algebra and attributed to a series of books. His equations can be defined as polynomial equations in several unknowns. The compilations of his books were called Arithmetica.

7. Eratosthenes

He’s best known as the person who calculated the circumference of the earth, also the first one to calculate the tilt of the Earth’s axis. Both of the calculations were remarkably accurate, therefore he became world famous for his incredibly accurate calculations.

8. Hipparchus

The intelligent and perspicacious Hipparchus, ancient Greek mythologist made many mathematical contributions throughout his lifetime. He was the founder of trigonometry and the first to develop a reliable method to predict solar eclipses. He possessed the first mathematical trigonometric table.

9. Hero of Alexandria

He described a method for iteratively computing the square root of a number. This method is known as the Hero’s formula in today’s world, thereby gaining became more famously known as the ‘Hero of Alexandria’.

10. Ptolemy

Ptolemy was a famous mathematician, astronomer, geographer, astrologer and a poet of a single epigram in Greek Anthology.

The author/writer and mathematician took the advantage of his knowledge over the two fields to write several scientific researches. The Great treatise is one of his renowned works now known as Almagest.

11. Xenocrates

Xenocrates of Chalcedon was a Greek philosopher, mathematician, and leader (scholarch) of the Platonic Academy from 339/8 to 314/3 BC.

Xenocrates is known to have written a book on numbers, theory of numbers and geometry. He had the unique talent of calculating the syllables out of an alphabet. One attempted to find the total number of syllables that could be made from the letters of the alphabet.

12. Anaxagoras

Anaxagoras gave a number of novel scientific accounts of natural phenomena. Due to his exceptional knowledge over mathematics and astronomy, he produced the correct explanation of eclipses and description of the sun as a fiery mass larger than the Peloponnese. He also explained meteors and rainbows.

13. Hypatia

Hypaitia of Alexandria was the daughter of a mathematician and took her father as an inspiration to become a mathematician herself. Not only was she a mathematician but a philosopher as well. She taught as the head at a school, her subject was the knowledge of Plato and Aristotle. She is the first woman to make valuable contributions in the field of mathematics. Hypaitia was the first woman to take the bold step to pursue with her dreams and became an inspiration to many young women who became the world’s most famous geniuses ever.

14. Antiphon
Antiphon was the first to give an upper and lower bound for the values of Pi by inscribing and then circumscribing a polygon around a circle and finally proceeding to calculate the polygons areas. The method was applied to squaring the circle. He made comprehensive changes in the world of mathematics through his profound knowledge over the subject such that is known and applied in the modern day.

15. Diocles
Diocles was a philosopher, priest, an emperor, mathematician and geometer. This famous mathematician was most popularly known for his work in the sub classification of geometry. His name is associated with the geometric curve called the Cissoid of Diocles. This method was used in solving the problem of doubling the cube.

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1. Srinivasa Ramanujan

Ramanujan the mathematical genius taught himself math after he dropped out of high school due to his failure in the English subject. He is most famously known for his contribution in analytical theory of numbers, elliptic functions, continued fractions and infinite series. He was also invited to England on his set of 120 theorems that he sent to Cambridge. He further made many mathematical demonstrations in his lifetime, all of which are beyond the scope of this article. He taught a greater valuable lesson, that failure isn’t permanent as he did not let his failure bring him down and continued to teach himself mathematics, which he was passionate about. He has been the inspiration of many mathematicians, not just in India but all over the world.

2. Aryabhata

Aryabhata from ancient history was actually the first person to figure out that earth was spherical and revolved around the sun, thereby discovering the nine planets and calculating the correct number of days in a year were 365. Therefore it wouldn’t be wrong to call him a scientist and an astronomer as well, as far back as the time and mythology suggests.

3. Shakuntala Devi

The most famous female Indian mathematician of all time, Shakuntala Devi, was more commonly known as the human computer. She was so called because of her incredible talent to solve calculations without using any calculator. In Dallas she even competed with a computer to give the cube root of 188138517 faster and she won! She went ahead to compete with UNIVAC the world’s fastest computer to solve the 23^rd root of a 201 digit number and she won that too! A woman with outstanding talent and outrageous world records!

4. D. R. Kaprekar

Dattathreya Ramchandra Kaprekar graduated from the prestigious University of Mumbai and pursued his career as a teacher. He made contributions towards various topics such as magic squares, recurring decimals, integers with special properties and much more. This mathematician even has a constant named after him!

5. Narendra Karmarkar

Karmarkar graduated from IIT Bombay in electrical engineering and went ahead to proceed with his studies in the U.S. to gain his PhD. He is best known for his work in inventing polynomial algorithms for linear programming. This fine mind created an overlap between international technology and mathematics to give birth to algorithms.

6. Harish-Chandra

The Indian originated American physicist and mathematician is famously known for infinite dimensional group representation theory. He made various contributions throughout his lifetime and has also be awarded with the cole prize by the American mathematical society.

7. C. R. Rao

C. R. Rao is a mathematical statistician is most famous for theory of estimation. He achieved his masters in mathematics from Andhra University after which he graduated in statistics from Calcultta University. He is also known for his contribution in discovering Cramer-Rao bound and the Rao-Blackwell theorem.

8. P. C. Mahalanobis

Prasanta Chandra Mahalanobis was another well renowned Indian statistician just like Rao. He graduated from university of Cambridge in physics and mathematics. Popular for his work in discovering the D2 statistics (used for divergence based groupings). He was also the founder of Indian Statistical Institute.

9. C. S. Seshadri

He graduated from Madras university in mathematics and studied further to gain his PhD from Bombay University. His main contributions are in algebraic geometry. Along with his contributions in geometry he also invented the Seshadri constant and the Naraisham-seshadri constant.

10. Satyendra Nath Bose

Till this date Bose must be the most famous Indian mathematician, specifically due to his association with the ingenious Albert Einstein. Bose sent his mathematical researches to Einstein and this lead to the discovery of the Bose-Einstein condensate phenomenon. He was rewarded by the Indian government for his contributions.

11. C. P. Ramanujam

Besides his passion in the field of mathematics he also enjoyed spending his leisure time listening to music. This brilliant mind achieved the power of knowledge and worked in the fields of number theory and algebraic geometry. He was eventually elected a fellow of Indian Academy of Sciences.

12. Brahmagupta

He gave four methods of multiplication and his main contribution was the introduction of zero and the fact that zero (0) stood for ‘nothing’ in the world of mathematics.

13. Bhāskara I
Born in the district of Mysore, this small town lad grew up to be the shining star. His contributions are mainly his proof of the fact that zero stood for ‘nothing’(the idea initially introduced by Bhramagupta). He made many calculations to prove so; division, permutation and combination theories. He also proved how the earth appears to be flat even though it’s a sphere.

14. Bhaskara II
Bhaskara II so called to avoid any confusion with the first. His work represented significant mathematical and astronomical knowledge. He is most known for his work in calculus and how it is applied to astronomical problems and computations. Not only did he deal with calculus but had vast knowledge over arithmetic, algebra, mathematics of planets and spheres.

15. Hemachandra
His most significant contribution in mathematics was his initial version of the Fibonacci sequence. He was not only a mathematician but also a scholar, polymath, poet who wrote on grammar, philosophy and contemporary history. Therefore his contributions are not only restricted to math but over all the various different fields that he had mastered over.

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The female mathematicians are discussed in order according to timeline:

1. Hypatia (AD 315-415)

Hypaitia of Alexandria was the daughter of a mathematician and took her father as an inspiration to become a mathematician herself. Not only was she a mathematician but a philosopher as well. She taught as the head at a school, her subject was the knowledge of Plato and Aristotle. She is the first woman to make valuable contributions in the field of mathematics. Hypaitia was the first woman to take the bold step to pursue with her dreams and became an inspiration to many young women who became the world’s most famous geniuses ever.

2. Emilie du Chatelet (1706-1749)

The French mathematician, author and physicist during the age of reason, or simply, Age of Enlightenment became well known for her work for her translation on Isaac Newton. She had vast knowledge over Newtonian physics and mechanics and gave an elaborate commentary on the Newton mechanics.

3. Maria Gaetana Agnesi (1718-1799)

The Italian mathematician, philosopher, humanitarian, theologian was an honorable lady with command over a wide variety of subjects. She was the first woman who not only became the first math professor but wrote the mathematical handbook as well. Her book comes under discussion in both integral and differential mathematics.

4. Sophie Germain (1766-1831)

A French mathematician, philosopher and author, Sophie Germain, was a dedicated and motivated woman. The young rebellious Sophie fought against her parents to get education, secretly reading her father’s books to gain knowledge. She was one of the pioneers of the theory of elasticity.

5. Ada Lovelace (1815-1852)

The world’s first computer programmer can to acknowledgement when she was translating the memoir of Charles Babbage. She did an analytical review and revised the memoir by adding her own method of calculating a sequence of Bernoulli numbers, the first computer program ever.

6. Sofia Kovalevskaya (1850-1891)

She was the first Russian mathematician, responsible for many contributions and evaluations. She made important contributions to analysis, partial differential equations and mechanics. She was the first woman to get appointed as a full professorship, as well as the first woman as editor of a scientific journal.

7. Mary Everest Boole (1832-1916)

She was the inventor of cooperative learning and creating activities that would make learning math more children friendly. Boole was self taught and progressed to become a mathematician and author of the book ‘Philosophy and Fun of Algebra’.

8. Emmy Noether (1882-1935)

A German and Jewish originated Emmy became the leading mathematician of her time. She developed theories of rings, fields and algebra. She was notified by history’s famous scientists and mathematicians as the most important in the history of mathematics!

9. Euphemia Haynes (1890-1980)

An African-American based woman who progressed to gain her PhD in mathematics. She contributed to the educational system in Washington DC, which was her place of residence. She taught at public schools and eventually became the first woman to chair the DC school board.

10. Mary Cartwright (1900-1998)

Mary Cartwright was a British mathematician who was the first woman to get a first class degree in mathematics. She went on further to gain her PhD and spent the rest of her life working on her thesis on zeros of entire functions. She contributed to simplifying elementary proof of the irrationality of pi. Henceforth, she became the first female mathematician to be elected Fellow of royal society. The list of accomplishments are immense and of great importance in the historical mathematical events.

11. Marjorie Lee Browne (1914-1979)

Marjorie was an African-American mathematician famous for her work, education and contributions to the world of numbers and equations. She was the first black woman who achieved her doctorate in math. She made many contributions to the African-American society the most notable being the introduction of computers in academics. She was a generous woman who spent her life focusing on social work. She encouraged and promoted math education for minorities and women.

12. Julia Robinson (1919-1985)

Robinson was the first woman elected by the National Academy of Sciences and president of American Academy of Arts and Sciences. Despite that fact that she remained un-well due to her health problems she never compromised on her mathematical education. She is most famously known for her work on Hilbert’s tenth problems and decision problems.

13. Katherine Johnson (1918-present)

Katherine Johnson was an American mathematician, physicist and space scientist most prominently known for the introduction of digital electronic computers at NASA. She spread her wisdom with her calculations in the trajectory for Project Mercury and Apollo 11 flight to the moon. She was an extraordinary woman with incredible talents.

14. Shafi Goldwasser (1958-Date)

The modern day mathematician, Goldwasser, is an American professor teaching mathematics and computer science at the well renowned universities, MIT and Weizmann Institute of science. She gained the Golden globe award for her work on theoretical computer science. She contributed with her profound research on zero-knowledge proof, complexity theory, computation number theory and cryptography.

15. Maryam Mirazakhani (1977-Date)

Mirazakhani is an Iranian mathematician and the first of the Iranian women to have multiple accomplishments starting from a very young age. She gathered a gold medal in the international mathematical Olympaid. She was also the first of to be honored with a Fields Medal, one of the most valuable and prestigious award in mathematics, she achieved the award for her work in understanding the symmetry of curved surfaces. Mirazakhani is currently working as a professor of mathematics at Stanford University. She’s an outstanding, inspirational and admirable woman.

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