There have been many amazing mathematicians through the ages but here are 6 who have undoubtedly pioneered and developed maths as we know and use everyday, in order from when they lived.

1. Pythagoras (c. 570 – c. 495 BC)

Pythagoras of the Greek island Samos was one of the first people (as far as we know) to push mathematics as the basis of everything.

Pythagoras is regarded as the first pure mathematician. Until he arrived, maths was more a hobby, not a science. He was a mystical philosopher who approached maths very differently from those of his time. He wasn’t trying to solve problems, he was interested in the principles of maths.

Some of his work included the famous “Pythagoras Theorem” which became one of the central foundations of geometry.

Pythagoras was fascinated by the properties of numbers and discovered irrational numbers was, which he saw as the key to everything. Because his approach was different to a regular mathematical mind, he made key discoveries few others would have.

2. Muhammad ibn Musa al-Khwarizmi (c. 780 – c. 850 AD)

Muhammad ibn Musa al-Khwarizmi was a Muslim mathematician and astronomer who lived in Baghdad. al-Khwārizmī famously introduced Hindu-Arabic numerals to the western world, in a technique of performing arithmetic that coined the term "algorithm".

But perhaps his most pioneering work was being the first to work on equations that were equal to zero and consequently inventing algebra. Latinized versions of some of his famous book titles have given us the words “algorithm” and “algebra”.

Muhammad ibn Musa al-Khwarizmi used a systematic, logical approach backed up with data, which set him apart from other mathematicians of the time.

A crater on the far side of the moon is named after him.

3. Archimedes (c. 287 – c. 212 BC)

If mathematics is a superhero in the Marvel Universe then Archimedes has to be Captain America. He pioneered so many mathematical concepts that are used to this day. He even invented branches of mathematics such as calculus. Some of his famous discoveries include:

1. The Sand Reckoner
   
   Archimedes set out to literally count the number of grains of sand in the entire universe. Sounds impossible? Archimedes had to figure out how to count a number with a large base. It meant he had to invent new names for large numbers, such as “myriad”. Along the way he discovered the law of exponents (for example 82 to indicate the number of times to use a number when multiplying it, in this case 2, to make 64).
   
   Archimede’s attempts to count the number of grains of sand crossed over into the realm of science as he worked on the hypothesis that the sun doesn’t move but the earth orbits it. At a time when Greeks had a very simple counting system, so Archimede’s technique of counting billions was remarkable. It meant that from now on maths could count numbers up to infinity.
   
   And how many grains of sand did Archimedes theorise would cover the universe? He came up with 8 1063 grains. Quite a desert full.
   
   
2. Discovering Pi
   
   Archimedes was the first person to use PI (π) in a calculation. To do this, Archimedes used a polygon. He drew a regular hexagon inside and outside a circle, and kept doubling the number of sides until he reached a 96-sided regular polygon. Archimedes showed that π is between 3 1/7 and 3 10/71.
   
   
3. The Odometer
   
   Yes, that’s right, the odometer that you see in every car to measure distance travelled, was invented by a Greek mathematician 2 thousand years ago. Archimedes’ odometer worked on the principle that every time a wheel goes around, it travels its own circumference. The odometer adds up those circumferences and marks when the wheel has travelled a mile. This way Archimedes was able to measure the distance travelled by a cart or chariot The same principle is used to this day!

No wonder he’s known as the father of mathematics.

4. Isaac Newton (1642 - 1726/27)

Newton is one of the most recognised and famous names in both the maths and science world.

Isaac Newton was a school dropout, taken out by his mother at age 12 to work on the farm. But the farming world’s loss was mathematics gain, as he eventually went back to school. Newton is perhaps most famous for his Theory of Gravity, but his contribution to maths was equally seismic. For instance, his Fundamental Theorem of Calculus was revolutionary. It began as a way to find any slope on a curve whose slope was constantly varying.

Newtown is also credited with the generalised binomial theorem which describes the algebraic expansion of powers of a binomial. He was also the first to use an infinite power series. He also developed a method for finding the roots of real valued functions.

Newtown made so many discoveries in his lifetime from physics, to optics and light and the laws of motion. He even found time to invent the cat flap. His book “Principia” or “The Mathematical Principles of Natural Philosophy”, published in 1867 is said to be the most significant scientific book ever written.

5. Sophie Germain (1776 - 1831)

The onset of the French Revolution kept young Sophie indoors where she started to read books on maths to escape her worries. One book was the story of Archimedes, a man so obsessed with maths he ignored the invading soldiers who killed him! Sophie was fascinated.

Her parents did not approve of her growing interest though, thinking maths was not a suitable subject for a young woman and so deliberately took away heating and light so she would go to bed. One morning they found her asleep in the library covered in blankets. The ink in the inkpot besider her had frozen. They eventually relented and supported her passion.

Today, Sophie Germain is regarded as the first woman who managed to make great strides in maths, developing a number theory, and finding solutions or proofs to other theories (such as Fermat’s last theorem). Sophie even had a numerical series named after her, the ‘Sophie Germain prime numbers’.

From learning maths by candlelight and living in a world where girls could not formally study the subject, Sophie’s passion for mathematics is in inspiration to this day.

6. Ada Lovelace (1815 - 1852)

In a time where women often weren't allowed to have careers, and in a field that has always been very masculine, Ada Lovelace stood out as a major female mathematician who is often cited as the first computer programmer.

While her father was the celebrated poet Lord Byron. Ada was drawn to science and maths. She was asked to translate an Italian mathematician’s notes that explained the famous “Analytical Engine” by Charles Babbage, which was like an early computer. She went beyond just translating however, and came up with an algorithm based on the sequence of Bernoulli numbers which could be programmed into the Engine. She was essentially coding and more or less invented computer programming as we know it. Charles Babbage himself called her “The Enchantress Of Numbers”. Her contribution to maths runs very deep, as we can see by the fact that Ada programming language (used by the U.S. Department of Defence) is named after her.

In 2009, Ada Lovelace Day was created to raise the profile of women in STEM (science, technology, engineering, and maths)