Along the course of history, scientists have made many discovers that have triggered a paradigm shift in the collective, mathematical attitude. One such case can be seen in life and works of Sir Isaac Newton.

The law of gravity, telescope reflector, method of fluxions - Newton studied the natural phenomena of his environment in order to establish  and prove scientific truths. Known as one of the greatest scientists of his epoque, Isaac Newton continues to be relevant today. While there are many mathematicians who have both inspired his works, and even aided in some of his discoveries, Newton worked principally by being inspired by the environment around him.

Discover the role of Newton in the history of mathematics, most notably in the calculation of the integral!

If you're interested in learning about more modern mathematicians, check out Rene Descartes!

The Early Life of Sir Isaac Newton

When discussing the history of mathematics, it is difficult to do so without mentioning the celebrated Newton. An English physicist, philosopher, astronomer, and mathematician, Isaac Newton was born in 1642 in Woolsthorpe, Lincolnshire in the UK.

His father died several months before his death and, consequently, Newton’s mother remarried when he was three years old. It was his maternal grandmother and his stepfather that looked over his up-bringing.

Newton took inspiration from Descartes
The physicist grew up in Woolsthorpe Manor

Newton was a very curious kid, observing the functioning of the machines around him. As a student, Newton was a bit scattered and always had his head in the clouds. Even still, he taught himself how to fabricate sundials, wind turbines, mechanical transport devices, kites, etc.

Some years later, his mother took him out of school with the goal of making him into a farmer even though, at his fourteen years of age, the future mathematician didn’t show any interest in that domain. His success can be traced to an old professor who managed to convince his mother to let him prepare Newton to enter the University of Cambridge.

It was there that he became, in 1661, a student of Trinity College of Cambridge. To avoid paying school fees, Newton performed domestic tasks for the school. This arrangement permitted him to study arithmetic, geometry, trigonometry, astronomy and optics. Isaac Barrow, the great mathematician and professor of Cambridge, took Newton under his wing. Newton eventually received his diploma in 1665.

After his graduation, the scientist spent his time elaborating several hypotheses and laws on universal gravitation and on the movement of bodies. He studied his environment and how the objects around him moved. He made great discoveries by studying the behaviour of light and the function of optics. During his career, on of Newton’s most celebrated inventions was the mirrored telescope.

But Newton didn’t stop there. The accomplished scientist also searched to elaborate his reflections on theology, chronology, alchemy and chemistry.

After a great career as a scientist, Newton distanced himself from the English capital to reside in Kensington, where he died in 1727. He was the first scientist to be buried in the Westminster Abbey.

Isaac Newton and his Work on Gravitation

Newton is known, before everything else, for his research on gravitation. According to legend, Newton sought to understand how the moon could rest in orbit around the earth. He observed and noted that, along an orchard, apples always fell. He discovered in that moment the force of attraction under which the apple had been subjected to and developed the law of gravity. He estimated that the reason the reason for the fall of the apple was the same as the reason why the moon rested close to the earth, despite the distance.

To verify his hypothesis, Newton put in place an equation according to which the force of gravity depends on the inverse square of the distance between two objects. We call this law the law of the inverse square.

To develop this, the scientist expanded his hypothesis to encompass stars like the sun, and other planets as well. However, Newton didn’t make any calculations on the relationship between the apple and the tree because the distance appeared to him too short in comparison with the stars and planets in the sky.

Nevertheless he is principally known for his research in gravity. Even today, the legend of the falling apple forms a part of history that we love to tell in science and mathematics courses.

The philosopher had a great epiphany
Discoveries are often made in the most unexpected places: Newton's was under an apple tree!

Newton's Discoveries: From Calculus to Optics

Even if Newton is principally known for his discoveries in the domain of physics, it is important to not forget his capabilities as a mathematician. Taken under the wing of Isaac Barrow during his studies at Trinity College of Cambridge, Newton confided with him a manuscript in which we wrote several different mathematical conclusions.

Named “On Analysis by Infinite Series,” Newton described and developed integral and differential calculus. Newton called this the method of fluxions.

Integral and differential calculus implied other mathematical calculations like:

  • The percentage change of quantities
  • The inclination of curves on a given point
  • The calculation of minimum and maximum values of functions
  • The calculation of areas comprising of curves

Once in the hands of Isaac Barrow, the maths professor showed the manuscript to many of Europe’s then great scientists. Newton became widely recognized as the founder of mathematical calculus and acquired a place amongst the greats of his time.

Newton also made himself known for what we call now Newton’s binomial. This is defined by the formula “(a+b)n,” which holds true for any value of n.

Legend has it that at the point of retirement, Isaac Barrow gave Trinity College of Cambridge the idea to hire Newton as the new professor of mathematics. Newton and the college unanimously accepted. The mathematician gave his first maths course in optics, one great passion that him and one of his predecessors, Euclid, shared.

Newton's Work on the Behavior of Light

Amongst all of his biggest researches, Newton payed particular attention to everything concerning optics. This passion began while the English scientist first took an interest in the behaviour of light.

For scientists of the era, white light was considered as homogeneous and it was believed that it could not be distorted.

Newton, like always, liked to and did challenge the certitudes of his time.

To do this, he used a transparent prism and exposed it to the rays of the sun. During these experiments, he realized that the light of the sun transformed itself into many rays of light which were all different colours. He called this a “spectrum.”

He introduced, from then, the term refrangibility, a phenomena that explains that the different colours in the rays of the sun, by the differences in the degrees of one property, can bend when in contact with certain objects. Objects whose material allows the light that enters it to change direction is called a “refracting object.”

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Newton's method of fluxions became hugely influential
Newton was also involved in setting the foundations for classical mechanics

Each colour that composes the rays of the sun possesses a different refrangibility. During contact with a prism, all of the colours of the spectrum don’t behave the same way. Newton studied them and took note of what he saw during these experiments.

All of his observations left an enormous mark on the domain of optics, which Newton continued to study for the rest of his life.

If you're interested in some more interesting and foundational mathematics principles, check out ancient Greek philosopher and mathematician Thales.

Newton's Famous Telescope Reflector

Newton’s discoveries concerning light and the phenomena of changing refrangibility greatly influenced the world of science. Newton took advantage of his role as a maths professor at Trinity College of Cambridge to continue to study the field of optics.

After having discovered the behaviour of spectrum of light and the different colours that came out of the face of a prism, Newton revisited the function of telescopes which were made at the time using lenses.

These lenses were fabricated using one material, glass, that modified the trajectory of beams of light. Newton decided to replace these lenses by mirrors with the idea that the colours could reflect from mirrors the same manner but more efficiently. It was in 1668 that Newton was ready to fabricate his modified telescope.

The telescope was made with a mirror of 3.3 cm and a magnification factor of about 40. The gifted scientist combined in this invention his love for mechanical objects with his obsession over the function of objects and light.

Some years after his invention, Newton acquired letters of nobility from the Royal Society, the association of accomplished mathematicians, to test his telescope and to create a patent for the machine. His status as a veritable genius in the sciences and maths was finally validated in the eyes of both his generation and for the years to come.

If you're interested in learning more about the famous mathematicians in history, check out this guide!

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