Sir Isaac Newton was not only one of the best physicists ever lived but he was also one of those scientists that contributed a lot to mathematics. He made most of his mathematical contributions while he was first a student then a professor at Trinity College, Cambridge between the years 1661 and 1696. Our world would not be the same today without the important discoveries of the son of this yeoman farmer.
The years 1665-66 were one of the worst for England when the Bubonic Plague devastated all big cities. 1665 is also the year when Newton got his BA When the school was shut down to fight the plague, Newton retreated to the family farm at Woolsthorpe. During those two years that he spent in seclusion doing nothing but devoting all his time to physics and mathematics, Newton discovered the law of gravity and made important advances in mathematics.
Here is a list of the 23 year old Newton's achievements during those two crucial years:
He discovered the law of universal gravitation, invented calculus (at the same time as but independently of Leibnitz in Germany), further developed the binomial theorem, and started his life-long studies in optics and the theory of colors.
There, during his two year stay at the farm, Newton discovered and proven that the same force that pulls a rock towards the earth (ie, gravity) is one and the same force that pulls the moon towards the earth and keeps it in orbit. He later on developed this into a "Principle of Universal Gravitation" which said any two objects in the universe attracted one another in direct ratio to the product of their masses, and in inverse ratio to the square of the distance between them.
Newton is best known for his 3 Laws of Motion:
Law 1 (Law of Inertia): If an object is at rest and there is no net force acting on it, it will remain at rest. If it is moving at a constant speed and no net force is acting on it, it will continue to move at that constant speed.
Law 2: F = ma, or: the net force acting on an object is its mass multiplied by the acceleration of the object. Thus if an object is moving at a constant speed, that is, if its acceleration is zero, then there is zero net force acting on it.
Law 3: To every action there is an equal and opposite reaction. If A is pushing B with a force of F, B is also pushing A in the opposite direction with a force of F. Sun attracts the Earth, and Earth attracts the Sun with the same force!
During 1668 and 1669, Newton worked on optics at the Cambridge University.
1669 is another important year in Newton's life since that's when Prof. Isaac Barrow resigned from the famous "Lucasian Chair" at Cambridge and offered it to Newton as its second occupant. Having the security of a good tenured position, Newton pressed on with his studies into the nature of light and optics with a renewed vigor.
Here is a summary of Newton's various contributions to the science of optics, some of which later on culminated in his 1704 book also titled "Optics."
Newton developed instruments to grind lenses into shapes other than spheres. He is the first in human history to discover that, when passed through a prism, the sun light is split into a bundle of different colored rays. On the basis of that observation he developed the first successful explanation of rainbows.
The great physicist has also discovered the telescope that is still known today by his name; invented a reflecting microscope in 1672, as well as a sextant which was independently discovered in 1731 by J. Hadley.
However, for all his daring discoveries in optics and the theory of colors, Newton was attacked vehemently during the 1670s. Sometimes it takes minds lesser than a genius a little lag time to catch up with the greatest discoveries of human history.
Even if Newton had died in his mid-twenties his place in the world of mathematics and science would've been secure enough. But he lived about 60 more years and pushed the frontiers of human reason and science even further – thanks to his extraordinary gifts as physicist and a mathematician.