"As simple to the mind as it is, this equation had boundless consequences for the primitive man because this form is the basis for all counting. Without the understanding of numbers these people could only trade in primitive ways. There was no exact way to count the number of sheep or cows that one owned nor how many men there were in the tribe. The discovery of counting led directly to rapid development of commerce and later to the important science of measurement."
"Unquestionably this equation of Pythagoras is the most used and far reaching of the theorems of geometry. It relates the lengths of three sides a, b, and c, of a triangle with a right angle. It proved for the first time a way to measure average lengths indirectly, and gave man a way to do mapping and surveying. The ancient Greeks used it to measure the distances of ships in the sea and the heights of buildings and other structures. Today scientists and mathematicians constantly use it to explain all types of theories."
"Archimedes said “Tell me where to stand, and I will move the earth”. His simple equation of the lever is the basis of all engineering, whether measured with a bar, with many gears, or with advanced cranes. It is used in the design of engines, and structures from bridges to buildings. All nuts and bolts work under this principle, as do the brakes on cars, the handles of doors and the best set of tools, all of which are types of levers."
"With the invention of the logarithm, Napier gave the world one powerful shorthand equation of mathematics. It allowed man to do multiplication, division, addition, and subtraction simply with the logarithms of numbers and used this equation to rapidly carry out many complicated operations using numbers that were very complex. The enormous impact of the logarithm in the area of astronomy and navigation is comparable to the computer revolution of today."
"Before the time of Newton, people had very little idea what “force” supported the planets in their orbits around the sun or the moon around the earth, or even that which was able to prevent man from flying off the surface of the earth toward space. Newton showed that every body is attracted to another by a force of gravity. This equation reveals that this force depends on the mass of the bodies. No one took notice of these little things because the forces were so weak."
"Over a century, this Scottish physicist discovered four famous equations to summarize man’s knowledge of electricity and magnetism. For these equations, he obtained an equation to predict the existence of the sound wave of a radio. To Maxwell, we owe all our sound on radio and TV, all our communications over long distances, and radar on earth, sea, and in space. These fundamental equations govern light, x-rays, and other electromagnetic radiations."
"The equations of Boltzmann describe how the behavior of gasses depends on the constant movement of atoms and molecules. Their great importance is inherent in and important paper in which the applications of gasses is explained: in engines that use vapor and internal combustion; in countless reactions among gasses used by chemists for modern medicine, plastics, and other substances; to understand time; and to explain violent processes of the sun, starts, and distant galaxies."
"One basic part of the technology of space, this equation confers the change of velocity of a spaceship when it burns the weight of its fuel. This equation is derived directly from one of the three great laws of the movement of Sir Isaac Newton. Without it, launching these special ships to the moon and planets, or even to orbit around the earth, would be nearly impossible; unfortunately this also makes war with rockets possible."
"This equation is inherent to the foundations of our nuclear age. To explain simply, one small quantity of matter can be converted into one large quantity of energy. This free nuclear energy, in one spectacular and violent form, is the basis for atomic hydrogen bombs. Yet man also has the ability to create nuclear fission in the form of nuclear reactors to supply heat and to generate electricity for our homes and factories."
"Light, one form of energy, is able to act separately, similar to a ball, and continuous like a wave. De Broglie discussed and reported these particular fundamentals, that light is composed of matter, and has wave properties. This equation has had a great effect on the field of physics, modern optics, and component electronics - transistors, for example - with many applications in radio, TV, computers, special ships, military arms, and other things. Also, it provided scientists with powerful electron microscopes."
Note* Via Thomas, Cecil. (2013). Ten Most Important Formulas on stamps issued by Nicaragua in 1971.
In 1971, Nicaragua issued ten stamps commemorating the "ten most important mathematical formulas". The back side of each stamp has a short text describing the equation and its utility. The stamps were a gift from Tim Klitz who is now a professor in the Psychology Department at Washington & Jefferson College. Cecil arranged the stamps in chronological order (by birthdate of the person credited with the equation).