How not to Think like
EONARDO da 
INCI
EONARDO da INCI
Don't procrastinate. Finish all projects.
Leonardo is described by historians as an inveterate procrastinator. He planned to write three books on mathematical subjects, but they were never published. His notebooks were filled with ingenious inventions and machines; most were never built or implemented. If they had been, it would have transformed Renaissance society. When he was in a funk, he would comment: "Tell me if anything was ever done." On his death bed he apologized to "God and Man for leaving so much undone."
Bookmark - Leonardo's Inventions / Leonardo's Telescope?
Communicate your ideas to others using standard notation.
Leonardo invented some of his own mathematical symbols and terms. Many scientists of his time did this because number notation was not standardized until after the invention of the printing press. This made it difficult for scientists and mathematicians to communicate their ideas to each other. The symbols used today for the numbers one through ten come down to us from ancient India by way of Greece, Rome, and the Moors in medieval Spain.
"Let no one read my principles who is not a mathematician."
Leonardo also used "mirror writing" going from right to left on the pages of his notebooks. He was left-handed so maybe this was a matter of convenience. He started every page on the "verso" or back side and worked over onto the front. Paper was expensive and scarce so Leonardo scribbled on every scrap he could find. These scraps were then assembled. Scholars have complained that Leonardo's notebooks are a terrible jumble of drawings and writings on myriad subjects like a continuous stream of consciousness. Two thirds of his notebooks have never been found.
"No certainty exists where none of
the mathematical sciences can be applied."
Develop some long-term relationships.
There is something ironic about the fact that the Mona Lisa was painted by a man with no women in his life. Leonardo da Vinci never married, and he never had any children. Most historians agree that Leonardo was gay, but that doesn't explain why he didn't have some long-term companions other than a 10 year-old boy he adopted.
Listen to Music composed by Leonardo
When he was a student, he was put on trial for lewd conduct. Perhaps this made him very cautious and secretive in later life. But as an engineer and scientist, was he too detached? He seems to be afraid of losing himself in another person when he writes: "The painter must be solitary ... For if you are alone you are completely yourself, but if you are accompanied by a single companion, you are half yourself." Leonardo wrote about love, but did he practice it?
"For in truth great love is born
of great knowledge of the thing loved."
Study basic math even if you are an art student.
Leonardo studied math on his own after he finished his apprenticeship as a painter. He had trouble with arithmetic and calculating square roots in particular. He doubted that some of the rules of arithmetic were even true. Consequently, he turned to empirical methods for solving geometry problems.
"Study the science of art and the art of science."
For example, to find the surface area of a cone, Leonardo rolled a real cone on a plastic surface. From that he measured the area. By experimenting with a real tetrahedron, he determined its center of mass. He discovered a way to create an ellipse by moving segments of a circle. Leonardo described himself as a "disciple of experience." He simply could not "do the math!"
Timeline of Leonardo's
Mathematical Work
Do not over-engineer your inventions.
If you tried to cook dinner in the kitchen designed by Leonardo for Ludivico Sforza, it would probably be your last supper. Leonardo learned the hard way not to over-engineer his designs on this project. He re-modeled the Duke's kitchen by automating the food preparation with some mechanical conveyor belts for moving dishes. He also built a much bigger, more powerful stove. For safety purposes, he installed a sprinkler system overhead to put out any kitchen fires. Leonardo then acted as the head chef on the day of the big banquet. He brought in more than a hundred of his friends to carve each dish as a work of art. You can guess what happened. The conveyor belts did not work; there was total confusion in the overcrowded kitchen; a fire broke out; the sprinkler system rained down on the food making a colossal mess. Leonardo's project should have been a dish washer.
Avoid fads in most things but especially intellectual pursuits.
Leonardo, like many other Renaissance mathematicians, became obsessed with the problem of squaring the circle. Artists and architects of the Renaissance wanted to establish a rational proportional relationship between the circle and the square. Leonardo believed that the quadrature of the circle was the most important problem in geometry. But it turned out to be a mission impossible.
"The quadrature of the circle by Archimedes
is well said and badly given."
Squaring the circle would require that pi, used in calculating the area of a circle, be a precise or a "rational" number. Leonardo did not know that pi is "irrational." The area of the circle is irrational, too. Lambert would prove all this 250 years later in 1761! Leonardo gave up on quadrature problems after 1510. It dashed his ambition of becoming the greatest mathematician of the renaissance.
The Lune-easy of Leonardo
Don't work for the military industrial complex.
In 1483, when Leonardo is 31 years old, he is hired by the Duke of Milan as a military engineer. Milan was the center of arms manufacture in Italy at this time. Why did the young painter make this career switch? Maybe he liked monkeying with machines, like guys working on their cars. He wrote in his notebook:
"Mechanics is the paradise of the mathematical sciences."
It must have paid well because in 1502, he changed jobs and went to work for none other than Cesare Borgia. His job description is chief architect and military engineer. Leonardo spends his last years working for the French Govenor, Charles d'Amboise, and King Francis I. The King gives him a stipend for his retirement, and he dies in 1519 at Cloux near Amboise.
"Science is the Captain, Practice the Soldier."
