Why da Vinci was not an engineer, scientist, or mathematician

Why da Vinci was not an engineer, scientist, or mathematician

Leonardo da Vinci is considered the quintessential “Renaissance Man,” one who excels at all forms of intellectual endeavors. He is honored as a genius, some say the greatest genius the world has ever known-an artist, a mathematician, a scientist, and an engineer. But does he deserve these accolades? No. And bestowing them upon him belittles those who truly are great mathematicians, scientists, or engineers.

Leonardo da Vinci definitely created great artwork, though for my taste he doesn’t match the grandeur, detail, or power of Michelangelo his peer. Da Vinci invented painting techniques like sfumato for creating a delicate shading for more realistic human features, though other techniques for which he is credited were actually developed by other painters such as and chiaroscuro that was developed and perfected by Caravaggio, Correggio, and Rembrandt1. I acknowledge he was a great artist-he created artwork that has been appreciated worldwide for centuries. But da Vinci, known for a problematic lack of attention, rarely finished any of his works. The Last Supper painting is incomplete2. His Gran Cavallo horse statue was never finished3. He left the monastery of San Donato before finishing the Adoration of the Magi that he had been commissioned to produce4. The list goes on. Even the Mona Lisa background seems to me drab and amateurish, like an attempt to just get the portrait done so he could move on, a fact described by a witness to the original painting, Giorgio Vasari, a biographer and painter himself5. Modern day art historians and fans of da Vinci make all kinds of excuses for his impatience and impulsiveness. One fan states that Vinci “fell victim to those individuals jealous of his genius labeled him a man who did not finish his commissions as the [Gran Cavallo] was meant to be made of bronze, not clay.”6 Another fan claims that the payment terms were so complex that he probably wouldn’t have received any compensation anyway. So get bored and leave-thankfully other artists, like Vincent van Gogh or Michelangelo, had a different attitude and struggled to complete their works out of passion and love.

Da Vinci Was Not a Mathematician

Although I’ve dabbled in art and art history, I am not an expert. However, I am an expert in mathematics, science, and engineering, having had a rigorous education in these fields and having worked for several decades in them. I’ve known true brilliant people in these areas. To my knowledge Leonardo da Vinci never wrote down an equation, even one as simple as basic algebra. He just didn’t seem to understand math7. Some credit him for understanding the golden ratio, but the golden ratio is simply two numbers-a width and a length-and had been known at least since the days of the Greek sculptor and mathematician Phidias, a thousand years before da Vinci8. Da Vinci came up with interesting mathematical ideas but never investigated one and never proved one. He spat out interesting possibilities in his notebooks, using a notation that has not been deciphered. Very few, if any, of his “mathematical ideas” turned out to be correct9. In fact, search the books, the Internet, or entire libraries, and you won’t find a single, tiny original contribution that da Vinci made to mathematics.

Mathematicians don’t guess at their answers. They study various techniques, sometimes for years. They learn how to use multiple mathematical models to find a solution. They compare alternative ways of performing calculations. They generalize the problems to solve categories of problems. They test their answers and try to find fault in them, try to tear the solution apart. Only after this long effort born of creative spark but nurtured by perseverance do they create something worthy of being labeled genius. Da vinci was far from a mathematical genius and giving him the title of mathematician demeans those who have spent their lives examining the beauty of numbers and their relationships.

Da Vinci Was Not a Scientist

Scientists practice the scientific method. They come up with hypotheses based on observations or the works of others, but that’s simply the very beginning. Every curious child imagines reasons why the world works the way it does. Most of them are fantastic and some turn out to be true. Ancient people thought the world was flat, supported by tortoises. But even the ancient Greeks, two thousand years before da Vinci, created the scientific method used by Archimedes, Aristotle, Hippocrates, Ptolemy, and many others10. Roger Bacon, two hundred years before da Vinci, was making discoveries and promoting the scientific method11. All that da Vinci did was write fantastic theories in his notebooks but never once devised experiments to test them. Had he done that, he would have found that most of his theories were completely wrong. Again, there is not a single known, novel scientific principle that can be attributed to da Vinci. But at that same time, real scientific geniuses like Nicolaus Copernicus were changing our understanding of the solar system forever. To call da Vinci a scientist is like calling a curious kindergartener a scientist. It is an insult to those real scientists who spend their lives not just observing and hypothesizing, but testing, poring over results, retesting, studying the works of others, refining their own work, creating new theories, and eventually giving us more knowledge about how the universe functions.

Da Vinci Was Not an Engineer

Da Vinci was often given credit for the inventions of others, simply drawing machines, bridges, weapons, and other devices that had been written up by others or actually built by others12. In fact most of his so-called inventions including diving suits and flying machines had been drawn up extensively by others13. Scientist Roger Bacon had drawn plans for an ornithopter 200 years before da Vinci and flying machines had been discussed and drawn since ancient times14. Modern attempts to build even a single one of da Vinci’s inventions have all failed because da Vinci didn’t understand materials or forces or structures or math or any engineering requirements. He never built any of his inventions; he simply drew them and in a few cases built small, non-working models. Engineering requires a deep understanding of mathematics and science. It also requires testing and experimenting and calculating and retesting and improving, leading to eventual success. As Thomas Edison famously said, it is 1 percent inspiration and 99 percent perspiration. It requires more than just dreaming and drawing, which is as far as da Vinci ever got. Honoring da Vinci as an engineer, let alone a brilliant one, denigrates the accomplishments of those engineers who spend years planning and measuring and calculating and building and rebuilding and creating the wonderful inventions that simplify or improve our lives.

Give Credit Where Credit is Due

In summary, da Vinci was a great artist, debatably one of the best who ever lived. Certainly the most famous. But to call him an engineer, scientist, or mathematician, let alone a brilliant one, is simply not true and is an insult to those who devote their lives and their energies to these important human endeavors.


  1. Marion Boddy-Evans, Painting in the Style of Old Masters: Sfumato and Chiaroscuro, retrieved July 26, 2011.
  2. Seen with my own eyes, the bottom left corner was never completed.
  3. Leonardo Da Vinci Paintings, Inventions & Biography!, retrieved July 26, 2011.
  4. Adoration of the Magi,retrieved July 26, 2011.
  5. Giorgio Vasari, Lives of Seventy of the most eminent Painters, Sculptors and Architects (of the Renaissance), 1550.
  6. Leonardo Da Vinci Paintings, Inventions & Biography!, retrieved July 26, 2011.
  7. How Not to Think Like Leonardo da Vinci, retrieved July 26, 2011.
  8. The Beauty of the Golden Ratio, retrieved July 26, 2011.
  9. Dirk Huylebrouk, Lost in Triangulation: Leonardo da Vinci’s Mathematical Slip-Up, retrieved July 26, 2011.
  10. Norman W. Edmund, Scientific Method History, retrieved July 26, 2011.
  11. Brian Clegg, Review – The First Scientist, retrieved July 26, 2011.
  12. Web Gallery of Art, Drawings of engineering themes, retrieved July 26, 2011.
  13. Leonardo: the Man, His Machines, retrieved July 26, 2011.
  14. Ornithopter Flying Machines: The Ancient Origins of an Invention, retrieved July 26, 2011.

Guidelines for lawyers dealing with experts

Most lawyers know the importance of treating experts with respect. Even if we turn out to be ignorant, arrogant, immature idiots, we hold the keys to presenting the facts and the analysis that will win your client’s case or at least put it in the best light possible given all of the facts. If we’re going to testify, you want us feeling good about it, about the client, about you, and about ourselves. Most attorneys know this but some, in the emotion of the “battle,” forget this. Here’s a checklist to serve as a reminder.

  • Have us give input into schedules. We know best how much work an analysis is going to take. And some of us have lives outside of work (not me, but I’ve heard that others do). Don’t give us a schedule without our input and expect us to meet it.
  • Don’t hire us just to keep us off the other side. I’ve had this happen. It’s flattering, but it’s also unethical. I need to make a living. Also I will never work for you again, and I will warn my colleagues about you.
  • Involve us with crafting the strategy. Don’t let us work in the dark and then complain, for example, that our invalidity argument hurts the non-infringement argument or vice-versa. And by the way, a great argument for one will always make the other much more difficult to show.
  • Involve us with claim construction. We have the appropriate experience to figure out a decent claim construction. Too often I’m called into a case where the claim construction makes little sense to me. I need to be educated about how the claims are construed and then I need to see if I can work with them. Sometimes adding or removing a word from the claim construction would make things significantly easier for me to understand and explain to the judge and jury.
  • Give us enough time to do our jobs. Maybe this is a pipe dream. Lately, cases have been more and more compressed and I’m brought in later, probably to save costs. But it hurts the case and stresses us out.
  • Don’t antagonize us. We’re they guys who are going to help your client by clarifying their position and explaining difficult concepts to the judge and/or jury. You don’t want us ticked off, even if we really are stupid jerks. You want us in a good frame of mind and happy about what we’re doing. At least until we’re done testifying.
  • Explain your positions to us patiently. If you can’t get us to understand it and adopt it, how can you get a judge or jury?
  • Don’t tell us we have to adopt your positions or we’ll lose the case. We’re independent and unbiased. The threat of losing the case is not a reason for us to support your position, and stating this can come back to haunt both of us eventually.
  • If things aren’t going well, meet face-to-face. It’s easier to communicate about difficult subjects. It’s easier to wave hands, draw diagrams, point to things. And it’s more likely for both to see each other as humans, not someone being difficult.
  • Don’t expect us to understand all the legal issues. I’ve met lawyers who didn’t understand all the legal issues. I actually do understand legal issues more than most experts because of my experience and my writing on the topic. Yet there are still gaps. And the lawyers can disagree. I’ve been in many long sessions where lawyers argued about legal issues.
  • Don’t believe you understand all the technical issues. Some of the lawyers I’ve met were once great engineers. Others have no engineering experience whatsoever. Some will take my word completely and others will fight me. I don’t mind reasoned debateā€”in fact I enjoy it. But remember that my understanding of the technical issues is ultimately what I will present in my reports and my testimony.
  • Be clear in your instructions. We know you’re in a hurry, but this is critical to getting good information. I’ve had cases where I got a quick call to do some analysis and then spent the weekend setting up equipment, getting results, and writing a report, only to find there had been a miscommunication about what was needed. Sure I get paid per hour, but I’d still like to know I’m doing something useful. I’m sure you and your client prefer that too.
  • Have us sit in on depositions. We can add a lot of knowledge and we can help craft the direction of the questioning. I was in one deposition where, searching the Internet, I found an expert’s presentation slides promoting a software method while she was testifying she would never ever use such an “unreliable” method. I’ve also had lawyers call me after a “very successful” deposition where they thought they’d uncovered some really useful facts but were asking questions about the wrong technology.
  • Don’t write the reports and expect us to just sign it. Our reputations and careers are on the line, not yours. Unfortunately, some experts do this and collect their checks. I won’t and neither will any expert worth his or her hourly rate.
  • Expect us to sleep some time. OK, the lawyers themselves get little sleep during a case. Me too. I just prefer that you act as though you care about my getting rest even though we both know I won’t. So don’t tell me to be available at midnight, ask me if I can please make myself available at midnight even though you know it’s a burden. It just sounds nicer.
  • Pay us on time or be honest about any problems. Sometimes clients run into financial trouble. I prefer to work for a client who is honest about financial trouble than one who constantly tells me “the check is in the mail.” Usually this is an issue with the client not the lawyer, but I’ve had lawyers misplace my final invoice, simply because they had moved onto other more pressing matters. My payment is a pressing matter, and a late or missing payment means I’m unlikely to be available the next time you need my expertise.
  • Don’t negotiate our fees after the case is over. This is just poor business practice and makes me not want to work with you again. The time for negotiation is before hiring me, not after I’ve put in time on the case.
  • Remember that our job is to be honest and unbiased. Expect us to point out the bad along with the good. If we find your client’s case doesn’t have merit, at least be happy we discovered that before the other party’s expert informed you at trial. You can settle early or limit the damages or just know that you did the right thing.