It's also pretty astounding how big of a gap there is between even people at the very top, people high enough so that none of us could really tell the difference on our own. Ex: Jeff Bezos realized at Princeton that he was thoroughly outclassed by a small group of people in his physics classes who seemed superhuman to him - but lots of Amazon's employees have described him as a genius who corrects them on novel technical subjects he's never seen before. Likewise, at least according to Paul Allen, Bill Gates was intimidated by some of his classmates in the math classes at Harvard (in particular, Math 55), yet he's described pretty much universally as a genius with a frightening technical aptitude (who also came up with a novel pancake sorting algorithm as an undergraduate just days after learning about the topic).
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I don't think the contest is even close. What sets da Vinci apart from the rest of the top minds is that da Vinci is the epitome of a polymath. He was so highly skilled in so many areas that it is a feat that I do not believe will be repeatable without modern technological intervention (extending life, nootropics, and technologically assisted information assimilation).
It's like having someone win the Nobel Prize in Chemistry, Physics, Medicine, the Copley Prize, Pulitzer Prize, Praemium Imperiale (sculpting award from Japan), the Turing Award and perhaps a few others. No such person exists. It's just not possible to be that amazing in all those areas. And especially for his time.
Take a look at a list of top minds. What do they all have in common? They excel to the extreme in one to a few areas but usually just one. Because it is not possible to be a top mind in many areas - there's just not enough brain power or time to accomplish this in a single human life.
This is why when I see the public voted lists of "top minds of all time", I don't put much weight into them. I do not think most people understand how far and away da Vinci is from the rest of the people in the usual top mind lists.
I'd say the likes of Von Neumann and Goethe rival Da Vinci in breadth and far surpass him in depth for fields outside of art. Someone like Thomas Jefferson has a decent case for being at/above Da Vinci, and frankly I don't think Jefferson is on the level of someone like Newton, not in sheer intellect.
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Von Neumann gets his areas of expertise in mathematics, physics, economics, statistics and computer science. What is missing from this list? Do you see my point, now, about why no one comes close to da Vinci? Goethe is less impressive than Von Neumann. Both amazing minds, no doubt. But it's like comparing a person who impressively ran 100Km to a person who ran 1,000,000Km in the same time.
Also, the depth da Vinci contributed to each area vastly surpasses any others in History, overall. I am not the only person to hold this opinion, of course.
There's a huge difference between having expertise in 20th century math / physics / economics / statistics / computer science and the wide range of 15th century topics Da Vinci wrote about. E.g.: is it harder to take seven high school classes or three graduate ones? If you read some of Von Neumann's papers (many of which were revolutionary), they're leagues beyond any amount of knowledge that existed in Da Vinci's time. Da Vinci, meanwhile, did not make the same level of academic contributions as someone like Neumann, and certainly not someone like Einstein or Newton.
Granted, you could also say that Da Vinci had a lot less to work with, so it's difficult to compare them. They're both brilliant enough that you almost find it hard to believe their wikipedia pages.
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You're correct, da Vinci's is far more impressive because of the time he was born in and accomplished the things he did. Imagine how scary this person would be if he was born today? A formal education built on the knowledge of yesteryear's top minds just does not compare to the world da Vinci was born into. It is also part of why many scientists regale da Vinci's accomplishments...it seems impossible to comprehend someone could take those subjects as far as he did without the benefit of the knowledge we have, today.
Let me make it easier on you: I do not think you're spending your time wisely debating this topic with me. No such person exists that tick as many boxes as da Vinci. No one known to history. It's not possible to come up with a more accomplished and varied polymath than da Vinci. You're not going to change my position because there's nothing to debate and I cannot objectively choose a different position. Even if I did, the facts would not change and I'd be wrong. We simply do not have another person in history to choose.
Newton, despite being a mega dick. No one changed Maths and Science like him. Tesla is two for ushering in the 2nd industrial revolution with the electric motor. Davinci's most interesting feat in my opinion was his heart valve which actually worked and to a point influenced modern design. Did he ever finish that bowl of soup?