Which are the greatest mathematicians of all times?

[a1call]

Originally Posted by rudy235

The most renowned would be without a doubt Sir Isaac Newton if it were a sort of popular contest where the general population with at least a high school education were polled.

But I am not looking for the most popular in the general consensus. I am thinking of the one who has influenced the course on mathematics in general.

I would say of those there is probably a short list of 5, 7, 12, 18. not a lot more. I believe if you take an extended approach many of those are French.

When it comes to mathematics, the greatest would definitely be incomprehensible to the masses, So they should not get a vote.
It's a bit like asking a group of Blind people, which color is the most beautiful.
You should instead get a vote from the mathematicians who are popular to cast a vote. Who do you think Newton would vote for if he gave an unbiased opinion?
Mind you, even Newton might have had difficulty comprehending Euler's thought process.

[rudy235]

Originally Posted by a1call

When it comes to mathematics, the greatest would definitely be incomprehensible to the masses, So they should not get a vote.
It's a bit like asking a group of Blind people, which color is the most beautiful.
You should instead get a vote from the mathematicians who are popular to cast a vote. Who do you think Newton would vote for if he gave an unbiased opinion?
Mind you, even Newton might have had difficulty comprehending Euler's thought process.

Well if I had to vote between Newton or Leibniz with regards to contribution in the specific area of Calculus my vote would be for the latter as I find he did a much better job. If I had to learn calculus with the nomenclature devised by Newton I don't think I would have made much progression.

[rudy235]

Well if I had to vote between Newton or Leibniz with regards to contribution in the specific area of Calculus my vote would be for the latter as I find he did a much better job. If I had to learn calculus with the nomenclature devised by Newton I don't think I would have made much progression.

Speaking of Leibniz I found these very informative articles (it's actually two different writings by a gentleman named one Albert Heisenberg from Brown University in Rhode Island

They address Newton and Leibniz ,

Leibniz's formulation of differential and integral calculus is both deeper and more generalized than Newton's 'fluxions.' Leibniz was probably the last "universal genius" (although Poincaré might have something to say about that). Leibniz was an all-around genius who didn't belong to a Royal Society like Newton did. Moreover, Newton was the head of the Royal Society - a very esteemed coterie of famed English thinkers - and accused Leibniz of plagiarism even though Leibniz invented a superior form of calculus independently. As a result of the priority dispute, Newton defaming Leibniz's name, and the fact that the English empire was to become the most dominant empire (not to mention the lingua franca of what would later become America, Canada, and Australia), Newton's legacy overshadowed that of Leibniz (a German who didn't have the same marketing machine behind him).
Ironically, we use Leibniz's notation, and the calculus we learn today is essentially Leibniz's (e.g. dx/dy etc.), and both Bernoulli and later Euler championed Leibniz's formalism over Newton's, relatively speaking, messy and incongruous work. Dx/Dy is straight from Leibniz.

Leibniz was undoubtedly a mathematical genius but because he isn't English and was engrossed in a priority dispute (thanks to Newton), his legacy was overshadowed for many years. Myths become historical truths, sadly. His ideas won out, however, and among those well-versed in the history of mathematics, he is classed in the same rank with Archimedes, Gauss, and Euler. A truly original thinker, a man of class and ethics, and scholar of inimitable genius.
Having said all that, Newton was a natural mathematical genius whose creations, among MANY other things, include the binomial theorem, optics, and the first (in Europe anyways) reflecting telescope. When you add in his role in launching the scientific revolution and grounding science as a rigorous applied-mathematical field, his reputation is very well-deserved. His remarkable magnum opus The Principia is one of the ten most important works ever written. Of course, all masterpieces are shrouded in myth: the Principia is incredible but it's also riddled with both conceptual and mathematical mistakes, and much of what we call "Newtonian" physics was actually done by Laplace, Lagrange, Hamilton and others. However in the grand scheme of things these are trivial matters when measured against the totality of the tome of genius.

Leibniz should be remembered as Newton's intellectual equal and nothing less. Though Newton's influence was greater because of what he did for science; Leibniz's scope of thought (math, physics, logic, ethics, law, etc) was incredible. History, unfortunately and unfairly, has its own prejudices.

I'll paste the second article at a latter day.

[a1call]

Originally Posted by a1call

When it comes to mathematics, the greatest would definitely be incomprehensible to the masses, So they should not get a vote.
It's a bit like asking a group of Blind people, which color is the most beautiful.
You should instead get a vote from the mathematicians who are popular to cast a vote. Who do you think Newton would vote for if he gave an unbiased opinion?
Mind you, even Newton might have had difficulty comprehending Euler's thought process.

<=>

Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."[4][5] Carl Friedrich Gauss remarked: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it.

https://en.wikipedia.org/wiki/Leonha...20replace%20it.

[Dobri]

Alexander Grothendieck
https://en.wikipedia.org/wiki/Alexander_Grothendieck

[rudy235]

Originally Posted by Dobri

Alexander Grothendieck
https://en.wikipedia.org/wiki/Alexander_Grothendieck

Just 3 days ago there was a very interesting article about him in the New Yorker which I read in its entirety. It is a longish article, about a 7500-word essay. I found it fascinating, Not only as a Mathematician (most of it is beyond my pay grade) but as an individual.

The New Yorker May 8th 2022

[Till]

Originally Posted by Dobri

Alexander Grothendieck
https://en.wikipedia.org/wiki/Alexander_Grothendieck

Recently, Peter Woit picked Grothendieck as the most influential person of the last 100 years in pure maths:
https://www.math.columbia.edu/~woit/wordpress/?p=12868