https://www.quora.com/Who-would-win-Ramanujan-vs-Gauss-vs-Euler
and
https://www.quora.com/Which-one-is-the-greatest-mathematician-Gauss-or-Euler
Rajat Singh (Indian) says :
Ramanujan (Indian) would obviously. He had the gift to reach places where logic of Euler or Gauss could not take them in 10 lifetimes. Euler and Gauss are at pinnacle of humanity but Ramanujan was more than that, a supernatural entity who pulled equations out of thin air. I am sure Ramanujan's work on partition of numbers is going to be proved even much more important than current age of mathematicians realise.
Chris John says :
On an IQ test, Ramanujan would score lower than both mentioned— that is, he was purely a mathematical thinker. He was poor in his own language as well as academic Sanskrit. He failed history, as well. Gaus and Euler were most definitely competent in the aforementioned subjects (barring Sanskrit, of course). Now, when it comes to mathematical forethought, Euler wins, hands down. Then comes Gauss, and finally Ramanujan. Euler was not just a mathematician who contributed to every field at the time, but advanced physics, too. This, Gauss did not do. Now, if I had to rank them in terms of IQ, here are their scores,
i. Euler— 19o
ii. Gauss— 178
iii. Ramanujan— 155
Strigiformes Wood says :
Euler would be ahead of Gauss, if we consider contribution to human knowledge in terms of papers published. Gauss would be ahead of Euler, if we consider intellectual density and prodigiously complex solutions provided.
So, in short:
Gauss: Density of work in mathematics is unparalleled
Euler: Volume of work in mathematics is unparalleled
However, Gauss was probably intellectually much superior to Euler. As, most of the solutions provided by Gauss were much more complex than any of Euler’s works.
Gauss’ realization that Euclidean geometry was inconsistent was probably the GREATEST conceptualization in the history of mathematics. This thing itself alone outweighs almost all contributions of all mathematicians, except probably the birth of calculus (i.e. the work of Newton and Leibniz).
Alon Amit says :
How well would past masters like Newton, Riemann, Gauss, Euler, Poincare, Abel, Galois, Cauchy, Jacobi and Ramanujan perform if they were to sit for present day challenges like the International Math Olympiad or Putnam/ IMC and asked to solve current problems like those set in the last decade or so?
Awfully. None of them would earn a gold medal.
Olympiad-style math problems have evolved over the last 50 years and developed their own style, assumptions, expectations, standard techniques and character. Doing well on the Putnam or IMO is not easy even for many present day mathematicians, and it’s altogether unreasonable to expect that mathematicians of 100 or 200 years ago would manage to handle them in the allotted number of hours. They would mostly find the questions bizarre.
Let’s look at a random recent IMO problem set, say the 2015 IMO held in Thailand. You can find the problem set here, just choose the appropriate year and language and hit download.
Problem 1: a combinatorial geometry problem about finite point configurations in the plane and the distances they span. For a modern olympiad problem practitioner, this one is fun and only mildly tricky – as well it should be, since it’s a P1, and ought to be disposed of in 25 minutes max if you are to do really well.
However, the grand old wizards named in the question (Newton, Gauss etc.) have never seen anything like it, ever. They would look at it askance, as it doesn’t even feel like a math question at all. Once they’ve digested what is really being asked, some of them may be able to handle it, but the sort of combinatorial analysis required here is quite alien to their way of thinking. My money is on Gauss and Poincaré. Newton, Riemann, Ramanujan and Galois – no way. Euler? If the question was phrased in Latin, and he was in a really good mood, maybe. None of them could write a perfect answer in minutes.
Problem 2: A really tricky problem in elementary number theory. Number theory is home turf for Euler, Gauss, Ramanujan, and sorta for Cauchy and Jacobi as well, but not that kind of number theory. Earning full marks obviously requires writing down a complete, lucid proof, which Ramanujan and Galois couldn’t do if their lives depended on it, and I seriously doubt any modern grader could parse what Newton or Riemann would have written down, if they wrote down anything at all.
Problem 3: Euclidean geometry. Many of those classical mathematicians would be able to easily handle most problems in Euclidean geometry, as this was very much a standard subject in their early training. But still, this one is exceedingly tricky, and without the rigorous training of modern contestants it may take them hours to crack it. I don’t think Galois would find it interesting enough to think about.
I’m not downplaying their genius, just highlighting that the phenomenal genius it took for Riemann to dream up Riemannian Geometry or the prime number formula just isn’t the sort of thing that lets you solve a modern, tricky Euclidean Geometry problem in minutes.
Problem 4: Also Euclidean geometry, though much easier (it’s a P4). Let’s pretend they all got this one.
Problem 5: HAHAHAHA!!! No, fucking, way. None of them would get a single point on this. The whole idea of an arbitrary real-valued function is completely unknown to most of our League of Legends. A “function” just didn’t mean for them what it means for us. They would assume the question is about some sort of smooth, elementary function, or (for a few of them), a power series. You can’t do anything with this question if you think of ff as a power series, and even if you miraculously do, that’s not what the question is asking.
Poincaré is the only one who would maybe understand that the question is about completely arbitrary functions, but this style of questions is, again, completely alien to him. Even with full training in functional equations (of the Olympiad ilk) this one is quite devilish, and I cannot imagine a world where Henri Poincaré figures out this whole style of problems and solves this particular meanie in an hour and a half. Just, no.
Problem 6: I can’t say too much about this one as I didn’t solve it myself. It’s super difficult, and once again, completely outside the realm of the familiar for our superheroes. So, again, just no. Not with those time constraints.
Of course, Putnam would be even harder, in much the same way.
I think the assumptions underlying this question are a bit off: math didn’t stand still since Newton or Poincaré. Olympiad problems generally don’t require any modern result (though they sometimes do, like combinatorial nullstellensatz), but they deeply rely on the culture of math problem solving which evolved in the 20th century, especially the latter half of it. Gauss, Jacobi and Poincaré would make extremely good students in a math olympiad training camp, but they would absolutely need one, a long one, and a whole lot of preparation before they even started, just to catch up on modern notions, definitions and nomenclature. As is, they are unfairly unprepared.
And Galois, I believe, would prefer to die in a duel all over again rather than sit in on an IMO paper.
and
https://www.quora.com/Which-one-is-the-greatest-mathematician-Gauss-or-Euler
Rajat Singh (Indian) says :
Ramanujan (Indian) would obviously. He had the gift to reach places where logic of Euler or Gauss could not take them in 10 lifetimes. Euler and Gauss are at pinnacle of humanity but Ramanujan was more than that, a supernatural entity who pulled equations out of thin air. I am sure Ramanujan's work on partition of numbers is going to be proved even much more important than current age of mathematicians realise.
Chris John says :
On an IQ test, Ramanujan would score lower than both mentioned— that is, he was purely a mathematical thinker. He was poor in his own language as well as academic Sanskrit. He failed history, as well. Gaus and Euler were most definitely competent in the aforementioned subjects (barring Sanskrit, of course). Now, when it comes to mathematical forethought, Euler wins, hands down. Then comes Gauss, and finally Ramanujan. Euler was not just a mathematician who contributed to every field at the time, but advanced physics, too. This, Gauss did not do. Now, if I had to rank them in terms of IQ, here are their scores,
i. Euler— 19o
ii. Gauss— 178
iii. Ramanujan— 155
Strigiformes Wood says :
Euler would be ahead of Gauss, if we consider contribution to human knowledge in terms of papers published. Gauss would be ahead of Euler, if we consider intellectual density and prodigiously complex solutions provided.
So, in short:
Gauss: Density of work in mathematics is unparalleled
Euler: Volume of work in mathematics is unparalleled
However, Gauss was probably intellectually much superior to Euler. As, most of the solutions provided by Gauss were much more complex than any of Euler’s works.
Gauss’ realization that Euclidean geometry was inconsistent was probably the GREATEST conceptualization in the history of mathematics. This thing itself alone outweighs almost all contributions of all mathematicians, except probably the birth of calculus (i.e. the work of Newton and Leibniz).
Alon Amit says :
How well would past masters like Newton, Riemann, Gauss, Euler, Poincare, Abel, Galois, Cauchy, Jacobi and Ramanujan perform if they were to sit for present day challenges like the International Math Olympiad or Putnam/ IMC and asked to solve current problems like those set in the last decade or so?
Awfully. None of them would earn a gold medal.
Olympiad-style math problems have evolved over the last 50 years and developed their own style, assumptions, expectations, standard techniques and character. Doing well on the Putnam or IMO is not easy even for many present day mathematicians, and it’s altogether unreasonable to expect that mathematicians of 100 or 200 years ago would manage to handle them in the allotted number of hours. They would mostly find the questions bizarre.
Let’s look at a random recent IMO problem set, say the 2015 IMO held in Thailand. You can find the problem set here, just choose the appropriate year and language and hit download.
Problem 1: a combinatorial geometry problem about finite point configurations in the plane and the distances they span. For a modern olympiad problem practitioner, this one is fun and only mildly tricky – as well it should be, since it’s a P1, and ought to be disposed of in 25 minutes max if you are to do really well.
However, the grand old wizards named in the question (Newton, Gauss etc.) have never seen anything like it, ever. They would look at it askance, as it doesn’t even feel like a math question at all. Once they’ve digested what is really being asked, some of them may be able to handle it, but the sort of combinatorial analysis required here is quite alien to their way of thinking. My money is on Gauss and Poincaré. Newton, Riemann, Ramanujan and Galois – no way. Euler? If the question was phrased in Latin, and he was in a really good mood, maybe. None of them could write a perfect answer in minutes.
Problem 2: A really tricky problem in elementary number theory. Number theory is home turf for Euler, Gauss, Ramanujan, and sorta for Cauchy and Jacobi as well, but not that kind of number theory. Earning full marks obviously requires writing down a complete, lucid proof, which Ramanujan and Galois couldn’t do if their lives depended on it, and I seriously doubt any modern grader could parse what Newton or Riemann would have written down, if they wrote down anything at all.
Problem 3: Euclidean geometry. Many of those classical mathematicians would be able to easily handle most problems in Euclidean geometry, as this was very much a standard subject in their early training. But still, this one is exceedingly tricky, and without the rigorous training of modern contestants it may take them hours to crack it. I don’t think Galois would find it interesting enough to think about.
I’m not downplaying their genius, just highlighting that the phenomenal genius it took for Riemann to dream up Riemannian Geometry or the prime number formula just isn’t the sort of thing that lets you solve a modern, tricky Euclidean Geometry problem in minutes.
Problem 4: Also Euclidean geometry, though much easier (it’s a P4). Let’s pretend they all got this one.
Problem 5: HAHAHAHA!!! No, fucking, way. None of them would get a single point on this. The whole idea of an arbitrary real-valued function is completely unknown to most of our League of Legends. A “function” just didn’t mean for them what it means for us. They would assume the question is about some sort of smooth, elementary function, or (for a few of them), a power series. You can’t do anything with this question if you think of ff as a power series, and even if you miraculously do, that’s not what the question is asking.
Poincaré is the only one who would maybe understand that the question is about completely arbitrary functions, but this style of questions is, again, completely alien to him. Even with full training in functional equations (of the Olympiad ilk) this one is quite devilish, and I cannot imagine a world where Henri Poincaré figures out this whole style of problems and solves this particular meanie in an hour and a half. Just, no.
Problem 6: I can’t say too much about this one as I didn’t solve it myself. It’s super difficult, and once again, completely outside the realm of the familiar for our superheroes. So, again, just no. Not with those time constraints.
Of course, Putnam would be even harder, in much the same way.
I think the assumptions underlying this question are a bit off: math didn’t stand still since Newton or Poincaré. Olympiad problems generally don’t require any modern result (though they sometimes do, like combinatorial nullstellensatz), but they deeply rely on the culture of math problem solving which evolved in the 20th century, especially the latter half of it. Gauss, Jacobi and Poincaré would make extremely good students in a math olympiad training camp, but they would absolutely need one, a long one, and a whole lot of preparation before they even started, just to catch up on modern notions, definitions and nomenclature. As is, they are unfairly unprepared.
And Galois, I believe, would prefer to die in a duel all over again rather than sit in on an IMO paper.
