Gauss v Euler
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 doogly
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Gauss v Euler
I am curious! Gauss v. Euler is one that has come up frequently. I always thought it was obviously Gauss. So obvious, that back in freshman year, when a comrade announced support for Euler over Gauss, we knew he was too drunk to continue being served. But lately I've run into more Euler types, and so I wonder what the forum thinks. Very small sampling also showed the pure math people were more likely to favor Euler, but this may just be because I don't roll with any geometers.
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Re: Gauss v Euler
I used to work in Chicago, in a department store
I used to work in Chicago, I did but I don't anymore
A woman came in, asked for a mathematician
"Which mathematician?" said I
Euler she said, so Euler I did
And I don't work there anymore.
I used to work in Chicago, I did but I don't anymore
A woman came in, asked for a mathematician
"Which mathematician?" said I
Euler she said, so Euler I did
And I don't work there anymore.
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Re: Gauss v Euler
Euler.
[math]e^{i \omega t}=\text{Cos}[\omega t]+i*\text{Sin}[\omega t][/math]
Without that our lives would be pretty much screwed.
[math]e^{i \omega t}=\text{Cos}[\omega t]+i*\text{Sin}[\omega t][/math]
Without that our lives would be pretty much screwed.
 doogly
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Re: Gauss v Euler
Chet wrote:Euler.
[math]e^{i \omega t}=\text{Cos}[\omega t]+i*\text{Sin}[\omega t][/math]
Without that our lives would be pretty much screwed.
This appears not to be due to Euler, but Roger Cotes.
http://www.maa.org/editorial/euler/How% ... 20Hits.pdf
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 Hackfleischkannibale
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Re: Gauss v Euler
Euler, because of his proof of the existence of god.
[math]\frac{a+b^n}{n} = x[/math] Therefore, god exists!
No, I won't explain it, ask wiki.
[math]\frac{a+b^n}{n} = x[/math] Therefore, god exists!
No, I won't explain it, ask wiki.
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Princeps Mathematicorum
You know, I can definitely see picking Euler over Gauss. You just have to have never heard of Gauss.
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Re: Gauss v Euler
I always preferred Euler because he's got this player look about him, all blind and shit but entertaining grandchildren whilst working on some math. "Yeah, whatever, don't care, at least now I have less distractions."
Gauss is more of a reserved type, "ripe but few", with that grumpy, smug old man stare. "I'm sorry as beautiful as your son's contributions are, I have entertained the same thoughts for 20 or so years and to praise it would be tantamoun"
Gauss shut up you pussy, just 'cause you don't have the balls to drop that knowledge on people, even if your achievements are probably greater than Euler's. Euler will smack you with his pimp cane
Gauss is more of a reserved type, "ripe but few", with that grumpy, smug old man stare. "I'm sorry as beautiful as your son's contributions are, I have entertained the same thoughts for 20 or so years and to praise it would be tantamoun"
Gauss shut up you pussy, just 'cause you don't have the balls to drop that knowledge on people, even if your achievements are probably greater than Euler's. Euler will smack you with his pimp cane
Re: Gauss v Euler
Gauss's achievements seem more impressive to me, but he was such a prick. Euler, on the other hand, was kickass in every way.
Of course, Ramanujan would have blown both out of the water had he been around longer.
Of course, Ramanujan would have blown both out of the water had he been around longer.

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Re: Gauss v Euler
Blatm wrote:Of course, Ramanujan would have blown both out of the water had he been around longer.
To say nothing of Abel.
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Re: Gauss v Euler
Or Galois. I would put Riemann above both of them, but as a big fan of number theory Gauss has a special place in my heart.
Re: Gauss v Euler
Gauss for quality, Euler for quantity. But I'm also a big Ramanujan fan. Galois died too young; those French cigarettes are pretty strong....
Anyway, these sorts of questions are difficult to answer, since the later guys mostly had access to the earlier guys' results. Ramanujan is a bit of an exception to that rule, though. Pity he didn't get proper training at an earlier age, and that he got sick from going to Europe.
Anyway, these sorts of questions are difficult to answer, since the later guys mostly had access to the earlier guys' results. Ramanujan is a bit of an exception to that rule, though. Pity he didn't get proper training at an earlier age, and that he got sick from going to Europe.
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Re: Gauss v Euler
For the 20th century: what about Erdős or Grothendieck?
Re: Gauss v Euler
Gauss and Euler are amazing and all, but Riemann might just be the greatest of all time. As for the 20th century, I'm gonna say it's a close call between Hilbert and Grothendieck...
Re: Gauss v Euler
Incompetent wrote:For the 20th century: what about Erdős or Grothendieck?
Easily Erdős. He was so much cooler, just read a short biography. Also, graph theory is awesome.
 doogly
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Re: Gauss v Euler
Riemann, really? I have a hard time putting him in the same class as Gauss. Am I missing some things?
I like Groethy but part of me wants to give it to Godel. I know his beastliness was mostly confined to logic (but also some GR!) but it was a truly revolutionary style. And for 20th century 'died too soon,' definitely Turing. That was tragic.
I like Groethy but part of me wants to give it to Godel. I know his beastliness was mostly confined to logic (but also some GR!) but it was a truly revolutionary style. And for 20th century 'died too soon,' definitely Turing. That was tragic.
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Re: Gauss v Euler
doogly wrote:but part of me wants to give it to Godel. I know his beastliness was mostly confined to logic (but also some GR!) but it was a truly revolutionary style.
Poor old Kurt. It's a bit scary how two of the greatest minds (Cantor & Gödel) to contemplate the infinite went a bit flakey. FWIW, mathematician & science fiction author, Rudy Rucker, had several telephone conversations with Gödel. One of the last phone calls was just a few weeks before Gödel died. He was getting quite paranoid towards the end, and couldn't stay on the phone for very long.
doogly wrote: And for 20th century 'died too soon,' definitely Turing. That was tragic.
As you might guess from my handle, I'm a fan of A. M. Turing. But I think of him more as an allrounder, and a founding father of computer science, rather than as a mathematician, per se.
I certainly recommend reading his biography to anyone vaguely interested in Turing, the Enigma machine, and the foundations of computer science. It was written by Andrew Hodges, one of Penrose's PhD students, who maintains a website dedicated to Turing.
http://www.turing.org.uk/
Last edited by PM 2Ring on Wed Mar 04, 2009 2:54 pm UTC, edited 1 time in total.
 Cleverbeans
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Re: Gauss v Euler
Euler, because he was the whole package. It's especially rare in math history to find such a well rounded human being who was a great mathematician, father, teacher, husband and public figure all at once. A very rare gem.
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Re: Gauss v Euler
Incompetent wrote:For the 20th century: what about Erdős or Grothendieck?
I guess that depends on whether you identify as a problemsolver or a theorybuilder. Actually, you really couldn't have picked a better pair of opposites Ramsey numbers or Grothendieck primes?
As for Riemann, here's a list.
 doogly
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Re: Gauss v Euler
Yeah, but then you have to untangle all the Stiglering. Tricky! And I want to get lunch first.
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Re: Gauss v Euler
I went for Euler out of the 2, but for mathematicians in general I would have gone for Godel, Neumann, and/or Erdos.
Re: Gauss v Euler
Gauss.
But for my money, the three greatest mathematicians of all time were Archimedes, Euler, and Gauss. No one else comes close (screw you, Newton).
But for my money, the three greatest mathematicians of all time were Archimedes, Euler, and Gauss. No one else comes close (screw you, Newton).
Re: Gauss v Euler
We've all forgotten about Cameronv. Inverse mathematics might be the most revolutionary breakthrough in science ever, and will completely change how we do things.
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Re: Gauss v Euler
TheQntty wrote:Incompetent wrote:For the 20th century: what about Erdős or Grothendieck?
Easily Erdős. He was so much cooler, just read a short biography. Also, graph theory is awesome.
I don't know, Grothendieck's biography is also pretty unusual: http://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html
I chose these two because they're kind of at opposite extremes with regard to the kind of areas in which they worked: Erdős posed and solved lots of easily stated and specific problems, with a large number of ingenious tricks, whereas Grothendieck was an architect of Big Theory, on a scale that is yet to be surpassed.
Re: Gauss v Euler
The Euler Lagrange equation is just too important. It demonstrates conservation of energy, momentum, charge......
Re: Gauss v Euler
t0rajir0u wrote:problemsolver or a theorybuilder
Interesting read. And a nice coincidence, because I consider Atiyah to be one of the greatest mathematicians of recent time. Much more than Erdos or Godel.
Between Euler and Gauss, I'd have to pick Gauss. Ancient? Euclid beats Archimedes and Pythagoras combined. Turn of the century goes to Poincare.
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Re: Gauss v Euler
Blatm wrote:We've all forgotten about Cameronv. Inverse mathematics might be the most revolutionary breakthrough in science ever, and will completely change how we do things.
Except Cameron says himself that he's not a mathematician!
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Re: Gauss v Euler
I've always liked otters...
Iono I prefer Johann Peter Gustav Lejeune Dirichlet because the Dirichlet function was the first everywhere discontinuous function I learned.
Between Gauss and Euler, I say Euler. I know Gauss from Electrostatics and statistics, while I know Euler from mechanics (Lagrangian) which I prefer.
I'm very biased in my views...
Iono I prefer Johann Peter Gustav Lejeune Dirichlet because the Dirichlet function was the first everywhere discontinuous function I learned.
Between Gauss and Euler, I say Euler. I know Gauss from Electrostatics and statistics, while I know Euler from mechanics (Lagrangian) which I prefer.
I'm very biased in my views...
Re: Gauss v Euler
Look this is Cameronv, it is not about who is great, but it is about understanding the whole realm of mathematics as 1 . Yesterday one of you greats unravelled the final mystery of mathematics in the forum(1=1) for me I observed, understand this please
The "undiffracted" value of linear is +1 at vector 19, is equal to the diffracted value of linear as 1 inverse/curved by sequence. Thus both are equal in value in the sequence. Curved is a diffraction of linear mathematics and most of space/mass and time are curved.
The "compacted" value of 1 curved/inverse is =+1 for time space , mass , energy , as K max Constant. Thus mathematics is inverse/linear without a doubt.
"Conal progression and inversion at vector 19" is the ONLY Mathematics that connects your linear mathematics to inverse/curved mathematics/linea, limited by zeros minimum and maximum, inverse and absolute.
The SUMMATION of all mathematics is thus Absolute 1, which by sequence is both inverse and linear "mathematical summation sequence" is thus the infinity sequence
Absolute 1 .0 .1+ .1.+1 .0 . 1 Absolute.
"thus is to see the whole of eternity in a grain of sand " is the final answer fellows, There is only one great, Absolute 1, one awesome we all exist by grace, and by grace great discoveries come to all of us.
The "undiffracted" value of linear is +1 at vector 19, is equal to the diffracted value of linear as 1 inverse/curved by sequence. Thus both are equal in value in the sequence. Curved is a diffraction of linear mathematics and most of space/mass and time are curved.
The "compacted" value of 1 curved/inverse is =+1 for time space , mass , energy , as K max Constant. Thus mathematics is inverse/linear without a doubt.
"Conal progression and inversion at vector 19" is the ONLY Mathematics that connects your linear mathematics to inverse/curved mathematics/linea, limited by zeros minimum and maximum, inverse and absolute.
The SUMMATION of all mathematics is thus Absolute 1, which by sequence is both inverse and linear "mathematical summation sequence" is thus the infinity sequence
Absolute 1 .0 .1+ .1.+1 .0 . 1 Absolute.
"thus is to see the whole of eternity in a grain of sand " is the final answer fellows, There is only one great, Absolute 1, one awesome we all exist by grace, and by grace great discoveries come to all of us.
Re: Gauss v Euler
Matterwave1 wrote:I know Gauss from Electrostatics and statistics, while I know Euler from mechanics (Lagrangian) which I prefer.
Gauss is much more wellknown in mathematical circles for his contributions to number theory. It's really quite a shame that he took a shine to physics and astronomy later on.
 doogly
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Re: Gauss v Euler
t0rajir0u wrote:Matterwave1 wrote:I know Gauss from Electrostatics and statistics, while I know Euler from mechanics (Lagrangian) which I prefer.
Gauss is much more wellknown in mathematical circles for his contributions to number theory. It's really quite a shame that he took a shine to physics and astronomy later on.
Well, I wouldn't say it is a shame... and his number theory is top notch, but I came to him for the geometry.
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Re: Gauss v Euler
These two sum up my view on the subject:
If we are thinking of all time greats, let us not forget Archimedes, Brahmagupta, Khayyam and the like.
I really don't think the field of mathematicians has a well defined norm.
stockford wrote:I always preferred Euler because he's got this player look about him, all blind and shit but entertaining grandchildren whilst working on some math. "Yeah, whatever, don't care, at least now I have less distractions."
Gauss is more of a reserved type, "ripe but few", with that grumpy, smug old man stare. "I'm sorry as beautiful as your son's contributions are, I have entertained the same thoughts for 20 or so years and to praise it would be tantamoun"
Gauss shut up you pussy, just 'cause you don't have the balls to drop that knowledge on people, even if your achievements are probably greater than Euler's. Euler will smack you with his pimp cane
Pathway wrote:You know, I can definitely see picking Euler over Gauss. You just have to have never heard of Gauss.
If we are thinking of all time greats, let us not forget Archimedes, Brahmagupta, Khayyam and the like.
I really don't think the field of mathematicians has a well defined norm.
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Re: Gauss v Euler
Gauss is to Beethoven as Euler is to Mozart. Now it's a composer war. Que the jokes about composition.
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Re: Gauss v Euler
thoughtfully wrote:Gauss is to Beethoven as Euler is to Mozart. Now it's a composer war. Que the jokes about composition.
I vote Wagner.
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Re: Gauss v Euler
...Kronecker?
 doogly
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Re: Gauss v Euler
Kronecker loses on account of "What good your beautiful proof on [the transcendence of] π? Why investigate such problems, given that irrational numbers do not even exist?" This is a silly thing to say.
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Re: Gauss v Euler
Both have a very avuncular charm, I'll give them that. Actually I'm reading a very very well written book called Men of Mathematics that's a' goin' through all these folk. Haven't quite gotten through it yet, but it did redeem Newton for me. (Always thought he was a curmudgeonly old bastard, turns out he was a mostly all right guy.)
But I like topology, and, arguably, that was Euler's doing in the first place. Oh, and Gauss didn't learn from Newton's mistake and let, nay, encouraged Riemann (from what I understand) into publishing nonEuclidean geometry because he was scared.
But I like topology, and, arguably, that was Euler's doing in the first place. Oh, and Gauss didn't learn from Newton's mistake and let, nay, encouraged Riemann (from what I understand) into publishing nonEuclidean geometry because he was scared.
Re: Gauss v Euler
ieattime20 wrote:Both have a very avuncular charm, I'll give them that. Actually I'm reading a very very well written book called Men of Mathematics that's a' goin' through all these folk. Haven't quite gotten through it yet, but it did redeem Newton for me. (Always thought he was a curmudgeonly old bastard, turns out he was a mostly all right guy.)
Take what you read in there with a grain of salt. That book is quite infamous for its chapter on Galois, most of which is just not true. The MAA called it "pretty free with the truth."

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Re: Gauss v Euler
ieattime20 wrote:Both have a very avuncular charm, I'll give them that. Actually I'm reading a very very well written book called Men of Mathematics that's a' goin' through all these folk. Haven't quite gotten through it yet, but it did redeem Newton for me. (Always thought he was a curmudgeonly old bastard, turns out he was a mostly all right guy.)
But I like topology, and, arguably, that was Euler's doing in the first place. Oh, and Gauss didn't learn from Newton's mistake and let, nay, encouraged Riemann (from what I understand) into publishing nonEuclidean geometry because he was scared.
Newton basically destroyed Leibniz because he kept insisting that he discovered calculus first. So, iono how swell of a guy Newton really was. XD

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Re: Gauss v Euler
auteur52 wrote:Take what you read in there with a grain of salt. That book is quite infamous for its chapter on Galois, most of which is just not true. The MAA called it "pretty free with the truth."
Zee von by herr Bell? Well, crap monkeys. Granted it was written back in '39, but is there anything else I need to doublecheck after reading?
And, well, do you have any other recommends? I have a preference for books that tell quirky stories, but I'd be especially interested in those discussing the topic of this post.
Matterwave1 wrote:Newton basically destroyed Leibniz because he kept insisting that he discovered calculus first. So, iono how swell of a guy Newton really was. XD
This may be one of the snags ^^ was talking about. From what I read, the accusations of plagiarism spewed mostly from their 'followers' and the two remained terse and civil throughout Newton's life. In any case, though dying in a shitty way, Liebniz got the last laugh by letting the Continent leave the UK behind in mathematics almost 100 years.
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Re: Gauss v Euler
Maybe you will like Grothendieck stories! He has come up here, these are some humbling ones:
In the early sixties, Grothendieck visited Harvard while Zariski was still a faculty member. Once, while Zariski was lecturing in a seminar, Grothendieck kept asking him why he didn't prove his result for all schemes, not just varieties, but Zariski simply responded that it didn't work. Eventually, Grothendieck could stand it no longer and went to the blackboard and began writing down a proof for schemes. While he did so, Zariski wrote down a counterexample. When Grothendieck realized he was wrong, Zariski said (in his heavily accented RussoItalian English) "In my time, I have had to learn many languages." At this, Grothendieck turned bright red from embarrassment.
Another time Zariski was lecturing and Grothendieck again asked him why he didn't generalize his work to schemes. This time Zariski merely said "Now now Alexander, we must show some self control."
Reported by Milne
In the early sixties, Grothendieck visited Harvard while Zariski was still a faculty member. Once, while Zariski was lecturing in a seminar, Grothendieck kept asking him why he didn't prove his result for all schemes, not just varieties, but Zariski simply responded that it didn't work. Eventually, Grothendieck could stand it no longer and went to the blackboard and began writing down a proof for schemes. While he did so, Zariski wrote down a counterexample. When Grothendieck realized he was wrong, Zariski said (in his heavily accented RussoItalian English) "In my time, I have had to learn many languages." At this, Grothendieck turned bright red from embarrassment.
Another time Zariski was lecturing and Grothendieck again asked him why he didn't generalize his work to schemes. This time Zariski merely said "Now now Alexander, we must show some self control."
Reported by Milne
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