- #71

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- #71

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- #72

^_^

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More people should be talking about Dirac...I feel sad.

- #73

mathwonk

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- #74

Gokul43201

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- #75

mathwonk

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- #76

Gokul43201

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- #77

Did anyone mention Euclid?

- #78

FulhamFan3

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To me Gibbs is the greatest american scientist of all time.

- #79

afton

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are some great ones like Newton and Einstein but we are all standing

on the shoulder of the giants.

- #80

Curious3141

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If you're including mathematicians and physicists, then 5 is probably not enough. :) But let me try (in no particular order, really):

1. Gauss (math)

2. Newton (math and physics)

3. Einstein (physics)

4. Euler (math)

5. Wiles (math)

Yeah, I know, the last one is going to be controversial but who among us has solved an age old vexing mathematical question in his/her lifetime ? ;)

If we're talking about greatest philosophers, I'd have to consider people like Gödel and Kant. If the criterion were greatest genius level accomplishments in a lifetime, Da Vinci would be right up there, but Newton would almost certainly be up there too. If sheer cognitive power were to decide the ranking, I'd need to include William James Sidis, who didn't accomplish all that much, but*could've*.

1. Gauss (math)

2. Newton (math and physics)

3. Einstein (physics)

4. Euler (math)

5. Wiles (math)

Yeah, I know, the last one is going to be controversial but who among us has solved an age old vexing mathematical question in his/her lifetime ? ;)

If we're talking about greatest philosophers, I'd have to consider people like Gödel and Kant. If the criterion were greatest genius level accomplishments in a lifetime, Da Vinci would be right up there, but Newton would almost certainly be up there too. If sheer cognitive power were to decide the ranking, I'd need to include William James Sidis, who didn't accomplish all that much, but

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- #81

tornpie

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I got a couple of females to add that held their own too

Olga Ladyzhenskaya

Emmy Noether

Sofia Kovalevskaya

I think I'd have to break up my list into math and physics. My list for math would probably look something like this though:

Gauss

Riemann

Euler

Hilbert

von Neumann

Doh, no room for Archimedes.

For physics:

Newton

Einstein

Dirac

Feynman

Maxwell

- #82

learningphysics

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I haven't seen these two mentioned yet (I didn't go through the entire thread tho):

Laplace

Fourier

Laplace

Fourier

- #83

X-43D

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I think that the best mathematical physicists (of today) are:

1. Edward Witten

2. Michio Kaku

3. Robert M. Wald (see http://physics.uchicago.edu/t_rel.html [Broken])

4. John Baez

1. Edward Witten

2. Michio Kaku

3. Robert M. Wald (see http://physics.uchicago.edu/t_rel.html [Broken])

4. John Baez

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- #84

Chrono

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X-43D said:I think that the best mathematical physicists (of today) are:

1. Edward Witten

2. Michio Kaku

3. Robert M. Wald (see http://physics.uchicago.edu/t_rel.html [Broken])

4. John Baez

Michio Kaku is probably the best one of today, I think. His first apperance on TechTV basically changed my life. Even more so after I read Hyperspace.

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- #85

mathwonk

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an english translation of riemanns works just came out and i am blown away by it. after spending my entire scientific career studying "riemann surfaces" i am learning things from his original papers i never understood before.

he dismisses things in 2 sentences that I thought were difficult. I recommend this work extremely highly, although I admit that even as an "expert" on this material it is taking me up to a week sometimes to read one page.

It is worth it though, since a week to understand something is less than 25 years not to.

It is now clear that much of the modern "sheaf theoretic" treatments of riemann roch theorems are nothing but an abstract reformulation of riemann's original conception of the topic.

what a visionary.

for example the riemann roch theorem, i.e. the problem of computing the number of independent meromorphic functions with pole divisor dominated by a given divisor D, is merely that of computing the rank of a certain matrix

from C^d to C^g, where d is the degree of the given divisor.

Riemann shows the kernel of the map has dimension one less than the dimension of the space of functions.

Hence the riemann inequality says; l(D)-1 = one less than the dimension of the space of meromorphic functiuons witrh pole divisor supported in D,

lies between d and d-g, i.e. l(D) -1 is at least d-g and at most d.

i.e. l(D) is at least d-g+1 and at most d+1.

this is riemanns famous inequality.

then the so called riemann roch theorem, computes this matrix more precisely as the g by d matrix with (i,j) entry wi(pj) where wi is the ith basic holomorphic differential, and pj is the jth point of the divisor D.

hence the rank of the matrix equals g - l(K-D) where K-D is the space of holomorphic differentials vanishing on D.

thus l(D)-1 + g-l(K-D) = d, i.e. l(D) = d+1-g + l(K-D), the full clasical RRT.

thats all. how simple is that? try getting that from any modern book, in that succint a form.

he dismisses things in 2 sentences that I thought were difficult. I recommend this work extremely highly, although I admit that even as an "expert" on this material it is taking me up to a week sometimes to read one page.

It is worth it though, since a week to understand something is less than 25 years not to.

It is now clear that much of the modern "sheaf theoretic" treatments of riemann roch theorems are nothing but an abstract reformulation of riemann's original conception of the topic.

what a visionary.

for example the riemann roch theorem, i.e. the problem of computing the number of independent meromorphic functions with pole divisor dominated by a given divisor D, is merely that of computing the rank of a certain matrix

from C^d to C^g, where d is the degree of the given divisor.

Riemann shows the kernel of the map has dimension one less than the dimension of the space of functions.

Hence the riemann inequality says; l(D)-1 = one less than the dimension of the space of meromorphic functiuons witrh pole divisor supported in D,

lies between d and d-g, i.e. l(D) -1 is at least d-g and at most d.

i.e. l(D) is at least d-g+1 and at most d+1.

this is riemanns famous inequality.

then the so called riemann roch theorem, computes this matrix more precisely as the g by d matrix with (i,j) entry wi(pj) where wi is the ith basic holomorphic differential, and pj is the jth point of the divisor D.

hence the rank of the matrix equals g - l(K-D) where K-D is the space of holomorphic differentials vanishing on D.

thus l(D)-1 + g-l(K-D) = d, i.e. l(D) = d+1-g + l(K-D), the full clasical RRT.

thats all. how simple is that? try getting that from any modern book, in that succint a form.

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- #86

wisredz

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Anyway, my list for mathematicians would include Isaac Newton, Leibniz, Euler, Riemann and Gauss.

The list for phsyicists consists of Isaac Newton, Prof. Feynman, Albert Einstein.

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latyph

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- #88

quasar987

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- #89

Sleazy Saint

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Cantor also belongs on the list. His brilliant ideas of the different cardinalities of infinite sets netted him huge amounts of flak from contemporary mathematicians. So much so, he had a nervous breakdown. But guess who ended up getting the last laugh?

I'm surprised that Godel wasn't mentioned more. I'm also surprised Descartes has't been mentioned.

Finally, not one person has mentioned Edward Lorenz, discoverer of the so-called "butterfly effect". He essentially jump-started interest in chaos theory, single-handedly

- #90

mathwonk

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but i am very impressed with his work, and (although i am guessing here, not having read but a tiny amount of gauss), i suspect gauss excelled at proving things rigorously.

riemann on the other hand apparently excelled at seeing true phenomena which lie deep, even when he could not completely prove them, due to lack of sufficiently sophisticated mathematics. he seems to have been inspired also by physical insight, to have faith in the correctness of his results.

so there are many different qualities which can make someone seem great. we are probably on shaky ground comparing them until we have read and understood them however, and this seems to be a job for more than one lifetime.

so far I am only through riemann's thesis, and about half of his abelian functions paper.

i admire Newton for his concept of limit, as basic to derivatives. It seems to me that the previous understanding of derivatives, due to fermat, and descartes, is insufficient to achieve the fundamental theorem of caculus in the generality of Newtons point of view. I also like Newton's proof of the integrability of monotone functions.

unfortunately i have read extremely little of Newton as well.

- #91

IsotropicSpinManifol

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why einstein is better than Newton

mc^2<mc^2

therefor

Newton < einstein

mc^2<mc^2

therefor

Newton < einstein

- #92

bomba923

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Personally, my top two are

Riemann (1st) &

Euler (2nd)

Riemann (1st) &

Euler (2nd)

- #93

mathwonk

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i like that list. interesting remark: riemann only published 9 papers, so he might not even get tenure at a state university these days. and he probably had no grant support. the paper in which he described the intrinsic curvature tensor did not even win the award he submitted it for. his story is really unbelievable. the idea that metric notions derived from observations of phenomena in the large may not hold in physics of the immeasurably small is due to him. he pointed out that if we assume rigid bodies mjy be transformed anywhere in space without changing their shape it only implies space has constant curvature. and that if this curvature happens to be positive, no matter how small, then space is necessarily finite. all this is decades before einstein. his development of necessary and sufficient conditions for functions to be represented by Fourier series resembles the standard treatment by zygmund studied today. his formulation of the concept of fractional differentiation via gamma functions and fractional integrals, relating it to abels equation is still the form used today. he basically invented topology. his theory of complex variables revolutionized the subject, and brought algebraic geometry out of the elementary stages into a flourishing deep theory. he invented differentiable manifolds, and generalized gauss's theory of curvature of surfaces to arbnitrary dimensions. he initiated the study of "moduli" spaces of geometric objects, primarily complex curves, and line bundles on them, and computed their dimensions. his riemann roch theorem serves as the model for generalizations up until the present time, by enriques-severi, hirzebruch, grotyhendieck, atiyah-singer, baum - fulton - macpherson,...

his clear precise definition fo the riemann integral takes about 5 lines, and is immediately followed by a characterization of riemann integrable functions that is immediately shown to be equivalent to saying the set of dicscontinuties has "measure" zero. this theory which is what most people asociate with his name, is merely a brief remark on his way to studying Fourier series.

it goes on and on... i don't really see how anyone person could have done all this.

oh i completely forgot his classic 8 page paper on prime numbers which posed the still unresolved riemann hypothesis, stated in hilbert's famous lecture, and worth a million dollars today to any solver.

and there are hundreds more pages I am not familiar with at all, propagation of waves, ...

his clear precise definition fo the riemann integral takes about 5 lines, and is immediately followed by a characterization of riemann integrable functions that is immediately shown to be equivalent to saying the set of dicscontinuties has "measure" zero. this theory which is what most people asociate with his name, is merely a brief remark on his way to studying Fourier series.

it goes on and on... i don't really see how anyone person could have done all this.

oh i completely forgot his classic 8 page paper on prime numbers which posed the still unresolved riemann hypothesis, stated in hilbert's famous lecture, and worth a million dollars today to any solver.

and there are hundreds more pages I am not familiar with at all, propagation of waves, ...

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- #94

Must catch up...

- #95

cronxeh

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Take a look at this list http://www.sali.freeservers.com/engineering/maths.html [Broken]

The last 100 years we've had quite a few great mathematicians, as good as any of the heavy hitter mathematicians like Euler, Gauss, and Riemann

The last 100 years we've had quite a few great mathematicians, as good as any of the heavy hitter mathematicians like Euler, Gauss, and Riemann

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- #96

LeBrad

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My favorite 3 are Euler, Gauss, and Ramanujan

- #97

quasar987

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In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?

Your precious grotindiek isn't even on that list wonk

And he died at 39 !mathwonk said:it goes on and on... i don't really see how anyone person could have done all this.

Your precious grotindiek isn't even on that list wonk

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- #98

- #99

cragwolf

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Euler

Riemann

Gauss

Fermat

Lagrange

Hilbert

Poincaré

Cantor

Kolmogorov

Grothendieck

Einstein

Newton

Maxwell

Bohr

Schrödinger

Rutherford

Dirac

Heisenberg

Pauli

Feynman

I suppose there are too many theoreticians and not enough experimentalists in the physicists list, but that's my bias. Physics goes nowhere without the work of experimentalists.

I find it difficult to properly judge the works of ancient Greeks, Arabs and Hindus, so I didn't include them, although Archimedes must surely rank as one of the greatest minds in history.

- #100

cragwolf

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mathwonk said:an english translation of riemanns works just came out and i am blown away by it.

Can you provide more details? I couldn't find it on Amazon or the web.

- #101

fourier jr

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- #102

cronxeh

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quasar987 said:In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?

I'm pretty sure its what you study in multivariable calculus in college

http://en.wikipedia.org/wiki/Analytical_geometry

- #103

selfAdjoint

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quasar987 said:In the list in cronxeh's post, René Descartes is said to have invented 'Analytical Geometry'. What do they mean? What's analytical geometry?

cronxeh said:I'm pretty sure its what you study in multivariable calculus in college

No, it's the study of geometry, and especially the conic sections, through their coordinate properties, getting their equations in various coordinate systems and deriving geometric properties from that. It was a pre-calculus course and gave students a deep feel for how coordinates behave, rotation matrices and such. I took it, a three hour course as a freshman in college, along with an advanced trig course. That meant we didn't get to calculus until the sophmore year, but I've never regretted it. I don't think the modern pre-calculus courses go deep enough.

- #104

EnumaElish

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How about Georg Cantor? "No one shall expel us from the Paradise that Cantor has created." -- David Hilbert

[Added later:] Oh, I see,**cragwolf** has already mentioned him.

[Even later:] and how about a cheer or two, for whomever invented zero?

[Added later:] Oh, I see,

[Even later:] and how about a cheer or two, for whomever invented zero?

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- #105

fourier jr

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