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  1. #1 famous mathematicians 
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    who are the famous mathematicians?

    1 pythagoras
    2 euler
    3 newton
    4 cantor
    5 gödel

    who else?


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  3. #2 Re: famous mathematicians 
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    Quote Originally Posted by siegfried
    who are the famous mathematicians?

    1 pythagoras
    2 euler
    3 newton
    4 cantor
    5 gödel

    who else?
    David Hilbert.


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    Gauss
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  5. #4 Re: famous mathematicians 
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    Quote Originally Posted by siegfried
    who are the famous mathematicians?

    1 pythagoras
    2 euler
    3 newton
    4 cantor
    5 gödel

    who else?
    Too many, too many to list. Halliday mentions Hilbert, Sunshinewarrior mentions 10 more. Of those that haven’t been mentioned yet, here are some of my favourite mathematicans.

    17. Niels Henrik Abel
    18. Augustin Louis Cauchy
    19. Joseph Louis Lagrange
    20. Richard Dedekind
    21. Henri Poincaré
    22. Emmy Noether
    23. Pál Erdős
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  6. #5 Re: famous mathematicians 
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    Quote Originally Posted by JaneBennet
    Quote Originally Posted by siegfried
    who are the famous mathematicians?

    1 pythagoras
    2 euler
    3 newton
    4 cantor
    5 gödel

    who else?
    Too many, too many to list. Halliday mentions Hilbert, Sunshinewarrior mentions 10 more. Of those that haven’t been mentioned yet, here are some of my favourite mathematicans.

    17. Niels Henrik Abel
    18. Augustin Louis Cauchy
    19. Joseph Louis Lagrange
    20. Richard Dedekind
    21. Henri Poincaré
    22. Emmy Noether
    23. Pál Erdős
    Serre
    Grothendiek
    Deligne
    Smale
    Kolmogorov
    Gelfand
    Pontryagin
    Harish Chandra
    Weyl
    Weil
    Siegel
    Kuratowski
    Milnor
    Fefferman
    Connes
    Witten
    Atiyah
    Browder
    Cohen
    Godel
    Morse
    Bomberi
    Mackey
    Vogan
    Thom
    Zagier
    Penrose
    Browder
    Birkhoff
    Hardy
    Weiner
    Wiles
    Perleman
    Griffiths
    Hirzebruch
    Elie Cartan
    Henri Cartan
    Laurent Schwartz
    Kac
    Lax
    Pontryagin
    Lefshetz
    Chern
    Singer
    Cantor
    Banach
    Hormander
    Zariski
    Zygmund
    Kakutani
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    What about Paul Dirac (1902-1984) who held the chair of Lucasian Professor of Mathematics at Cambridge (now held by Stephen Hawking) and spent the last 10 years of his life at Florida State University?
    I suppose Dirac would be considered to be a theoretical physicist rather than a mathematician.
    "there is no God,and Dirac is his Prophet."
    (Wolfgang Pauli on Dirac's views about religion.
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    Euclid
    Archimedes
    Leibniz
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    No one mentioned John Conway.
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    Or Hermann Minkowski.
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    Quote Originally Posted by Harold14370
    Euclid
    Archimedes
    Leibniz
    Descartes

    Archimedes was the best in my opinion.

    He had what all the other mathematicians had already as far as formulas.

    Then he actually applied them out in the field, and noted strange differences in the expected and the actuality.




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    William McCormick
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    John Nash
    Erwin Schrödinger ?
    Disclaimer: I do not declare myself to be an expert on ANY subject. If I state something as fact that is obviously wrong, please don't hesitate to correct me. I welcome such corrections in an attempt to be as truthful and accurate as possible.

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    Benoît Mandelbrot? It was he who coined the term “fractal”. :-D
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    Quote Originally Posted by Faldo_Elrith
    serpicojr
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    Amen, brother!

    What about Srinivasa Ramanujan? He definately counts. Apparently he didn't have such a great knowlege of advanced math, but was really good with numbers.

    I have a quote in one of my maths books:

    "No, it (1729) is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways"

    This was his reply to G.H.Hardy, who visited him in hospital. Ramanujan asked about the registration plate of the taxi Hardy had came in, and Hardy replied "1729, an uninteresting number." Ramanujan instantly replied as above.
    Chance favours the prepared mind.
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    Ferdinand von Lindemann, who was the first to prove that is transcendental (not the root of any polynomial equation with rational coefficients), deserves a mention. :wink:
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    Quote Originally Posted by JaneBennet
    Ferdinand von Lindemann, who was the first to prove that is transcendental (not the root of any polynomial equation with rational coefficients), deserves a mention. :wink:
    I do not like him. I think he was wrong.


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    William McCormick
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    Quote Originally Posted by William McCormick
    Quote Originally Posted by JaneBennet
    Ferdinand von Lindemann, who was the first to prove that is transcendental (not the root of any polynomial equation with rational coefficients), deserves a mention. :wink:
    I do not like him. I think he was wrong.


    Sincerely,


    William McCormick
    I doesn't matter whether you like him or not. The fact that is trancendental has been proved rigorously. It is not a debatable point.
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    What about George Lemaître?
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    What about Sophie Germain?
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    I want to include Sophus Lie, he of the groups.
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    Q: What's the difference between famous mathematicians

    and mathematician who are eminent or well-regarded in their field?

    A: If you ask for a list of the former, all the professional mathemticians will give you a list of the latter!

    PS: I suspect some of my submissions also fell within the 'latter' category, and I'm not even a professional (or amateur) mathematician.
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    Quote Originally Posted by sunshinewarrior
    Q: What's the difference between famous mathematicians

    and mathematician who are eminent or well-regarded in their field?

    A: If you ask for a list of the former, all the professional mathemticians will give you a list of the latter!

    PS: I suspect some of my submissions also fell within the 'latter' category, and I'm not even a professional (or amateur) mathematician.
    If you only want names of mathematicians that would be named correctly by the people that Jay Leno stops in the street then the answer is that no mathematicians are famous. None of them are professional athletes.

    So then you ask people who know something about mathematics and you get the longer and more interesting list of eminent mathematicians.
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    Quote Originally Posted by Guitarist
    I want to include Sophus Lie, he of the groups.
    My group theorist is Ludwig Sylow.
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by William McCormick
    Quote Originally Posted by JaneBennet
    Ferdinand von Lindemann, who was the first to prove that is transcendental (not the root of any polynomial equation with rational coefficients), deserves a mention. :wink:
    I do not like him. I think he was wrong.


    Sincerely,


    William McCormick
    I doesn't matter whether you like him or not. The fact that is trancendental has been proved rigorously. It is not a debatable point.

    I do not see that as a fact. If it is a simple and obvious fact, maybe you could share it with me.


    Sincerely,


    William McCormick
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    Quote Originally Posted by William McCormick
    Quote Originally Posted by DrRocket
    Quote Originally Posted by William McCormick
    Quote Originally Posted by JaneBennet
    Ferdinand von Lindemann, who was the first to prove that is transcendental (not the root of any polynomial equation with rational coefficients), deserves a mention. :wink:
    I do not like him. I think he was wrong.


    Sincerely,


    William McCormick
    I doesn't matter whether you like him or not. The fact that is trancendental has been proved rigorously. It is not a debatable point.

    I do not see that as a fact. If it is a simple and obvious fact, maybe you could share it with me.


    Sincerely,


    William McCormick
    You can find a proof that pi is transcendental in books on algebraic number theory and sometimes in books on complex analysis. Here is a link to an on-line proof.
    http://www.po28.dial.pipex.com/maths/docs/pi.html. This link actually gives two proofs, one due to Lindeman and one due to Hermite.
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by William McCormick
    Quote Originally Posted by DrRocket
    Quote Originally Posted by William McCormick
    Quote Originally Posted by JaneBennet
    Ferdinand von Lindemann, who was the first to prove that is transcendental (not the root of any polynomial equation with rational coefficients), deserves a mention. :wink:
    I do not like him. I think he was wrong.


    Sincerely,


    William McCormick
    I doesn't matter whether you like him or not. The fact that is trancendental has been proved rigorously. It is not a debatable point.

    I do not see that as a fact. If it is a simple and obvious fact, maybe you could share it with me.


    Sincerely,


    William McCormick
    You can find a proof that pi is transcendental in books on algebraic number theory and sometimes in books on complex analysis. Here is a link to an on-line proof.
    http://www.po28.dial.pipex.com/maths/docs/pi.html. This link actually gives two proofs, one due to Lindeman and one due to Hermite.
    That is like saying that a square 2"x 2" has an area of exactly 4". Or a square with the area of 4" is exactly 2" by 2" square. That would in actuality be false.

    The reason is that a real object never has perfectly square corners. Just does not happen.

    Of course it would be splitting hairs.

    But to me I don't even begin to understand the purpose of transcendental. Or how it would help to accomplish anything or make anything more clear or understandable.

    Pi is just a ratio of a circles diameter to circumference. As area of a square is just a ratio of its sides.

    The ratio of a circles area compared to a squares area is 0.785/1 considering pi has a value of 3.14 You could make both more accurate.

    If there is some purpose to transcendental. Or some higher understanding about it, I would love to know what it is. I just do not see it saying anything to me.

    I did some research into real machined circles and found some amazing things. If you have a precise circle and roll it on a precise surface. It rolls a repeatable distance, much like a gear on a gear bar.

    If your wheel gets particles debris stuck to it. It will roll a shorter distance in one roll then originally before it had small debris. So that in actuality the shortest path around a circle is not to follow the circle. It would be to go just outside the circle and return to the circle in straight lines.

    It simulates a bumpy road. And everyone knows that a wheel covers less distance per revolution, while going over a bumpy road. This one still gets me. But it shows that Archimedes was really after truth. He could not understand it either. He spent a good portion of his life working and proving this. Eventually he did understand it.

    But most miss the blatantly obvious. Including me.





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    William McCormick
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  29. #28  
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    Quote Originally Posted by William McCormick

    That is like saying that a square 2"x 2" has an area of exactly 4". Or a square with the area of 4" is exactly 2" by 2" square. That would in actuality be false.

    The reason is that a real object never has perfectly square corners. Just does not happen.

    William McCormick
    But in mathematics the areeas of a 2" x 2" square is exactly 4 square inches and if a square has area 4 square inches it is precisely 2" x 2 ". That is the nature of mathematics.

    The fact that a machinist making an approximation could not reach that ideal is irrelevant.

    I am afraid that you do not understand what mathematics is and what it is not. Pi is transcendental. And there are more transcendental real numbers than there are real numbers that are not transcendental. That is just the way it is. It can be proved rigorously. There is no room for debate on the issue.

    You need to either study mathematics a bit more and understand what it is all about or take up a different hobby. It sounds to me as though you may have some clever ideas, but they are not mathematical ideas. You may, for instance, have a clever idea of how to approximately construct a square with the same area as a circle. But you cannot, using only an ideal compass, and ideal straight edge, and an ideal pencil, construct a square that has exactly the same area as a circle. Lindemann was correct.
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by William McCormick

    That is like saying that a square 2"x 2" has an area of exactly 4". Or a square with the area of 4" is exactly 2" by 2" square. That would in actuality be false.

    The reason is that a real object never has perfectly square corners. Just does not happen.

    William McCormick
    But in mathematics the areeas of a 2" x 2" square is exactly 4 square inches and if a square has area 4 square inches it is precisely 2" x 2 ". That is the nature of mathematics.

    The fact that a machinist making an approximation could not reach that ideal is irrelevant.

    I am afraid that you do not understand what mathematics is and what it is not. Pi is transcendental. And there are more transcendental real numbers than there are real numbers that are not transcendental. That is just the way it is. It can be proved rigorously. There is no room for debate on the issue.

    You need to either study mathematics a bit more and understand what it is all about or take up a different hobby. It sounds to me as though you may have some clever ideas, but they are not mathematical ideas. You may, for instance, have a clever idea of how to approximately construct a square with the same area as a circle. But you cannot, using only an ideal compass, and ideal straight edge, and an ideal pencil, construct a square that has exactly the same area as a circle. Lindemann was correct.
    I am saying that in real life mathematics is not that accurate compared to the reality. The guys who actually do the work know how far math can go in the real world.

    I use math more then most of the individuals that do real things everyday. Because I took the time to find the exact ratios that exist between the ideal world of the mathematician and the real world.

    That statement that you cannot create a circle and square of the same area is ridiculous. Just as ridiculous as trying to create a square with an exact area of four square inches, and sides exactly two by two. Atoms just don't work like that, the corners are slightly rounded.

    So you cannot create a perfect square with all the tools on earth.

    Sincerely,


    William McCormick
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    Quote Originally Posted by William McCormick
    That statement that you cannot create a circle and square of the same area is ridiculous.
    It depends how you do it. You may be able to do it in some ways, but not others.

    If you have circle of radius r, and you want to draw a square of side , I’m sure you can do it using every sophisticated CAD tool at your disposal. But you must understand that this particular problem went all the way back to the time of the ancient Romans and Greeks, when shape-creating techinology was limited to just compass and ruler (and often ruler with no measurement markings at all). If you want to create a square of the same area as a given circle, using just compass and ruler and nothing else, then the problem is logically impossible. This can be proved using field theory. If you want more details, I’m sure river_rat or DrRocket will be able to fill you in.
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    Quote Originally Posted by JaneBennet
    back to the time of the ancient Romans and Greeks, when shape-creating techinology was limited to just compass and ruler (and often ruler with no measurement markings at all).
    Actually they had some sophisticated tools Jane, read up on the Quadratrix of Hippias
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Quote Originally Posted by JaneBennet
    Quote Originally Posted by William McCormick
    That statement that you cannot create a circle and square of the same area is ridiculous.
    It depends how you do it. You may be able to do it in some ways, but not others.

    If you have circle of radius r, and you want to draw a square of side , I’m sure you can do it using every sophisticated CAD tool at your disposal. But you must understand that this particular problem went all the way back to the time of the ancient Romans and Greeks, when shape-creating techinology was limited to just compass and ruler (and often ruler with no measurement markings at all). If you want to create a square of the same area as a given circle, using just compass and ruler and nothing else, then the problem is logically impossible. This can be proved using field theory. If you want more details, I’m sure river_rat or DrRocket will be able to fill you in.
    I am not arguing. I appreciate you sharing where all this stuff comes from.


    The link says theorem, the theorem for a squares area is two of its sides multiplied by each other.

    The circle is a bit more interesting but just a geometric figure with a formula for its area just like a squares.

    To me just another ratio.

    I admit without the ratio of pi I would have a hard time figuring it out.

    But if you drew a 400 sided polygon, and asked me to square it, I would have to use a formula as well.

    I would use the formula for a parallelograms area, made up of two of the isosceles triangles formed by one of the polygons sides and two imaginary rays, from both ends of the one side of the polygon, back to the center of the polygon.

    A circle is an infinite polygon. But once you prove its ratio, you just need that ratio to solve it. The ratio of a squares area is two of its sides multiplied by each other.

    The same is true of triangles.

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    William McCormick
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    Quote Originally Posted by William McCormick
    Quote Originally Posted by DrRocket
    Quote Originally Posted by William McCormick

    That is like saying that a square 2"x 2" has an area of exactly 4". Or a square with the area of 4" is exactly 2" by 2" square. That would in actuality be false.

    The reason is that a real object never has perfectly square corners. Just does not happen.

    William McCormick
    But in mathematics the areeas of a 2" x 2" square is exactly 4 square inches and if a square has area 4 square inches it is precisely 2" x 2 ". That is the nature of mathematics.

    The fact that a machinist making an approximation could not reach that ideal is irrelevant.

    I am afraid that you do not understand what mathematics is and what it is not. Pi is transcendental. And there are more transcendental real numbers than there are real numbers that are not transcendental. That is just the way it is. It can be proved rigorously. There is no room for debate on the issue.

    You need to either study mathematics a bit more and understand what it is all about or take up a different hobby. It sounds to me as though you may have some clever ideas, but they are not mathematical ideas. You may, for instance, have a clever idea of how to approximately construct a square with the same area as a circle. But you cannot, using only an ideal compass, and ideal straight edge, and an ideal pencil, construct a square that has exactly the same area as a circle. Lindemann was correct.
    I am saying that in real life mathematics is not that accurate compared to the reality. The guys who actually do the work know how far math can go in the real world.

    I use math more then most of the individuals that do real things everyday. Because I took the time to find the exact ratios that exist between the ideal world of the mathematician and the real world.

    That statement that you cannot create a circle and square of the same area is ridiculous. Just as ridiculous as trying to create a square with an exact area of four square inches, and sides exactly two by two. Atoms just don't work like that, the corners are slightly rounded.

    So you cannot create a perfect square with all the tools on earth.

    Sincerely,


    William McCormick
    When Lindeman proved that pi was transcendental he proved it for a value of pi related to an ideal circle. The ideal circle doesn't exist in reality because the definition of it is the set of all dots at the same distance from another dot. To do this in real life you would need infinite precision which cannot be achieved. The limit is defined by the particles that, as we see it, build up your world. Therefore it is not interesting to talk about rounded corners or something like that because it wasn't included in Lindemans proof.
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    Quote Originally Posted by thyristor
    When Lindeman proved that pi was transcendental he proved it for a value of pi related to an ideal circle. The ideal circle doesn't exist in reality because the definition of it is the set of all dots at the same distance from another dot. To do this in real life you would need infinite precision which cannot be achieved. The limit is defined by the particles that, as we see it, build up your world. Therefore it is not interesting to talk about rounded corners or something like that because it wasn't included in Lindemans proof.
    I still do not get the proof of Lindeman. What did he prove?

    Anything not square has to rely on some sort of formula.


    Sincerely,


    William McCormick
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    Quote Originally Posted by William McCormick
    Quote Originally Posted by thyristor
    When Lindeman proved that pi was transcendental he proved it for a value of pi related to an ideal circle. The ideal circle doesn't exist in reality because the definition of it is the set of all dots at the same distance from another dot. To do this in real life you would need infinite precision which cannot be achieved. The limit is defined by the particles that, as we see it, build up your world. Therefore it is not interesting to talk about rounded corners or something like that because it wasn't included in Lindemans proof.
    I still do not get the proof of Lindeman. What did he prove?

    Anything not square has to rely on some sort of formula.


    Sincerely,


    William McCormick
    He proved that there is no polynomial with integer coefficients that has pi as a zero.
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    Quote Originally Posted by DrRocket

    He proved that there is no polynomial with integer coefficients that has pi as a zero.

    What does that actually mean? I read the words however I get nothing significant or useful from it. You may have the most wonderful thing on earth there. I just don't see anything in it yet.

    Could you use very small and understandable words? I do well with those.



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    William McCormick
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    He proved that there is no series P(x,n)=
    a<sub>0</sub>+a<sub>1</sub>x<sup>1</sup>+a<sub>2</sub>x<sup>2</sup>...a<sub>n</sub>x<sup>n</sup> ,where a and n are integers, such that when P(x,n)=0 x can have the value of pi.
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    Quote Originally Posted by thyristor
    He proved that there is no series P(x,n)=
    a<sub>0</sub>+a<sub>1</sub>x<sup>1</sup>+a<sub>2</sub>x<sup>2</sup>...a<sub>n</sub>x<sup>n</sup> ,where a and n are integers, such that when P(x,n)=0 x can have the value of pi.

    Seriously run that by me slowly in simple terms. What does it actually mean to life on earth?




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    William McCormick
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    Quote Originally Posted by William McCormick
    Quote Originally Posted by thyristor
    He proved that there is no series P(x,n)=
    a<sub>0</sub>+a<sub>1</sub>x<sup>1</sup>+a<sub>2</sub>x<sup>2</sup>...a<sub>n</sub>x<sup>n</sup> ,where a and n are integers, such that when P(x,n)=0 x can have the value of pi.

    Seriously run that by me slowly in simple terms. What does it actually mean to life on earth?




    Sincerely,


    William McCormick
    It means tht we are all going to die.
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  41. #40  
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    Quote Originally Posted by DrRocket
    It means tht we are all going to die.

    That bad?


    Aren't we all going to die anyway?



    Sincerely,


    William McCormick
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  42. #41  
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    Enough. Let’s get back on topic. :x

    August Ferdinand Möbius (1790–1868), German mathematician best known for the one-sided Möbius strip. And for Möbius transformations in the study of complex numbers. In number theory, the Möbius function is also named after him.
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  43. #42  
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    Gottfried Wilhelm von Leibniz (1646-1716): was a German philosopher, mathematician, and logician who is probably most well known for having invented the differential and integral calculus (independently of Sir Isaac Newton). In his correspondence with the leading intellectual and political figures of his era, he discussed mathematics, logic, science, history, law, and theology.

    http://mally.stanford.edu/leibniz.html

    Mitchell Jay Feigenbaum (1944-): is a mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants.

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

    Leonardo da Vinci (1452-1519): Prevalent in the major works of Leonardo Da Vinci and underlying many of his design compositions, is the Golden Ratio ("Golden Mean"), a ratio of approximately 1:1.618, found in nature and creation, and inherent in the Fibonacci sequence. The Golden Rectangle, the Golden Triangle, and the Golden Pyramid, all based on the Golden Ratio are all appear prominent in the work of Leonardo Da Vinci.

    http://mathematicianspictures.com/LE...olden_Mean.htm

    Rene Descartes (1596-1650): René Descartes made many notable contributions to mathematics. In 1618 Descartes journeyed to Holland, where he met Isaac Beeckman, a thirty year-old student of medicine who was astounded at the range of Descartes' scientific curiosity. Over the next few weeks Descartes showed Beeckman how to apply algebra and mathematics to many problems. He showed him how mathematics could be applied to a more precise spacing and tuning of lute stings, proposed algebraic formula to determine the raise in water level when a heavy object was placed in water, drew a geometric graph that showed how to predict the accelerating speed of a pencil falling in a vacuum at any time during a two hour period, and showed how a spinning top stays upright and how this could be used to help man become airborne. Beeckman's journal showed us that by the end of 1618, Descartes was already applying algebraic equations to solve geometric problems, and that it was then, not later as many sources say, that he invented analytical geometry.

    http://library.thinkquest.org/3531/mathhist.html

    Bernhard Riemann (1826-1866): was one of the leading mathematicians of the nineteenth century. In his short career, he introduced ideas of fundamental importance in complex analysis, real analysis, differential geometry, number theory, and other subjects. His work in differential geometry provided the mathematical basis for the general theory of relativity.

    http://www.usna.edu/Users/math/meh/riemann.html
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  44. #43  
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    Names I didn't see mentioned, that strike me as big omissions:

    Raoul Bott
    Simon Donaldson
    Hironaka
    Kontsevich
    Robert Langlands
    Lefschetz
    David Mumford
    William Thurston
    Shing-Tung Yau
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