Of course my choosing of Mathematicians was very subjective and my reasoning for excluding Cantor would probably be that besides his beginnings in number theory, his work was exclusively directed towards Set Theory. Of course then you could look at Fermat being on the list and say the same, but I included him just because of my obsession with his theorems.

Honestly, I don't know how Fourrier made the cut especially with Cauchy omitted.

BaldFriede wrote: Let me just remark something: Today we don't have many problems thinking about the number zero; we are used to it. But to people in former times the zero was not an easy concept. Let me give you an example. There are three apples lying on the table. If all three are eaten, how many apples remain? You will say "zero of course", but there are also zero pears, zero cherries, zero peaches and zero pineapples, to name but a few of the millions of things of which there are zero. Why the heck should we especially name zero apples? Just because there had been three before? No, "zero" is not a concept we encounter in the world of things, it is a pure mathematical concept. Which is why the invention of this number was so very important for mathematics.

Let me just remark something: Today we don't have many problems thinking about the number zero; we are used to it. But to people in former times the zero was not an easy concept. Let me give you an example. There are three apples lying on the table. If all three are eaten, how many apples remain? You will say "zero of course", but there are also zero pears, zero cherries, zero peaches and zero pineapples, to name but a few of the millions of things of which there are zero. Why the heck should we especially name zero apples? Just because there had been three before?
No, "zero" is not a concept we encounter in the world of things, it is a pure mathematical concept. Which is why the invention of this number was so very important for mathematics.

BaldFriede wrote: i is NOT an irrational number. Imaginary numbers and real numbers exist side by side, the only difference between them being that the imaginary number is a real number being multiplied with i. Not exactly.  To begin, you should use the term "complex number" rather than "imaginary number" as the latter is anachronistic mostly because it is misleading (ain't nothing imaginary about them).  Also the set of complex numbers contains as a subset the set of real numbers.  In other words, real numbers are indeed complex numbers (and consequently, irrational numbers are also complex). A complex number without a real component is still called an imaginary number; there is nothing anachronistic about that. So my definition is absolutely correct. I did not mention complex numbers at all to avoid complications. Your definition is absolutely correct, I agree, but it still uses unfortunate, albeit conventional, language.  It is horrible, in my opinion, that the term "imaginary" is used in textbooks in any way at all--it should be scraped completely.  But I'm not gonna get into another argument over semantics with you.

NaturalScience wrote: Good to see a real mathematician hanging out here...I'm just a simple electrical engineer who once had aspirations at taking real analysis.

I've never cared much for analysis as I simply don't have the intuition for it.  My interests are in the foundational aspects of math (set theory, logic, etc.).

To my understanding, though, electrical engineers are generally perceived as the most "mathematical" of engineers since they use some fairly sophisticated techniques.


Edited by WinterLight - July 01 2008 at 10:24

BaldFriede wrote: NaturalScience wrote: moreitsythanyou wrote: rileydog22 wrote: BaldFriede wrote: Georg Cantor is definitely missing on the list. Bertrand Russel should be on the list too, in my opinion. Absolutely agreed.  Without Cantor, we may not have had the motivation for set theory.  However, Russell's work is generally perceived as important historically only.  (Also realize that many mathematicians don't think highly of logicians--it's childish, I admit, but it's quite true.)  I would also add Hilbert, Godel, Tarski, and Erdos to this list. By the way, Einstein is better known for his contributions to physics, but he had to invent a great part of the mathematics needed for his General Theory of Relativity himself. Einstein (as well as Newton and Euclid) really don't deserve a spot anywhere on a list of great mathematicians:  he didn't "invent" any of the mathematics involved in general relativity (that stuff--differential geometry and tensor analysis--was well known and had already been applied in other areas of physics like fluid dynamics and electromagnetic field theory). I must admit though that the beauty of e i *pi + 1 = 0 has never ceased to amaze me. The 5 most important numbers in the world combined into one formula, two of them being irrational, two others the most basic numbers in the world (and the neutral elements of addtion and multiplication), and one the square root of -1. I think you mean "identity" rather than "neutral elements." Actually, three of them are irrational.  i cannot be expressed as the quotient of two integers.  Doesn't a number have to be real in order to be considered irrational, though? not sure myself. You are correct.  The irrationals are a subset of the reals, and i is not a real number. i is NOT an irrational number. Imaginary numbers and real numbers exist side by side, the only difference between them being that the imaginary number is a real number being multiplied with i. Not exactly.  To begin, you should use the term "complex number" rather than "imaginary number" as the latter is anachronistic mostly because it is misleading (ain't nothing imaginary about them).  Also the set of complex numbers contains as a subset the set of real numbers.  In other words, real numbers are indeed complex numbers (and consequently, irrational numbers are also complex). For each and every real number there exists an imaginary number and vice versa. And then there are the complex numbers, which consist of a sum of a real number and an imaginary number. A complex number has the form a + b*i, with a and b being real numbers. See my comment above. Interestingly complex numbers can be displayed in a coordinate system, with the real part of the number being the x-coordinate and the imaginary part the y-coordinate (this correlation is arbitrary, by the way, and could as well have been chosen the other way round). (2;3), for example, would mean the complex number 2 + 3*i. Instead of giving the Cartesian coordinates it is often very useful to give the polar coordinates of an imaginary number, which show the distance from the center of the coordinate system and the angle to a certain ray (usually given in radians) when dealing with complex numbers, especially when using roots. In fact, the complex numbers are isomorphic to the plane (unioned with "infiinity").

Leibniz>Newton at mathematics alone IMO. 

Of course, it's impossible to top Newton's achievements when you include physics and other achievements outside of "pure mathematics." 

This thread may give me nightmares.

Math is apparently good. Numbers larger than 1,000 are likely to give me anxiety attacks (as well as anything less than -10, irrational, imaginary, or anything that has a letter or symbol to represent it).


Edited by stonebeard - July 01 2008 at 00:25

obiter wrote: None of the above although Gauss is the obvious choice. My vote goes to .... Srinivasa Ramanujan

My vote went for Euler. But Ramanujan is...special.

The most beautiful formula in mathematics, however, is e^iπ + 1 = 0. It combines the five most important numbers in mathematics in one formula:
0 is the neutral element of addition and thus one of the basic numbers of mathematics. Interestingly it took mankind some time to "discover" this number; its discovery was one of the most important breakthroughs in mathematics.
1 is of course equally important, being the neutral element of multiplication and the basis of all counting.
π is of course the most important number in geometry and trigonometry. It is approximately 3.14159265359...., a non-periodic decimal fracture. It is defined as the ratio of a circle's circumference and its diameter.
e is just as equally important in calculus as π is in geometry. It is the basis of natural logarithm; it's value is approximately 2.7182818284590...
i is the square root of -1. Some people may say "you can't draw the square root out of a negative number", but mathematicians invented a new kind of numbers for that, the so called "imaginary numbers". Their basis is i; it is the square root of -1. It is very important for solving polynomials.
These five numbers are probably the five most important numbers in mathematics. To see them combined in one formula, together with the three basic arithmetic operations (addition, multiplication, exponentiation; subtraction, division and extracting roots are merely the inverses of these operations), is sheer beauty.