Gauss QQC

Quote:

In his Disquisitiones Gauss also created the modern rigorous approach to mathematics. He had become impatient with the loose writing and sloppy proofs of his predecessors, and resolved that his own works would be beyond criticism in this respect. As he wrote to a friend, 'I mean the word proof not in the sense of the lawyers, who set two half-proofs equal to a whole one, but in the sense of the mathematician where 1/2 proof=0 and it is demanded for proof that every doubt becomes impossible.' The Disquisitiones is composed in this spirit and in Gauss's mature style, which is terse, rigid, devoid of motivation, and in many places so carefully polished that it is almost unintelligible.

Question:
It does seem a waste to have a work so polished that it is not easy to understand, especially when you are writing for your work to be read and understood by others (unlike Newton, who purposefully wrote in a difficult style). Why would anyone spend hours and hours of their time to be as terse as possible, especially when it is not required that one be extremely terse?

Comment: I thought that it was interesting to read about Gauss, and how he was such a brilliant mathematician. One wonders though, how when one can be so brilliant, and yet fail to let the public be aware of your ideas, how ultimately brilliant you are.... His feat at age three of spotting a mistake in the bookkeeping is definitely the mark of an extremely smart and intelligent person. I especially like his point of how, in math, 1/2 proof + 1/2 proof = 0, or simply does not equal anything of meaning, which makes especially clear the importance of having a well-grounded math foundation and understanding that all the steps are necessary when solving a problem.

Euler QQC

Quote: "It was through his work that the symbols e, π, and i (=sqrt(-1)) became common currency for all mathematicians, and it was he who linked them together in the astonishing relation e^(πi) = -1. This is merely a special case (put θ=π) of his famous formula e^(i θ) = cosθ+ i sinθ, which connects the exponential and trigonometric functions and is absolutely indispensable in higher analysis. Among his other contributions to standard mathematical notation were sin x, cos x, the use of f(x) for an unspecified function, and the use of Σ for summation....

Question: Is there anything that Euler didn't do? (other than not discover calculus)

Comment: I think that this is pretty amazing, the type of formulas and notations that he impressed upon the world of mathematics. Since we all use these notations in math class, I think Euler is a pretty relevant person. I was especially surprised by the fact that e raised to the power of i times pi equals -1, since this seems to defy the logic of an imaginary number. I don't know what the specific ramifications of this equation are, but they seem to suggest that i is a number that has a comprehensible value (other than sqrt(-1)). All this and 13 children, too! I am surprised that anybody could get anything done with 13 kids running around, even if they were very-well behaved. I was a little disappointed, however, when I read that the bridges of Konigsberg problem really was unsolvable.

Liebniz

Quote: (Whoa, no image this time. Could this be an actual one line quote?!)All this, in an age when even the most intelligent and well-educated people considered Genesis to be the final authority in such matters [as pertaining to the subject of the origin of the world and life].

Question: Since when does well-educated and intelligent have anything to do with understanding Genesis as the authority on the human condition and origin? That is, is viewing Genesis as an end all authority on the matter make one ill-educated and a moron? This is certainly what the article seems to say.

Comment: I don't really see how one could consider someone that understands Genesis as the authority on the matter of the origin of the world and the universe as thick. Tell that to all the scientists and physicists and biologists that believe that Genesis is the end-all authority. Certainly Leibniz's ideas are pretty standard and in-line with the prevailing modern thought today. Certainly his understanding of how the earth formed could be 100% right. It just remains that his and modern science's understanding of how the earth got here in the first place is not necessarily being viewed in the right light. It is certainly possible for the earth to have formed exactly as Leibniz described (not that I agree with him, but we'll go with it for now). Perhaps not probably in point of view, but definitely possible. What the real objection here is, of course, is that the idea that to be a modern thinker and to be labeled as smart, intelligent, well-educated, and high-minded one has to believe in evolution, or at least the deist understanding of the universe, is a rather limited viewpoint. I feel rather upset, considering the fact that those that do feel that Genesis answers a considerable number of questions that evolutionary biology, universal geological study, and philosophical metaphysics (based on these evolutionary terms) cannot, nor will ever answer. Genesis might not answer all questions, but it certainly answers all the questions that we need to know the answers to. Needless to say, I mean not to offend, but I don't go around calling Darwinists that believe that evolution answers all questions about life, the universe, and everything moronic blockheads, or at least half-wits, which is, again, certainly what the above quote suggests.