Carl Friedrich Gauss, the ``Prince of Mathematics,'' exhibited his calculative powers when he corrected his father's arithmetic before the age of three. His revolutionary nature was demonstrated at age twelve, when he began questioning the axioms of Euclid. His genius was confirmed at the age of nineteen when he proved that the regular n-gon was constructible if and only if n is the product of prime Fermat numbers. At age 24 he published Disquisitiones Arithmeticae, probably the greatest book of pure mathematics ever.
Gauss built the theory of complex numbers into its modern form, including the notion of ``monogenic'' functions which are now ubiquitous in mathematical physics. The other contributions of Gauss are quite numerous and include the Fundamental Theorem of Algebra (that an n-th degree polynomial has n roots), the Law of Least Squares, foundations of statistics and differential geometry. He was the premier number theoretician, proving Euler's Law of Quadratic Reciprocity. He also did important work in several areas of physics. Much of Gauss's work wasn't published: unbeknownst to his colleagues it was Gauss who first discovered doubly periodic elliptic functions, non-Euclidean geometry, quaternions, foundations of topology, the ``butterfly'' procedure for rapid calculation of Fourier series, and even the rudiments of knot theory. Also in this category is the Fundamental Theorem of Functions of a Complex Variable (that the line-integral over a closed curve of a monogenic function is zero): he proved this first but let Cauchy take the credit.
2006-09-30 15:06:03
·
answer #1
·
answered by Austin Semiconductor 5
·
0⤊
0⤋
Abraham Lincoln, who knows...lol
2006-09-30 22:03:53
·
answer #2
·
answered by Anonymous
·
0⤊
0⤋