09 December 2003

Update: Hilbert's 16th Problem (and the tale of two paranoid Swedish birds) Let k be an integer such that k is larger than or equal to zero, and let H be the Hilbert number. In this paper, we use the method of describing functions to prove that in the Liénard equation, the upper bound for H(2k+1) is k. By applying this method to any planar polynomial vector field, it is possible to completely solve the second part of Hilbert's 16th problem. Hilbert's original German text Mathematische Probleme 16 BBC NEWS | Science/Nature | Historic maths problem 'cracked' Elin Oxenhielm Update (Tesugen) Slashdot | Swedish Student Partly Solves 16th Hilbert Problem unstruct.org: Swede Solves 100 year old Math Puzzle Yishao Zhou's Comments Elin Oxenhielm's Response Mathematicians dispute proof of century-old problem: Mystery remains as journal withdraws paper. 6:15:06 PM    comment []  trackback []