Is a Positive Polynomial FORCED to be a Sum of Squares??

In this video we ask the interesting question "Is a positive polynomial forced to be a sum of squares?" This problem is central in a whole branch of mathematical research on detecting when functions are nonnegative. In the video we discuss: 1) Why nonnegative polynomials in one variable are forced to be sums of squares (we give a proof outline). 2) Why quadratic polynomials in many variables that are nonnegative are sums of squares. This involves a dive into some linear algebra. 3) An example of a polynomial that is nonnegative but not a sum of squares!! #SumsOfSquares #PositivePolynomials #MotzkinPolynomial Find me here: www.mohamedomar.org GET MY BOOK ON AMAZON!! ======================== "Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures" https://www.amazon.com/Number-Theory-Toward-Cryptography-Undergraduate/dp/1978457464 CHECK OUT OTHER TYPES OF VIDEOS: ================================ Improve Your Putnam Math Competition Performance: https://www.youtube.com/playlist?list=PLBiVnG9A5gcdLg0Im3qewDrgcMxpbjcqN ------------------------------------------------------ Math Theorems: https://www.youtube.com/playlist?list=PLBiVnG9A5gccu9O8aCjVsynisfQLQyGOe ------------------------------------------------------ GRE Math Subject Test: https://www.youtube.com/playlist?list=PLBiVnG9A5gceFbk7oTBHALETI2SUmplIL ------------------------------------------------------ Road to RSA Encryption: https://www.youtube.com/playlist?list=PLBiVnG9A5gcc-KuE3-pF8M6rWllIvOqIj ------------------------------------------------------- CHECK ME OUT ON THE INTERNET!! ============================== Website: www.mohamedomar.org Twitter: @mohamedomarphd Instagram: profomarmath YouTube: www.youtube.com/ProfOmarMath And of course, subscribe to my channel!