concerning the locations of the roots and critical points of a complex polynomial, in the special case of polynomials with sufficiently high degree. Recognition British mathematician and Fields medalist Timothy Gowers remarked on Tao's breadth of knowledge: An article by New Scientist writes of his ability: Tao has won numerous mathematician honours and awards over the years. He is a Fellow of the Royal Society, the Australian Academy of Science (Corresponding Member), the National Academy of Sciences (Foreign member), the American Academy of Arts and Sciences, the American Philosophical Society, and the American Mathematical Society. In 2006 he received the Fields Medal; he was the first Australian, the first UCLA faculty member, and one of the youngest mathematicians to receive the award. He was also awarded the MacArthur Fellowship. He has been featured in The New York Times, CNN, USA Today, Popular Science, and many other media outlets. In 2014, Tao received a CTY Distinguished Alumni Honor from Johns Hopkins Center for Gifted and Talented Youth in front of 979 attendees in 8th and 9th grade that are in the same program from which Tao graduated. In 2021, President Joe Biden announced Tao had been selected as one of 30 members of his President's Council of Advisors on Science and Technology, a body bringing together America's most distinguished leaders in science and technology. In 2021, Tao was awarded the Riemann Prize Week as recipient of the inaugural Riemann Prize 2019 by the Riemann International School of Mathematics at the University of Insubria. Tao was a finalist to become Australian of the Year in 2007. As of 2022, Tao has published over three hundred articles, along with sixteen books. He has an Erdős number of 2. He is a highly cited researcher. Research contributions Dispersive partial differential equations From 2001 to 2010, Tao was part of a well-known collaboration with James Colliander, Markus Keel, Gigliola Staffilani, and Hideo Takaoka. They found a number of novel results, many to do with the well-posedness of weak solutions, for Schrödinger equations, KdV equations, and KdV-type equations. Michael Christ, Colliander, and Tao developed methods of Carlos Kenig, Gustavo Ponce, and Luis Vega to establish ill-posedness of certain Schrödinger and KdV equations for Sobolev data of sufficiently low exponents. In many cases these results were sharp enough to perfectly complement well-posedness results for sufficiently large exponents as due to Bourgain, Colliander−Keel−Staffilani−Takaoka−Tao, and others. Further such notable