Task: Question Answering
Input (English): Context_1 : Raúl Arturo Chávez Sarmiento (born 24 October 1997) is a Peruvian child prodigy in mathematics. At the age of , he won a bronze medal at the 2009 International Mathematical Olympiad, making him the second youngest medalist in IMO history, behind Terence Tao who won bronze in 1986 at the age of 10. Context_2 : Ömer Cerrahoğlu (born 3 May 1995) is a Romanian child prodigy in mathematics. At the age of , he won a gold medal at the 2009 International Mathematical Olympiad, making him the third youngest gold medalist in IMO history, behind Terence Tao and Raúl Chávez Sarmiento. Since then, he won three more silver medals at the 2010, 2011 and 2013 IMO's missing the gold by only 1, 2 and 1 points respectively and one more gold medal at the IMO 2012 in Argentina. He was born in Istanbul from a Romanian mother and a Turkish father and when he was 5 years old, he moved with his family in Baia Mare, Romania. He currently studies at MIT. Context_3 : In the week before the incursion, it was revealed that the Colombian government, with assistance from the United States' FBI and DEA, had wiretapped several satellite phones that were used by FARC forces in Southern Colombia. According to an unnamed Colombian military source, an international call made by Venezuelan President Hugo Chávez to Raúl Reyes on one of these phones was intercepted by authorities on February 27. The source claimed that Chávez called Reyes to inform him that the release of three FARC hostages held captive for almost 7 years had been completed, and the intercepted call was then used to track Reyes to a location in Colombia, near the Ecuadorian border. Context_4 : Terence Chi-Shen Tao FAA FRS (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. s of 2015 , he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao was a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. Context_5 : Raúl de la Cruz Chaparro (born 3 May 1953) is an Argentine former footballer who played at both professional and international levels as a midfielder. In 2012, he became manager of Sarmiento de Resistencia. Context_6 : In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number "k", there exist arithmetic progressions of primes with "k" terms. The proof is an extension of Szemerédi's theorem. The conjecture was probably stated at least in 1770. Context_7 : The Siege of Castelnuovo was an engagement during the Ottoman-Habsburg struggle for control of the Mediterranean, which took place in July 1539 in the walled town of Castelnuovo, present-day Herceg Novi, Montenegro. Castelnuovo had been conquered by elements of various Spanish tercios the year before during the failed campaign of the Holy League against the Ottoman Empire in Eastern Mediterranean waters. The walled town was besieged by land and sea by a powerful Ottoman army under Hayreddin Barbarossa, who offered an honorable surrender to the defenders. These terms were rejected by the Spanish commanding officer Francisco de Sarmiento and his captains even though they knew that the Holy League's fleet, defeated at the Battle of Preveza, could not relieve them. During the siege the Barbarossa's army suffered heavy losses due to the stubborn resistance of Sarmiento's men. However, Castelnuovo eventually fell into Ottoman hands and almost all the Spanish defenders, including Sarmiento, were killed. The loss of the town ended the Christian attempt to regain control of the Eastern Mediterranean. The courage displayed by the Old Tercio of Naples, however, was praised and admired throughout Europe and was the subject of numerous poems and songs. Context_8 : Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS). These books elaborate on several theories from notable personas, such as Ethan Akin, Martin Schechter, and Terence Tao, in the mathematical industry. The books in this series are published only in hardcover. Context_9 : In linear algebra, the restricted isometry property characterizes matrices which are nearly orthonormal, at least when operating on sparse vectors. The concept was introduced by Emmanuel Candès and Terence Tao and is used to prove many theorems in the field of compressed sensing. There are no known large matrices with bounded restricted isometry constants (computing these constants is strongly NP-hard, and is hard to approximate as well), but many random matrices have been shown to remain bounded. In particular, it has been shown that with exponentially high probability, random Gaussian, Bernoulli, and partial Fourier matrices satisfy the RIP with number of measurements nearly linear in the sparsity level. The current smallest upper bounds for any large rectangular matrices are for those of Gaussian matrices. Web forms to evaluate bounds for the Gaussian ensemble are available at the Edinburgh Compressed Sensing RIC page. Context_10 : Kaisa Sofia Matomäki (born April 30, 1985) is a Finnish mathematician specializing in number theory. Since September 2015, she has been working as an Academic Research Fellow in the Department of Mathematics and Statistics, University of Turku, Turku, Finland. Her research includes results on the distribution of multiplicative functions over short intervals of numbers; for instance, she showed that the values of the Möbius function are evenly divided between +1 and −1 over short intervals. These results, in turn, were among the tools used by Terence Tao to prove the Erdős discrepancy problem. fact_1 : Raúl Arturo Chávez Sarmiento (born 24 October 1997) is a Peruvian child prodigy in mathematics. fact_2 : Terence Chi-Shen Tao FAA FRS (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics. Question: What subject are both Terence Tao and Raúl Chávez Sarmiento good at?
Output (English): mathematics