that it contained the original text in a little square on the page, and surrounding it were commentaries written over time by different people. In this way the Talmud had evolved, and everything that was discussed was carefully recorded. Despite being impressed, Feynman was disappointed with the lack of interest for nature and the outside world expressed by the rabbis, who cared about only those questions which arise from the Talmud. Education Feynman attended Far Rockaway High School, which was also attended by fellow Nobel laureates Burton Richter and Baruch Samuel Blumberg. Upon starting high school, Feynman was quickly promoted to a higher math class. An IQ test administered in high school estimated his IQ at 125—high but "merely respectable", according to biographer James Gleick. His sister Joan, who scored one point higher, later jokingly claimed to an interviewer that she was smarter. Years later he declined to join Mensa International, saying that his IQ was too low. When Feynman was 15, he taught himself trigonometry, advanced algebra, infinite series, analytic geometry, and both differential and integral calculus. Before entering college, he was experimenting with mathematical topics such as the half-derivative using his own notation. He created special symbols for logarithm, sine, cosine and tangent functions so they did not look like three variables multiplied together, and for the derivative, to remove the temptation of canceling out the 's in . A member of the Arista Honor Society, in his last year in high school he won the New York University Math Championship. His habit of direct characterization sometimes rattled more conventional thinkers; for example, one of his questions, when learning feline anatomy, was "Do you have a map of the cat?" (referring to an anatomical chart). Feynman applied to Columbia University but was not accepted because of their quota for the number of Jews admitted. Instead, he attended the Massachusetts Institute of Technology, where he joined the Pi Lambda Phi fraternity. Although he originally majored in mathematics, he later switched to electrical engineering, as he considered mathematics to be too abstract. Noticing that he "had gone too far", he then switched to physics, which he claimed was "somewhere in between". As an undergraduate, he published two papers in the Physical Review. One of these, which was co-written with Manuel Vallarta, was entitled "The Scattering of Cosmic Rays by the Stars of a Galaxy". The other was his senior thesis,