Princeton University is a private Ivy League research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the most prestigious universities in the world. The institution moved to Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University.

The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest endowment per student in the United States. Princeton provides undergraduate and graduate instruction in the humanities, social sciences, natural sciences, and engineering to approximately 8,500 students on its 600 acres (2.4 km2) main campus. It offers postgraduate degrees through the Princeton School of Public and International Affairs, the School of Engineering and Applied Science, the School of Architecture and the Bendheim Center for Finance. The university also manages the Department of Energy's Princeton Plasma Physics Laboratory and is home to the NOAA's Geophysical Fluid Dynamics Laboratory. It is classified among "R1: Doctoral Universities Very high research activity" and has one of the largest university libraries in the world.Princeton uses a residential college system and is known for its upperclassmen eating clubs. The university has over 500 student organizations. Princeton students embrace a wide variety of traditions from both the past and present. The university is a NCAA Division I school and competes in the Ivy League. The school's athletic team, the Princeton Tigers, has won the most titles in its conference and has sent many students and alumni to the Olympics.

As of October 2021, 75 Nobel laureates, 16 Fields Medalists and 16 Turing Award laureates have been affiliated with Princeton University as alumni, faculty members, or researchers. In addition, Princeton has been associated with 21 National Medal of Science awardees, 5 Abel Prize awardees, 11 National Humanities Medal recipients, 215 Rhodes Scholars and 137 Marshall Scholars. Two U.S. Presidents, twelve U.S. Supreme Court Justices (three of whom currently serve on the court) and numerous living industry and media tycoons and foreign heads of state are all counted among Princeton's alumni body. Princeton has graduated many members of the U.S. Congress and the U.S. Cabinet, including eight Secretaries of State, three Secretaries of Defense and two Chairmen of the Joint Chiefs of Staff.

Yale University is a private Ivy League research university in New Haven, Connecticut. Founded in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the world.Chartered by Connecticut Colony, the Collegiate School was established in 1701 by clergy to educate Congregational ministers before moving to New Haven in 1716. Originally restricted to theology and sacred languages, the curriculum began to incorporate humanities and sciences by the time of the American Revolution. In the 19th century, the college expanded into graduate and professional instruction, awarding the first PhD in the United States in 1861 and organizing as a university in 1887. Yale's faculty and student populations grew after 1890 with rapid expansion of the physical campus and scientific research.

Yale is organized into fourteen constituent schools: the original undergraduate college, the Yale Graduate School of Arts and Sciences and twelve professional schools. While the university is governed by the Yale Corporation, each school's faculty oversees its curriculum and degree programs. In addition to a central campus in downtown New Haven, the university owns athletic facilities in western New Haven, a campus in West Haven, and forests and nature preserves throughout New England. As of 2021, the university's endowment was valued at $42.3 billion, the second largest of any educational institution. The Yale University Library, serving all constituent schools, holds more than 15 million volumes and is the third-largest academic library in the United States. Students compete in intercollegiate sports as the Yale Bulldogs in the NCAA Division I – Ivy League.

As of October 2020, 65 Nobel laureates, five Fields Medalists, four Abel Prize laureates, and three Turing Award winners have been affiliated with Yale University. In addition, Yale has graduated many notable alumni, including five U.S. Presidents, 19 U.S. Supreme Court Justices, 31 living billionaires, and many heads of state. Hundreds of members of Congress and many U.S. diplomats, 78 MacArthur Fellows, 252 Rhodes Scholars, 123 Marshall Scholars, and nine Mitchell Scholars have been affiliated with the university. Yale is a member of the Big Three. Yale's current faculty include 67 members of the National Academy of Sciences, 55 members of the National Academy of Medicine, 8 members of the National Academy of Engineering, and 187 members of the American Academy of Arts and Sciences. The college is, after normalization for institution size, the tenth-largest baccalaureate source of doctoral degree recipients in the United States, and the largest such source within the Ivy League. It also is a top 10 (ranked 7th), after normalization for the number of graduates, baccalaureate source of some of the most notable scientists (Nobel, Fields, Turing prizes, or membership in National Academy of Sciences, National Academy of Medicine, or National Academy of Engineering).