The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.
The terms philosophy of mathematics and mathematical philosophy are frequently used as synonyms. The latter, however, may be used to refer to several other areas of study. One refers to a project of formalizing a philosophical subject matter, say, aesthetics, ethics, logic, metaphysics, or theology, in a purportedly more exact and rigorous form, as for example the labors of scholastic theologians, or the systematic aims of Leibniz and Spinoza. Another refers to the working philosophy of an individual practitioner or a like-minded community of practicing mathematicians. Additionally, some understand the term "mathematical philosophy" to be an allusion to the approach taken by Bertrand Russell in his books The Principles of Mathematics and Introduction to Mathematical Philosophy.
Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a certain problem in Ramsey theory.
The number gained a degree of popular attention when Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977, writing that, "In an unpublished proof, Graham has recently established ... a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof." The 1980 Guinness Book of World Records repeated Gardner's claim, adding to the popular interest in this number. According to physicist John Baez, Graham invented the quantity now known as Graham's number in conversation with Gardner himself. While Graham was trying to explain a result in Ramsey theory which he had derived with his collaborator B. L. Rothschild, Graham found that the quantity now known as Graham's number was easier to explain than the actual number appearing in the proof. Because the number which Graham described to Gardner is larger than the number in the paper itself, both are valid upper bounds for the solution to the Ramsey-theory problem studied by Graham and Rothschild.
A directed infinity is a type of infinity in the complex plane that has a defined angle θ but an infinite absolute value r. For example, the limit of 1/x where x is a positive number approaching zero is a directed infinity with angle 0; however, 1/0 is not a directed infinity, but a complex infinity. Some rules for manipulation of directed infinities are:
Thanos is a fictional character appearing in comic books and other media published by Marvel Comics. The character first appeared in Iron Man #55 (Feb. 1973) and was created by writer-artist Jim Starlin. Debuting in the Bronze Age of Comic Books, the character has been featured in over three decades of Marvel continuity and a self-titled series. The character's name is a derivation of Thanatos, the personification of death and mortality in Greek mythology. Thanos has appeared in other Marvel-endorsed products, including animated television series, arcade and video games, films, toys, and trading cards. Thanos was ranked number 47 on IGN's top 100 comic book villains of all time.