Odd Objects
In many constructions, this set can often times be a source of concern (even if it is not really a problem), because of its weird nature compared to other sets. It is closed and open in every topology.
What is the empty set?
This is the subject of the talk Ashwin gave. It states that we cannot have a^n+b^n = c^n for n>2 and a,b,c >0 are integers.
What is Fermat's Last Theorem?
In this seminal 9-page work, the Riemann hypothesis was born. Although it was Riemann's only paper on number theory, it is one of the most important papers ever published in math. It gave birth to analytic number theory techniques still used today, such as the zeta function.
What is "On the Number of Primes Less Than a Given Magnitude"?
This famous school is where Terence Tao did his PhD. He almost failed his quals because he had to study for the first time in his life and instead played too many video games lmao.
What is Princeton?
This famous category theorist is often called the "Queen of Category Theory" for her work in the area and published the book "Category Theory in Context". Some in this room are currently learning algebra from her.
Who is Emily Riehl?
This is the 3d version of a parallelogram. Double points if u can spell it (spelling bee style)!
What is a parallelepiped?
This is the only Millenium prize problem to have been solved. It was solved by Grigori Perelman who rejected multiple prizes and even a million dollars for his solution.
Poincare Conjecture
This paper might fall under applied math which many here might object to but alas I write the questions. This paper by Shannon (known for his entropy) later became a book (he changed the word A to The in the title when he realized how significant his work was). It invented information theory and has tens of thousands of citations.
A Mathematical Theory of Communication
This theorem by Tao (proven in the year of my birth) shows that there are sequences of primes with arbitrarily long arithmetic progressions. Tao has further extended the theorem to Gaussian primes.
Green-Tao Theorem
The highest award in mathematics is named after this Canadian mathematician, who got his PhD from JHU in 1887!
Who is Fields?
This object shares its name with a famous red dog. It is a special algebra generated by a vector space with an attached quadratic form. Some examples include the reals, complex numbers, the bicomplex numbers, the biquaternions, and the split bi-quaternions.
What is a Clifford algebra?
This conjecture is often called the 3n+1 conjecture for the details of its statement. Many people will try to immediately solve it at first glance despite it being one of the hardest math problems of all time.
What is the Collatz Conjecture?
This paper by Poincare is one of his most famous. It essentially founded algebraic topology and introduced homotopy and homology. It had a early form of Poincare duality and raised the Poincare conjecture. It also coined the term homeomorphism.
What is Analysis Situs?
When he was 24 Terence Tao became a full professor at this institution where he still teaches today. He is the youngest person to get that rank at this university.
What is UCLA?
He gives his name to the postdoc position filled by many lovely professors such as Maru and Ashwin and Park. There is a chair in the department named after him and he was the inaugural professor in the math dept at JHU.
Who is JJ Sylvester?
This is the term for a map that gives an iso between V tensor cross W and W tensor cross V for some vector spaces V,W. It is also a term used for hairstyling.
What is a braiding?
Although some might consider this a physics problem, it is a Millenium prize problem. In the last ten years, Terence Tao made significant progress and was hopeful his solution may solve the entire thing although he did not. This conjecture concerns a particularly nasty set of PDEs.
What is Navier Stokes?
This paper was written by Grothendieck and published in a Japanese journal in 1957. It gave birth to the idea of Abelian categories as well as equivalence of categories. It was a major leap in homological algebra. Its main idea was to observe that modules over a ring and sheaves of abelian groups are the same concept.
What is Grothendieck's Tohoku paper? aka Sur quelques points d'algèbre homologique
This joke about logs was told by Tao during his lecture on youtube "Small and Large Gaps Between Primes"
What is:
"What did the drowing number theorist say? Log log log log log log log."
This famous mathematician spent time as a professor at JHU where he wrote a book on Italian algebraic geometry. He has a famous topology named after him.
Who is Oscar Zariski?
Professor Brown described this as his favorite mathematical object. Part of its name can be found in most kitchens. It is a fractal that is a 3d analog of the Cantor Set in 1d and the Sierpinski carpet in 2d.
What is the Menger Sponge?
This problem was solved independently by Turing and Church around the same time with different methods. This result is often used to show the undecidability of other problems, by translating them into this one. It has the same flavor of result as the incompleteness theorems of Godel. Double points if you say the name of the theorem the way I want.
What is the halting problem or for double points
Entscheidungsproblem?
This paper by Alan Turing was written in 1952 to describe how patterns in nature arise out of homogeny by the "reaction-diffusion" model. In it Turing uses basic ODEs to show how symmetries can be broken.
What is The Chemical Basis of Morphogenesis?
This fields medalist said of Tao "It has been said that David Hilbert was the last person to know all of mathematics, but it is not easy to find gaps in Tao's knowledge, and if you do then you may well find that the gaps have been filled a year later. ".
Who is Timothy Gowers?
JHU boasts this as the oldest math journal in continuous publication in the Western Hemisphere. Among others, Hermann Weyl, Andre Weil, and Henri Cartan have served on its editorial board. Fields medalist Cédric Villani has speculated that "the most famous article in its long history" may be a 1958 paper by John Nash, "Continuity of solutions of parabolic and elliptic equations".
What is The American Journal of Mathematics?