Fundamental Fields
This field of mathematics studies shapes, sizes, and properties of space.
What is Geometry?
This ancient problem asks if there exists a set of numbers that satisfy the equation an + bn = cn for integers n > 2 . It was famously proven by Andrew Wiles in 1994.
What is Fermat’s Last Theorem?
This formula states that a2 - b2 = (a - b)(a + b) , a key identity in algebra.
What is the Difference of Squares formula?
This Swiss mathematician introduced the function notation f(x), made major contributions to calculus and graph theory, and has a famous number associated with him: e .
Who is Leonhard Euler?
Known as the study of how things change or the study of infinity. This branch of mathematics involves limits, derivatives, and integrals.
What is Calculus?
This problem concerns a sequence where each term is generated by taking a positive integer, halving it if even, or tripling it and adding one if odd. Despite extensive testing, no counterexample has been found.
What is the Collatz Conjecture?
Given ax2 + bx + c = 0, this formula finds its roots.
What is the Quadratic Formula?
This 17th-century mathematician and physicist is known as the “Father of Calculus” and formulated the laws of motion and universal gravitation.
Who is Isaac Newton?
This area of math explores groups, rings, and fields, often abstracting arithmetic.
What is abstract algebra?
This unsolved problem predicts that all nontrivial zeros of a certain function lie on the critical line Re(s) = 1/2. It has deep implications in number theory, particularly regarding prime numbers.
What is the Riemann Hypothesis?
This theorem states that differentiation and integration are inverse operations.
What is the Fundamental Theorem of Calculus?
This 17th-century French mathematician and philosopher co-developed the foundation of calculus, formulated laws of probability, and has a famous triangle named after him (taught in Algebra!).
Who is Blaise Pascal?
Concerned with the properties of space that are preserved under continuous transformations, this field is sometimes called “rubber-sheet geometry.”
What is Topology?
This problem, one of the Millennium Prize Problems, asks whether every problem whose solution can be verified in polynomial time can also be solved in polynomial time.
What is P vs NP?
This formula connects five of the most fundamental mathematical constants.
What is Euler's Identity?
This ancient Greek mathematician is known as the “Father of Geometry” and wrote The Elements, one of the most influential mathematical texts of all time.
Who is Euclid?
This advanced field of mathematics applies real and complex analysis to study properties of integers, particularly prime numbers.
What is Analytic Number Theory?
This lesser-known Millennium Prize problem deals with the well-posedness of a fundamental equation in mathematical physics, describing how fluids behave over time in three-dimensional space.
What is the Navier-Stokes Existence and Smoothness Problem?
This integral transform decomposes a function into its constituent frequencies, commonly used in signal processing and physics.
What is the Fourier Transform?
This Indian mathematician, born in 1887, made groundbreaking contributions to number theory, infinity series, and modular forms, despite having no formal training. His lost notebook continues to inspire modern research.
Who is Srinivasa Ramanujan?