Oiler's Formulae
This famous identity, often referred to as "the most beautiful equation in mathematics" allows us to define what it means to raise a number to an imaginary power.
What is e^(ix) = cos(x) + i*sin(x)?
A set with an operation that associates an element of the set to every pair of elements of the set, this operation is associative, has an identity element, and every element of the set has an inverse element.
What is a group?
This theorem states that every self-adjoint bounded linear operator on a finite-dimensional Hilbert space has at least one eigenvalue.
What is the Spectral Theorem
This Baltimore Ravens guard "retired" at the age of 26 after 3 seasons in the NFL to obtain a PhD in mathematics at Princeton. He is now an assistant professor of mathematics at MIT.
Who is John Urschel?
This early mathematical tool, often associated with Ancient China, was used for counting and performing arithmetic operations.
What is an abacus?
Known as "Euler's other number," this value is the limiting difference between the natural log and the harmonic series.
What is the Euler-Mascheroni Constant?
A p-Sylow subgroup of a finite group has this number of elements.
What is p^n, where p^n is the highest power of p dividing dividing the order of the group?
The Lebesgue measure of the Cantor set is this value.
What is 0?
Most widely known for authoring the Alice in Wonderland series under the pen name Lewis Carroll, this man also published prolifically in numerous mathematical fields, including linear algebra and the study of elections (Charles Dodgson)
Who is Charles Dodgson?
The Pythagorean theorem, which relates the sides of a right triangle, was first discovered by this civilization.
Who are the Babylonians?
This expression relates the faces, vertices, and edges of geometric objects to a quantity determined by the number of "holes" it has.
What is the Euler Characteristic Formula (V + F - E = χ)?
This theorem states that every separable field extension of finite degree is simple.
What is the primitive element theorem
The dual space of C([a,b]), the space of continuous functions on [a,b], is this space.
What is the space of Radon measures on [a,b]?
While his term as the 20th president of the United States did not last long, this man published a proof of the Pythagorean theorem while a congressman from Ohio
Who is James Garfield?
This unsolved problem in mathematics, proposed in 1637, went unproven for 358 years until it was finally solved in 1994 by Andrew Wiles.
What is Fermat's Last Theorem?
This provides an alternative expression for the Riemann Zeta function, and, interestingly, features an index over all prime numbers.
What is the Euler Product?
An integral domain in which every nonzero proper ideal factors into a product of prime ideals.
What is a Dedekind domain?
The Lebesgue integral is an incredible tool for real- and complex-valued functions, but for more general vector spaces, you'll need this integral construction.
What is the Bochner integral?
The lead guitarist and current frontman for the rock band Queen abandoned his studies in math and physics as his band reached superstardom. After decades on tour, he returned to school and completed a PhD in astrophysics at the age of 56.
Who is Brian May?
Proved in 1976, this major theorem was the first in history to be proven using a computer, sparking debates about the nature of mathematical proof.
What is the Four-Color Theorem?
This construction gives us a way to categorize "how irrational" a real number is by associating to each a sequence. A terminating sequence means the number is rational.
What are continued fractions?
This is the Galois group of x^4 - 2x^2 - 2.
What is the dihedral group
D_8, sometimes called
D_4.
A strange consequence of this theorem seems to defy the conservation laws of matter. It holds that it is possible to cut a solid ball into a finite number of pieces, and by re-assembling them in a particular way, form 2 solid balls, identical to the original.
What is the Banach-Tarski theorem?
Most famous for starring in numerous lead roles in family Christmas movies, this actress studied mathematics and published a paper during her undergraduate studies at UCLA. Throughout her acting career, she has continued to publish nonfiction works aimed at middle- and high-school girls studying mathematics.
Who is Danica McKellar?
This mathematician died at the young age of 20 in a duel. Despite this, he has accomplished way more than you have, and the ideas he pioneered are studied today in an field named after him.
Who is Evariste Galois?