Algebra and Number Theory are cornerstones of modern mathematics. At their heart, these fields study the underlying structures governing numbers and abstract entities, ranging from rings, fields, and ...

A vector $m = (m_1,\ldots, m_n) \in \mathbf{Z}^n\backslash\{0\}$ is called an integer relation for the real numbers $\alpha_1,\ldots, \alpha_n$, if $\sum \alpha_im_i ...

Zero is definitively an even number, mathematicians confirm. The formal definition states an even number is any whole number ...

For all but one positive integer triplet (a, b, c) with a ≼ b ≼ c and b ≼ 6, we decide whether there are algebraic numbers α, β and ϒ of degrees a, b and c, respectively, such that α + β + γ = 0. The ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...