The quest to approximate irrational numbers with fractions reveals hidden patterns, surprising hierarchies and enduring mathematical mysteries ...

Decimal represents values internally using three integers: a sign, a coefficient, and an exponent. In this way, numbers of any size and with any number of decimal places can be represented exactly.

Note: Some of the code here is old and was written when I was learning C++. It might be possible that code is not safe or making wrong assumptions. Please use with caution. Pull requests are always ...

Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement ...

While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental ...

The recent discussion about the consistency of arithmetic made me want to brush up on my logic. I’d like to learn a bit about axioms for arithmetic that are weaker than Peano arithmetic. The most ...

Although quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent ...

We will see that the famous intractible 1959 Kadison–Singer Problem in C*-algebras is equivalent to fundamental open problems in a dozen different areas of research in mathematics and engineering.