Because an effort is likely impossible and impractical does not mean it is not worth attempting. The Navier-Stokes equations and turbulent flow represent the last great classical problem in physics. Since the time of Leonard Euler and Jean-Baptiste le Rond d’Alembert, many have devoted much of their lives to working on these problems. Although they …

# Category Archives: Mathematics

## Deming and Statistics

In God we trust. All others must bring data. — W. Edwards Deming Deming revolutionized quality management with his emphasis on data-driven decision-making. His 1950s lectures on Statistical Product Quality Administration in Japan were instrumental in Japan’s post-war economic growth, helping it become the world’s second-largest economy. Deming was awarded the National Medal of Technology …

## Gödel and Time

$\mathrm{LL}$ cosmological solutions with non-vanishing density of matter known at present ${ }^1$ have the common property that, in a certain sense, they contain an “absolute” time coordinate, ${ }^2$ owing to the fact that there exists a one-parametric system of three-spaces everywhere orthogonal on the world lines of matter. It is easily seen that …

## Underlying Assumptions

How Can Any Part of Mathematics Be Proven? The answer lies in demonstrating that a mathematical statement must be true if the underlying simpler math is also true. It is a great difficulty to show the increment from 1 to 2. Between 1910 and 1913, a three-volume work was published on this subject. Titled Principia …

## Boole and Laws of Thought

George Boole, in the 1840s, proposed that variables could represent more than just numbers. Boole’s work, published in “An Investigation of the Laws of Thought” (1854), introduced algebra with two values: 1 (true) and 0 (false). Instead of traditional algebraic operations, Boolean algebra uses AND, OR, and NOT, also known as conjunction, disjunction, and complement. …

## Liouville and Numbers

In 1844, Joseph Liouville demonstrated that the decimal representations of certain numbers were infinitely long and lacked pattern. This idea, which suggests that numbers do not necessarily have an exact and finite value, was first proposed by Greek philosopher Zeno in the 5th century BCE. Zeno’s paradoxes are based on the infinite divisibility of space. …

## Complex Polynomials

The Fundamental Theorem of Algebra states that the field of complex numbers is algebraically closed, implying that every polynomial equation of degree n has n roots within the complex numbers, with at least one being a solution where the polynomial evaluates to zero. Historically, the theorem’s origin traces back to the conjectures by Albert Girard …

## Personal Equation

1796, Maskelyne, Astronomer Royal of Britain, dismissed his assistant for what he believed to be persistent inaccuracies in the timing of observations, specifically delays of approximately half a second. This decision unknowingly set the stage for the development of an important concept in measurement science: the personal equation. Maskelyne’s published their mixed observational results. After …

## Origins of Graph Theory

Graph theory emerged in the 18th century, connecting geometry with fields like topology and set theory. Leonhard Euler formulated graph theory during his time in Königsberg, now Kalingrad. His seminal work began with the 1736 paper, “The Seven Bridges of Königsberg.” Residents of Königsberg enjoyed crossing the city’s seven bridges in one outing – considered …

## Revisiting \(e\) History

\(e\), defined by the limit \(\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n\) and approximating 2.71828, is characterized by its irrational and transcendental nature, indicating it cannot be depicted as a quotient of two integers nor as a solution to any non-trivial polynomial equation with rational coefficients. John Napier, a Scottish mathematician and theologian, significantly contributed to …