Counting means **enumerating** the elements of a finite set of objects, such as the marbles in a jar, assigning each item a different number, that is, a unique **label**. But counting can also be an operation utterly **abstract** from the relationship with physical objects, performed on numbers present only in the mind of those who are counting.

The ability to count has evolved in humans for at least 40,000 years, as evidenced by tallies and notches found on bones and bone fragments discovered at a prehistoric site in South Africa. …

The **standard** or canonical form of a linear equation is:

in which 𝑎 and 𝑏 are **coefficients**, that is, known numbers, and 𝑥 is a **variable**, i.e., the placeholder of a quantity that can take on multiple values. The 𝑥, for which the exponent 1 is implied (𝑥¹), is also the **unknown** or the quantity you want to know the value of by solving the equation.

In the most common case, in which 𝑎≠0, the equation has only **one solution**:

The slope of a line in the Cartesian plane is the **inclination** of the line with respect to the abscissa axis. Usually indicated with the letter 𝑚, it is expressed by a number that describes both the **steepness** and the **direction** of the line. It corresponds to the ratio between the change in the 𝑦-coordinate and the change in the 𝑥-coordinate:

Δ𝑦 (read “delta y”) is the change in 𝑦, i.e., the **difference** between the 𝑦-coordinates of any two points on the line. Δ𝑥 (read “delta x”) is the change in 𝑥, i.e., the difference between the 𝑥-coordinates of those…

Born into a very modest family, with an authoritarian father totally disinterested in his son’s mathematical talent, Gauss was nevertheless a child prodigy, a *wunderkind*, as they say in German.

An anecdote told by various sources — we do not know to what extent adhering to historical truth — reports that in 1784, a just nine years old Gauss, who was attending a school in Braunschweig, near Hanover, brilliantly solved a task assigned to the class by a teacher named Büttner, who thought with that task of keeping his students busy for a long time.

Büttner had assigned the students…

A curious series of palindromic numbers is obtained by multiplying by themselves numbers composed of strings of 1 (the 1’s must be at least two to have a product that has more than one digit):

The series of palindromes ends here. If you get to ten 1’s per factor, the product is no longer a palindrome:

A **number** is essentially an **abstraction**. It is the **concept** of a given **quantity**. It presupposes the cognitive ability to analyze our experience of the world, recognizing **similarities** and **differences** of all kinds, from the most evident to the most subtle.

Similarities and differences allow us to **catalog** experiences and sensations. We learn from an early age to **isolate** the **common** traits of what we observe. In this way, we form concepts that transform collections of perceptions into objects of thought: we bite an apple, no longer just a rounded, fragrant thing with a juicy pulp.

Thanks to the capacity…

La relatività speciale o ristretta, pubblicata da Einstein nel 1905, portò alla luce aspetti del mondo fisico che rivoluzionavano profondamente la visione dell’Universo su cui era basata la cosiddetta fisica classica. La teoria sviluppata da Einstein aveva a suo fondamento due soli princìpi:

- le leggi fisiche, a cominciare da quelle della meccanica, sono valide in tutti i sistemi di riferimento inerziali [1];
- la luce si propaga nel vuoto a velocità costante indipendentemente dallo stato di moto della sorgente o dell’osservatore.

Da questi due postulati derivavano conseguenze sconcertanti per il senso comune. La relatività ristretta dimostrò che non esistono uno spazio…

Our galaxy, the Milky Way, together with about seventy other galaxies, is part of a cluster called the Local Group, which extends for about 10 million light-years. The two largest and most massive galaxies of the Local Group are Andromeda (M31) and the Milky Way, followed by another spiral, the Triangle Galaxy (M33). The fourth galaxy of the group by mass and size is the Large Magellanic Cloud, which is considered a minor galaxy, as it is a Milky Way’s satellite.

The glue that holds the Local Group together is the mutual gravitational attraction between the several galaxies that are…

In 1968, Eric E. Becklin and Gerald Neugebauer, two Caltech astronomers, managed to scan the central parsecs of the Milky Way in four different infrared wavelengths, obtaining the best results at 2.2 µm. Overcoming 25 magnitudes of obscuration due to the dust in the interposed spiral arms, they discovered swarms of stars huddled together with an unlikely density, compared to the enormous distances that, in the galactic periphery, separate the Sun from its neighbors. An article published in *Scientific American *in April 1974 (R.H. Sanders and G.T. …

Betelgeuse, the red supergiant in Orion, has always been one of the most observed and studied stars by astronomers. Despite the nearly 1,500 scientific papers that have been dedicated to it from 1850 to today, it is surprising how much our knowledge of this magnificent star is still inaccurate. In particular, Betelgeuse’s exact distance and radius have been the subject of a long series of estimates, none of which has so far managed to agree once and for all the researchers interested in the question.

A new article, published on 13 October in *The Astrophysical Journal*, is part of this…

Science writer with a lifelong passion for astronomy and comparisons between different scales of magnitude.