Arithmetic
Explore mathematics articles on the theme of arithmetic.
PodcastTerence Tao and AI: what they are changing in mathematics
Terence Tao, a Fields Medalist, shares his experience with AI in mathematical research: an exploration partner that is transforming the way problems are formulated.
PodcastAckermann-Péter function: recursion without bounds
With a surprisingly simple definition, the Ackermann–Péter function generates numbers of a staggering size. This mathematical construction, born out of research into computability, shows how quickly a recursive procedure can exceed all the usual bounds.
PodcastMersenne primes: discover perfect numbers
The search for Mersenne primes very quickly leads us to examine gigantic numbers.
PodcastYear 2038 bug: the 32-bit timestamp problem explained
A massive bug related to the way computers represent large numbers looms on January 19, 2038, at 3:14:08 a.m.
PodcastEdward Kasner: the man behind googol and googolplex
Staggeringly large numbers invented by an eccentric mathematician that would inspire an iconic domain name...
PodcastRegular polygons with integer-coordinate vertices: one proof for all n
Discrete geometry is a recent field of research concerned with "discrete objects," such as graphs and tilings. But it also offers a fresh perspective on problems that are difficult to solve in a continuous setting, including the existence of regular polygons with integer-coordinate vertices.
PodcastInteger points on a line: methods of solution
Many problems in discrete geometry are simply stated and can be used in teaching to make certain concepts easier to understand. Searching for points with integer coordinates on a line naturally leads to applications of theorems from number theory.
PodcastMoving on the discrete plane: generating sets and minimality
Exploring how one can move around a grid leads to the concepts of generating sets and minimality. This example shows the power of discrete geometry as a tool for better visualizing and exploring complex ideas from classical geometry or algebra.
PodcastKnuth and Conway notations for mind-boggling numbers
When it comes to representing extremely large numbers, the standard operations, including exponentiation, are no longer enough. With considerable imagination, Donald Knuth and John Conway devised notations to overcome this limitation.
PodcastLong and short scales: billion, trillion, milliard—how to name large numbers
From colossal fortunes to the limits of mathematical language, words struggle to keep pace as numbers explode. From long and short scales, through international conventions, to mathematicians' bold inventions, the way we name extremely large quantities tells a story in which language, science and imagination meet.
Skewes's numbers: enormous bounds in number theory
Skewes's numbers are among the large numbers encountered in arithmetic.
PodcastDiscrete lines: the birth of a new geometry
Problems involving representation on a pixelated screen belong to discrete geometry. But beyond mere aesthetic considerations, are these new subjects of study—including discrete lines—tools for exploring Euclidean geometry more deeply, or objects of a new geometry?
PodcastArchimedes' Sand Reckoner: counting the grains of sand in the universe
If the universe is finite, then it can be filled with grains of sand. Yes, it would take a great many, but the quantity required would still be a finite number—one that can be expressed. Drawing on the most advanced astronomical knowledge of his time, Archimedes set out to do just that.
PodcastTheaetetus and the diagonal: why stop at √17?
How should we understand the famous passage in the Theaetetus where Theodorus mysteriously stops at the square root of 17? A new hypothesis emerges, involving continued fractions and triangular numbers.
PodcastCédric Aubouy, math clown and author of “Je ne sais pas”
Cédric Aubouy, a mathematical clown and founder of the L’île logique company, agreed to meet us to mark the publication of his first novel, Je ne sais pas ou la disparition des mathématiciens.
Timeless mathematical puzzles | Tangente
Puzzles have been part of human culture since earliest antiquity. At first, inventing puzzles was bound up with mythology or religion; gradually, it became a purely intellectual game, independent of any purpose or practical application.
Roman numerals and modern passions | Tangente
Controversy in Lutetia, in March MMXXI. The Carnavalet Museum, devoted to the history of Paris, has allegedly "abolished Roman numerals" from its new visitor experience on the pretext that they represent "an obstacle to understanding", claims the Italian daily Corriere della Serra.
A spiral of digits | Tangente
An entertaining blend of arithmetic and graphics lets us display the successive terms of an arithmetic sequence visually. This calls for some explanation—and decoding!
Happy is one who, like a number... | Tangente
Starting with an integer, apply a simple rule to obtain a new number. Repeat the process with the result, and so on... Depending on the pattern followed by this sequence—cyclic, constant from some point onward, and so on—the starting number is described as happy, perfect... But sometimes the pattern is still unknown.
196: a very curious number! | Tangente
A palindrome, or palindromic number, reads the same from right to left as from left to right, like 514,415. Here is a simple recipe for finding one.