Math for everyone
Mathematical content accessible to everyone
Paul Erdős and the probabilistic view of arithmetic
With the development of probability theory in the early 20th century, a new field of inquiry opened up in arithmetic: the statistical study of integers. Paul Erdős was among the first mathematicians to grasp the significance of this new approach.
Why not base 12? The advantages of the duodecimal system
If you talk to people about the history of arithmetic, whatever your specific subject, you can expect someone to ask this question at the end: why is our numeral system base 10 when base 12 would be so much more practical?
Applying the Chinese remainder theorem to RSA cryptography
The Chinese remainder theorem finds, among other things, applications in cryptography
Chinese remainder theorem: history and applications | Tangente
The Chinese remainder theorem owes its name to ancient Chinese mathematicians’ interest in the arrangement problems it describes. Originally a source of puzzles, it has since found more practical applications, particularly in cryptography.
A logarithm beneath the hyperbola | Tangente Magazine
Although Napier introduced them purely as an aid to calculation, logarithms gradually permeated every branch of mathematics. Their fundamental nature emerged particularly clearly through their connections with geometry, trigonometry and the hyperbola.
Logarithms in everyday life | Tangente
Logarithms are also used to establish laws that attempt to account for human subjectivity.
Logarithms come to the table | Tangente Magazine
I'm speaking of a time that those under twenty cannot know...
Jean-Pierre Kahane: A committed mathematician
Jean-Pierre Kahane, who passed away last June at the age of 90, left his mark on his era in many ways: through his work in analysis, which earned him international renown and election to the Académie des sciences; and through his commitment, both political and in the popularization of mathematics.
The inverse of the exponential function
The introduction of logarithms can be traced back to the Renaissance, when they were used to solve computational problems. They have since found more theoretical applications and today even lie at the heart of some cryptographic systems—and hence of our computers.
Logarithms: A whole vocabulary
Logarithmic derivative, logarithmic spiral, logarithmic scales... and a raccoon.
John Napier's astonishing inventions
John Napier of Merchiston, the Scottish gentleman whose death four centuries ago is being commemorated this year, was no revolutionary. Yet his wondrous invention of logarithms made him one, opening up a new world for mathematics far beyond computation.
A lovely transformation
An operation on complex numbers turns lines into circles and vice versa. A transformation worth keeping in mind when tackling problems involving lines and circles…
A detour through complex numbers
Taking a detour, part way through a proof, by way of complex numbers can lead to one of those redeeming "mathematical surprises".
A bit of etymology | Tangente
The vocabulary specific to complex numbers is the work of several mathematicians across the centuries
? as in comic
The classics of mathematical humor often borrow some of their gems from the vocabulary of complex numbers…
Teaching complex numbers in France
Complex numbers, though they may seem self-evident in the wording of today's school curricula, have not always been part of the high-school teaching corpus.
Complex numbers according to Adrien Douady | Tangente
The film Dimensions offers a look at a number of spectacular representations of complex numbers. Don't wait to rediscover it!
The zeta function and the Riemann hypothesis
The most important problem in contemporary mathematics can be stated in entirely elementary terms, requiring only a rudimentary knowledge of complex analysis. Despite mathematicians' titanic efforts, the Riemann hypothesis remains stubbornly out of reach.
The complex exponential
How can the classical exponential function be extended to complex numbers? Will its usual properties be preserved? Although the resulting extension is easy to study, the associated notion of a complex logarithm is more elusive. It was the subject of controversy in the 18th century.
Marden's theorem
Complex numbers, born of impossible calculations, found an unlikely geometric interpretation. This meeting of algebra and geometry is beautifully illustrated by theorems about the roots of a complex polynomial.