Analysis
Explore mathematics articles on the theme of analysis.
Hong Wang wins 2026 Fields Medal for 3D Kakeya proof
Mathematician Hong Wang becomes the third woman to receive the Fields Medal, for solving the century-old Kakeya needle problem in three dimensions together with Joshua Zahl.
Do you think in words when solving an equation?
Neuroscience reveals that the brain processes mathematics through networks distinct from those of natural language, calling into question our understanding of mathematical cognition.
Measuring infinity: how Borel and Lebesgue went beyond Newton
Explore Lebesgue measure, Borel's normal numbers and the foundations of probability theory through the history of mathematics.
Normal numbers: The Library of Babel hides your password
Explore the normal numbers defined by Borel in 1909, revealed through the literary analogy of Borges's Library of Babel. A meeting point of number theory, probability, and analysis.
How a specialist in probability becomes a pillar of the Republic of Professors
A portrait of Émile Borel, the illustrious mathematician of the Belle Époque, who combined a brilliant scientific career with political engagement and a fight for justice.
This papyrus buried by Vesuvius in 79 AD was read unopened
Researchers have succeeded in reading a papyrus scroll charred by Vesuvius in 79 AD, using tomography, phase contrast, and artificial intelligence.
Hilbert's 6th problem solved: the Newton-Boltzmann-Navier-Stokes link finally proven
A team of mathematicians has finally solved Hilbert's sixth problem, linking the equations of Newton, Boltzmann, and Navier-Stokes after 125 years of research.
Leibniz and the best of all possible worlds: mathematics and philosophy
How Leibniz uses mathematics to justify the existence of the best of all possible worlds through infinitesimal calculus, symmetry, and philosophy.
Newton on space and the divine: a philosophical and historical analysis
Isaac Newton revolutionized our understanding of space by conceiving it as an absolute mathematical framework, distinct from the bodies within it.
Whitehead: logical harmony of mathematics and philosophy
A journey into the thought of Alfred North Whitehead, who laid the foundations of the Principia Mathematica with Russell and developed a metaphysics of the cosmos in which God and mathematics work together in the world's unfolding.
Terence 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.
Two locally identical yet different tori break 150 years of geometry
Two tori plainly impossible to tell apart locally yet topologically distinct: a discovery that breaks a rule geometry has accepted for 150 years.
The Boltzmann equation: from molecular chaos to macroscopic equilibrium
Formulated in 1872 by the Austrian physicist Ludwig Boltzmann (1844–1906), this equation describes how a gas or fluid evolves toward equilibrium. It bridges molecular collisions at microscopic scales and the macroscopic world.
Skewes's numbers: enormous bounds in number theory
Skewes's numbers are among the large numbers encountered in arithmetic.
Plotting algebraic curves in the 18th century: Newton’s and Cramer’s analytic methods
How did Gabriel Cramer plot algebraic curves in 1750? Discover Newton's analytical parallelogram and Cramer's analytical triangle.
Gabriel Cramer: the journey of an 18th-century Genevan mathematician
Explore Gabriel Cramer's journey, from his education in Geneva to his European Grand Tour among the leading mathematicians of his day.
Beyond convexity | Tangente
The intuitive idea behind convexity seems entirely natural. Yet one cannot help wondering whether slightly altering the formal definition might lead to other interesting ideas… Here too, convexity is just as fruitful!
Convexity in finance | Tangente
Mathematics plays an important role in finance. In recent years, returns on capital have been drastically reduced for various economic and political reasons. In Europe today, negligible returns on capital are becoming the norm, yet inflation remains very real, at around 5%.
A modern theory with ancient roots | Tangente
It was during the twentieth century that convexity emerged as a mathematical discipline in its own right. Before then, eminent mathematicians had occasionally glimpsed the potential value of this notion in geometry and analysis.
Poincaré's qualitative approach to analysis | Tangente
Every high-school student learns how to express the real roots of a quadratic equation explicitly in terms of square roots. This becomes much more difficult for higher-degree equations and impossible from degree five onward.