Jean-Baptiste Joseph Fourier, in studying the conduction of heat in solid bodies, devised a way to analyze it using an infinite series of trigonometric terms. Similar mathematical problems arise in almost every branch of physics, and Four...

Commonly known by the name Helge, Niels Fabian Helge von Koch is best remembered for devising geometrical constructs that are now called the Koch curve and the Koch snowflake (or star). He was also an expert on number theory and wrote exte...

Henri Cartan has made monumental contributions in essentially every field of algebraic topology, including analytical functions, the theory of sheaves, homological theory, and potential theory. His most important works include Homological ...

The French mathematician Jules Henri Poincaré (1854-1912) initiated modern combinatorial topology and made lasting contributions to mathematical analysis, celestial mechanics, and the philosophy of science. Henri Poincaré was...

In spite of a relatively short career, Hermann Minkowski played an important role in the development of modern mathematics. His work formed the basis for modern functional analysis, and he did much to expand the knowledge of quadratic form...

The engineer, mathematician, and inventor Heron of Alexandria (active ca. AD 60) ranks among the most important scientists of the ancient Roman world in the tradition of Aristotelian experimentation. Heron, about whose personal life virtua...

An ordinary differential equation (ODE) is an equality involving a function containing an unknown and the derivative(s) of that function. The order of an ordinary differential equation is determined by the order of the highest-order deriva...

Named for David Hilbert (1862-1943), Hilbert presented his paradox (also known as Hilbert's hotel paradox) as an explanation of infinity and an extension of Cantor's continuum hypothesis. In revealing his paradox, Hilbert posited a hotel w...

David Hilbert (1862-1943), a mathematician from the University of Goettingen, launched his program during an address to the International Congress of Mathematicians in the summer of 1900. Hilbert contended that all mathematical principles,...

Among the celebrated physicians in history, none is more widely recognized than Hippocrates of Cos. If modern doctors know a name from antiquity, it will be that of Hippocrates, whether from the bowdlerized Oath, supposedly written by this...

Two objects are topologically equivalent if one object can be continuously deformed to the other. In one or two dimensions, this is something we can visualize: to continuously deform a surface means to stretch it, bend it, shrink it, expan...

John Hubbard is perhaps most well known for his early work on Mandelbrot sets in which he discovered the so called pictures in1976. As part of this work Hubbard also had a great interest in polynomials and exponential functions. His more r...

Swiss mathematician and physicist Daniel Bernoulli (1700-1782) brought a high level of mathematical rigor to the study of natural phenomena, particularly phenomena associated with liquids and gases. He was especially fascinated with the b...

Curve with two separate branches, one of the conic sections. In Euclidean geometry, the intersection of a double right circular cone and a plane at an angle that is less than the cone's generating angle (the angle its sides make with its c...

In mathematics, one of a set of functions related to the hyperbola in the same way the trigonometric functions relate to the circle. They are the hyperbolic sine, cosine, tangent, secant, cotangent, and cosecant (written “sinh,&rdquo...

Non-Euclidean geometry, useful in modeling interstellar space, that rejects the parallel postulate, proposing instead that at least two lines through any point not on a given line are parallel to that line. Though many of its theorems are ...