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Without mathematics there is no art.
— Luca Pacioli, Italian mathematician (1445 – 1517)

### Poetry

Mathematical language can heighten the imagery of a poem; mathematical structure can deepen its effect. Feast here on an international menu of poems made rich by mathematical ingredients.

### Short Story

Ted Chang’s division by zero

### Paintings and Sculptures

Dorothea Rockburne’s artwork

Paul Erdős Biography [1, 2, 3]

“My brain is open” – Paul Erdős

Paul Erdős was born on March 26, 1913 in Budapest, Hungary to a Jewish family whose name was originally Engländer. Though the times of antisemitism was behind them, the Hapsburgs did not want to be reminded of their Jewish neighbors. Thus, Paul’s father picked a common Hungarian name that means “from the woods”. It’s approximate pronunciation is air-dish. His parents Lajos and Anna had two daughters who died just days before Paul was born. This would make his mother extremely protective of Paul. He would get his introduction to mathematics from his parents who were both mathematics teachers; a profession that was held in high regard in Hungary which boasted an outstanding educational system.

It turned out that Paul was a childhood prodigy who had an affinity for numbers. He would learn to count when his mother left for teaching. One day when Paul was just four years old a visitor, who after Paul had calculated the number of seconds he had lived, decided to give Paul a tricky question. He asked, “What is 150 minus 200?” Paul went quiet for a moment as his mind went of into unknown territory. Then he smiled and yelled excitedly, “150 below zero!” This was no small feat. He just independently discovered negative numbers! He would later down play his calculating abilities, but he would always remark with pride “his discovery” at the age of four.
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In college, we often learn of many infinite series that give the value of pi including one called the Leibniz series, named after Gottfried Leibniz. It is also called the Gregory–Leibniz series, recognizing the work of James Gregory. This unnecessarily attributes the discovery to the west, however, the formula was first discovered in India by Madhava of Sangamagrama and so is also called the Madhava–Leibniz series. Indian mathematicians made vast and fundamental contributions to our modern mathematics.

$\pi=4\sum_{k=0}^{\infty}\frac{(-1)^{k}}{2k+1}$

IMAGE: This knot has Gauss code O1U2O3U1O2U3.

In his article “The Combinatorial Revolution in Knot Theory”, to appear in the December 2011 issue of the Notices of the AMS, Sam Nelson describes a novel approach to knot theory that has gained currency in the past several years and the mysterious new knot-like objects discovered in the process.

As Nelson reports in his article, mathematicians have devised various ways to represent the information contained in knot diagrams. One example is the Gauss code, which is a sequence of letters and numbers wherein each crossing in the knot is assigned a number and the letter O or U, depending on whether the crossing goes over or under. The Gauss code for a simple knot might look like this: O1U2O3U1O2U3.

In the mid-1990s, mathematicians discovered something strange. There are Gauss codes for which it is impossible to draw planar knot diagrams but which nevertheless behave like knots in certain ways. In particular, those codes, which Nelson calls *nonplanar Gauss codes*, work perfectly well in certain formulas that are used to investigate properties of knots. Nelson writes: “A planar Gauss code always describes a [knot] in three-space; what kind of thing could a nonplanar Gauss code be describing?” As it turns out, there are “virtual knots” that have legitimate Gauss codes but do not correspond to knots in three-dimensional space. These virtual knots can be investigated by applying combinatorial techniques to knot diagrams. Read the article here.

UCLA mathematicians devise an algorithm based on data from the Los Angeles Police Department for the Hollenbeck area east of downtown. Read the article here.

This is a link to Terence Tao’s “retired” lecture Structure and randomness in the prime numbers. Mathematicians with Terence’s talent appear only once in a generation and he is arguably the best living mathematician in the world.

View a public lecture by Terence Tao on the topic here.

Great guy and great mathematician. View some of his published papers.