Re -Train Your Brain To Happiness: Five Brilliant Mathematicians And Their Impact On The Modern World

Of course there have been many more brilliant mathematicians than five as the above heading suggests.

We owe a great debt to scores of mathematicians who helped lay the foundation for our modern society with their discoveries. Here are some of the most important.

Math. It's one of those things that most people either love or hate. Those who fall on the hate side of things might still have nightmares of showing up for a high school math test unprepared, even years after graduation. Math is, by nature, an abstract subject, and it can be hard to wrap your head around it if you don't have a good teacher to guide you.

But even if you don't count yourself a fan of mathematics, it's hard to argue that it hasn't been a vital factor in our rapid evolution as a society. We reached the moon because of math. Math allowed us to tease out the secrets of DNA, create and transmit electricity over hundreds of miles to power our homes and offices, and gave rise to computers and all that they do for the world. Without math, we'd still be living in caves getting eaten by cave tigers.

Our history is rich with mathematicians who helped advance our collective understanding of math, but there are a few standouts whose brilliant work and intuitions pushed things in huge leaps and bounds. Their thoughts and discoveries continue to echo through the ages, reverberating today in our cellphones, satellites, hula hoops and automobiles. We picked five of the most brilliant mathematicians whose work continues to help shape our modern world, sometimes hundreds of years after their death. Enjoy!

Isaac Newton (1642-1727)

We start our list with Sir Isaac Newton, considered by many to be the greatest scientist of all time. There aren't many subjects that Newton didn't have a huge impact in — he was one of the inventors of calculus, built the first reflecting telescope and helped establish the field of classical mechanics with his seminal work, "Philosophiæ Naturalis Principia Mathematica." He was the first to decompose white light into its component colors and gave us the three laws of motion, now known as Newton's laws. (You might remember the first one from school: "Objects at rest tend to stay at rest and objects in motion tend to stay in motion unless acted upon by an external force.")

We would live in a very different world had Sir Isaac Newton not been born. Other scientists would probably have worked out most of his ideas eventually, but there is no telling how long it would have taken and how far behind we might have fallen from our current technological trajectory.

Carl Gauss (1777 - 1855)

Isaac Newton is a hard act to follow, but if anyone can pull it off, it's Carl Gauss. If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever. Carl Friedrich Gauss was born to a poor family in Germany in 1777 and quickly showed himself to be a brilliant mathematician. He published "Arithmetical Investigations," a foundational textbook that laid out the tenets of number theory (the study of whole numbers). Without number theory, you could kiss computers goodbye. Computers operate, on a the most basic level, using just two digits — 1 and 0, and many of the advancements that we've made in using computers to solve problems are solved using number theory. Gauss was prolific, and his work on number theory was just a small part of his contribution to math; you can find his influence throughout algebra, statistics, geometry, optics, astronomy and many other subjects that underlie our modern world.

John von Neumann (1903-1957)

John von Neumann was born in Budapest a few years after the start of the 20th century, a well-timed birth for all of us, for he went on to design the architecture underlying nearly every single computer built on the planet today. Right now, whatever device or computer that you are reading this on, be it phone or computer, is cycling through a series of basic steps billions of times over each second; steps that allow it to do things like render Internet articles and play videos and music, steps that were first thought up by John von Neumann.

Von Neumann received his Ph.D in mathematics at the age of 22 while also earning a degree in chemical engineering to appease his father, who was keen on his son having a good marketable skill. Thankfully for all of us, he stuck with math. In 1930, he went to work at Princeton University with Albert Einstein at the Institute of Advanced Study. Before his death in 1957, von Neumann made important discoveries in set theory, geometry, quantum mechanics, game theory, statistics, computer science and was a vital member of the Manhattan Project.(pictured above).

Alan Turing (1912 - 1954)

Alan Turing a British mathematician who has been call the father of computer science. During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine. Being able to break Nazi codes gave the Allies an enormous advantage and was later credited by Winston Churchill as one of the main reasons the Allies won the war.

Besides helping to stop Nazi Germany from achieving world domination, Alan Turing was instrumental in the development of the modern day computer. His design for a so-called "Turing machine" remains central to how computers operate today. The "Turing test" is an exercise in artificial intelligence that tests how well an AI program operates; a program passes the Turing test if it can have a text chat conversation with a human and fool that person into thinking that it too is a person.

Alan Turing's career and life ended tragically when he was arrested and prosecuted for being gay. He was found guilty and sentenced to undergo hormone treatment to reduce his libido, losing his security clearance as well. On June, 8, 1954, Alan Turing was found dead of apparent suicide by his cleaning lady.

Turing's contributions to computer science can be summed up by the fact that his name now adorns the field's top award. The Turing Award is to computer science what the Nobel Prize is to chemistry or the Fields Medal is to mathematics. In 2009, then British Prime Minister Gordon Brown apologized for how his government treated Turing, but stopped short of issuing an official pardon.

Benoit Mandelbrot (1924-2010)

Benoit Mandelbrot landed on this list thanks to his discovery of fractal geometry.
Fractals, often-fantastical and complex shapes built on simple, self-replicable formulas, are fundamental to computer graphics and animation. Without fractals, it's safe to say that we would be decades behind where we are now in the field of computer-generated images. Fractal formulas are also used to design cellphone antennas and computer chips, which takes advantage of the fractal's natural ability to minimize wasted space.

Mandelbrot was born in Poland in 1924 and had to flee to France with his family in 1936 to avoid Nazi persecution. After studying in Paris, he moved to the U.S. where he found a home as an IBM Fellow. Working at IBM meant that he had access to cutting-edge technology, which allowed him to apply the number-crunching abilities of electrical computer to his projects and problems. In 1979, Mandelbrot discovered a set of numbers, now called the described by science-fiction writer Arthur C. Clarke as Mandelbrot set, that were "one of the most beautiful and astonishing discoveries in the entire history of mathematics." (To learn more about the technical steps behind drawing the Mandelbrot set, click over to the infographic I made last year for a class that I'm taking.)

Benoit Mandelbrot died of pancreatic cancer in 2010.

With thanks to Shea Gunter at MNN

And now a movie about Alan Turing:

'Imitation Game' trailer gives us Benedict Cumberbatch as code-breaker Alan Turing.

The first trailer for the "The Imitation Game," starring Benedict Cumberbatch as codebreaker Alan Turing, has arrived — and it has Oscar bait written all over it.

The drama tells the true story of gifted British mathematician Alan Turing and his efforts to crack Nazi Germany's "unbreakable" Enigma code. Taking place during "the darkest days of WWII," audiences will be transported back to Britain’s top-secret code-breaking center, Bletchley Park, where Turing and his team made history.

Turing, widely considered considered the father of computer science and artificial intelligence, unfortunately was later charged by his own government with "gross indecency," after admitting to having a sexual relationship with another man. Forced to take hormone injections, he was later found dead at age 41 from an apparent suicide.

In recognition of his accomplishments, Queen Elizabeth last year gave Turing a rare posthumous royal pardon. Justice Minister Chris Grayling, who requested the pardon, said the mathematician "deserves to be remembered and recognised for his fantastic contribution to the war effort and his legacy to science. A pardon from the Queen is a fitting tribute to an exceptional man."

This article by Michael d'Estries and also at MNN.

In the past there was another movie about the Enigma machine.