7 Brilliant Mathematicians and Their Impact on the Modern World

Math. It's one of those things that is easy to 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 wouldn't be where we are today. (And yes, some may argue that that might not have been such a bad thing.)

Regardless, our history is rich with mathematicians who helped advance our collective understanding of math, but there are a few standouts whose work and intuition pushed progress in leaps and bounds. Their vision and discoveries continue to echo through the ages, reverberating today in our cell phones, satellites, hula hoops, and automobiles. We picked some of the most remarkable 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 significant impact on—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 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 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.

Emmy Noether (1882-1935)

Born Amalie Emmy Noether, Emmy Noether was a German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics.

She is particularly known for Noether's Theorem, which establishes a fundamental connection between symmetries in physics and conserved quantities. This theorem has had a significant impact on the field of theoretical physics and is considered a cornerstone of modern theoretical physics.

Noether's work continues to influence both mathematics and physics. Her contributions are foundational in various branches of mathematics, such as abstract algebra, algebraic geometry, and topology. Her theorem remains a cornerstone in theoretical physics, providing deep insights into the conservation laws that govern physical systems.

Emmy Noether's legacy is a testament to her brilliance, perseverance, and the enduring impact of her ideas on multiple fields of study. Despite facing barriers as a woman in academia during a time when this wasn't the norm, Noether's work has left a lasting legacy and continues to inspire mathematicians and physicists to this day.

John von Neumann (1903-1957)

John von Neumann was born János Neumann 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 a 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 von Neumann.

Von Neumann was a child prodigy who 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.

Remarkably, Von Neumann proposed a theory of global warming caused by human activity, noting that the Earth was only 6 degrees F (3.3 C) colder during the last glacial period. In 1955, he wrote: "Carbon dioxide released into the atmosphere by industry's burning of coal and oil—more than half of it during the last generation—may have changed the atmosphere's composition sufficiently to account for a general warming of the world by about one degree Fahrenheit."

Alan Turing (1912-1954)

Alan Turing was a British mathematician who has been called 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 some historians as one of the main reasons the Allies won the war.

Besides helping to stop Nazi Germany from achieving world domination, Turing was instrumental in the development of the modern 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.

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, Turing was found dead of an apparent suicide.

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 Mandelbrot set. In a documentary titled "The Colours of Infinity," science-fiction writer Arthur C. Clarke described it as "one of the most beautiful and astonishing discoveries in the entire history of mathematics." Learn more about the technical steps behind drawing the Mandelbrot set.

Mandelbrot died of pancreatic cancer in 2010.

Maryam Mirzakhani (1977-2017)

Maryam Mirzakhani was an Iranian mathematician known for her visionary work in the field of complex geometry and particularly for her contributions to the study of moduli spaces of Riemann surfaces.

She made history in 2014 when she became the first Iranian and first woman to be awarded the prestigious Fields Medal, generally considered the highest honor in mathematics. Her work combined insights from various areas of mathematics, including hyperbolic geometry, topology, and dynamics, and had implications not only in pure mathematics but also in theoretical physics and other fields.

Her work was notable for its singular creativity and elegance and for the way in which she developed innovative techniques to study geometry. Tragically, she passed away in 2017 at the age of 40, but her contributions continue to inspire the mathematical community, particularly those interested in the intersections of geometry, topology, and complex analysis.