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

Photo: Wikimedia Commons

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

Photo: Wikimedia Commons

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

Photo: Wikimedia Commons

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.

Alan Turing

Photo: Wikimedia Commons

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

Photo: Wikimedia Commons

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.

At Hawthorne-based SpaceX, high school students learn to reach for the stars

By Sandy Mazza, Daily Breeze

POSTED: 08/20/16, 5:01 PM PDT | UPDATED: 2 HRS AGO

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Hundreds of standout college engineering students launch their careers each year as SpaceX interns, working long hours beside some of the country’s best rocket engineers at the trailblazing Hawthorne commercial spaceflight company.

But only a few high school students get the same opportunity.

A handful of teens are chosen annually from Hawthorne’s three high schools to walk through the glass doors at 1 Rocket Road and join the visionary team at Space Exploration Technologies Corp.’s headquarters.

They aren’t tasked with building rockets, of course. But they are assigned work that’s crucial to keeping the round-the-clock company running smoothly. They’re stationed in the heart of the operation, in the information-technology lab, where they troubleshoot computer problems and maintain employee work stations.

“We try to have close partnerships with Hawthorne high schools,” said community outreach manager Lilian Haney. “We treat it like our regular college intern program. The students have to submit resumes and cover letters.”

Teachers recommend their best science and engineering students from Da Vinci science, design and communications charter schools, Hawthorne Math & Science Academy and Hawthorne High School. SpaceX then chooses a few of those hopefuls each year.

Inside the giant gleaming white rocket-building warehouse, students learn about the real world from the perspective of a company focused on expanding human access to Mars and beyond.

“I find it amazing that humans can send stuff to space and how far we’ve come,” said Vincent Ornelas, a new graduate of Da Vinci Schools in Hawthorne who snagged one of the coveted spots this summer. The 19-year-old is about to start college classes at Loyola Marymount University studying mechanical engineering.

When he began his SpaceX internship, Ornelas said he’d built robots at school but they were just toys. Working among top-notch engineers taught him that, above all, success takes a lot of work.

“I had no idea what I was getting into. I knew they wanted to go to Mars but I learned there’s a lot to that. It’s a real situation here. It’s important.

“On the robotics team at school, we went from designing a robot to making a finished product in six weeks. I have a couple mentors who work here. There’s a lot of structure behind what’s done.”

There are three Da Vinci Schools students, including Ornelas, working as interns there now. Natasha Morse, the school’s director of real-world learning, said students covet the spots.

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“Students are just always so excited to be in the environment of SpaceX,” Morse said. “They feel like an adult employee. It really motivates them for college.”

Rachael Tucker, manager of the company’s high school interns, said she looks for candidates who are great students and eager to learn.

“Most of them are in awe of the sheer volume of work. It can be a little overwhelming,” Tucker said. “But most are eager to go out and explore and learn what they can. This job really gets them out of their shells. You can’t be shy here.”

Interns participate in weekly classes about the company’s specialties — complex electrical hardware and software built from the ground up, computer science, mathematical modeling, rocket manufacturing, structural engineering and launch pad infrastructure.

The challenges are constant. Since the inaugural launch of the Falcon 9 in 2010, SpaceX has suffered crashes, an explosion, and aborted and delayed launches. But there were more successes than failures and, last year, the company became the first to bring a rocket back to Earth from orbit intact.

SpaceX continues to grow rapidly and is increasing the number of launches as it works toward creating a near-perfect reusable rocket. Reusability, company founder Elon Musk believes, is the key to expanding access to space.

Musk, who also founded Tesla Motors — which has a design studio next door to SpaceX in Hawthorne — and now owns SolarCity, among other ventures, regularly works at the SpaceX office’s open-air cubicles and engineering and testing labs.

Molly Mettler, 19, has been interning at SpaceX for two years, and hasn’t had a full conversation with the famous inventor-engineer-entrepreneur, but has heard him speak at lectures.

“He’s really smart,” she said, adding that Musk is one of the topics her friends usually ask about, along with what the rockets and work environment are like.

Mettler recently started college at UC Davis, where she hopes to mesh her love of engineering with animal science. Veterinary medicine often lags behind modern advances, she said, and there is room for engineering innovations in fields like prosthetics.

She started her internship after her sophomore year but has continued to return because she enjoys the work. The experience she got fixing computers also landed her a part-time job at college.

“It’s a very fast-paced company that’s always constantly moving forward and changing,” Mettler said. “In a sense, your work is never finished and the time pressure makes problems more difficult.”

Day to day, she gets to watch the rockets and Dragon capsules being built, piece by piece. And she can hobnob with the engineers to learn more about their cutting-edge creations. New spacecraft can be seen at all stages of development on the work floor, attended by teams of workers. A cafeteria that looks over the operations provides low-cost, healthy meals.

In the midst of work stations, launch operations and feeds from the International Space Station are constantly monitored on giant screens in a glassed-in command center.

“I was definitely more to myself when I started,” she said. “As a high-schooler working at SpaceX, you want to live up to and exceed expectations.”

The Next Generation Science Standards: what do they mean for afterschool?

The Next Generation Science Standards (NGSS) offer a powerful new vision for American science education for the 21st century. NGSS brings long-needed reforms to national and state K-12 science education standards, incorporating decades of new research on how students best learn science—by actively investigating topics and solving real-world problems, just like real scientists and engineers do!

So far, NGSS has been adopted by 16 states and the District of Columbia, as well as several individual schools and districts. If it hasn’t already, NGSS will soon be influencing how your students are expected to learn STEM. To help program providers understand how afterschool fits in to the NGSS, the Afterschool Alliance has developed a new guide, Getting Started with the Next Generation Science Standards.

Key components of our new NGSS guide

An explanation and history of how NGSS was developed and who the key collaborators were.
The underlying philosophy of the NGSS, which encourages kids to learn science by doing.
An overview of the standards themselves.
How afterschool providers can work with partner schools and use NGSS as a way to improve their practice.

Back in April, we hosted a webinar that digs into the research behind the standards, and offers a couple examples of how afterschool programs are thinking about NGSS. Watch the recording, and stay tuned for our next NGSS-related webinar in September.

In the meantime, we hope you’ll enjoy Getting Started with the Next Generation Science Standards, and share it with other educators who might find this resource useful!

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