The future of creativity in algebra | Algebra 1 | Khan Academy

[Music] Hi everyone, Sal Khan here. If you look at most of human history, the top artists, the top musicians were also mathematicians, and also scientists, and also engineers. This convergence between creativity and mathematics and science and engineering is only accelerating in the careers of the future. Algebra and creativity are going to be that much more empowering. But don't take my word for it: you're about to meet some of my close friends who can better draw that link between algebra and creativity and work of the future.

[Music] The math underpins everything in our universe, so it impacts every corner of our society. But over the past decade in particular, the advances in computer technology and introduction of machine learning and artificial intelligence have been massive. We're only learning more and more and building better and better systems, and math underpins all of that. It's fundamental to all of those systems. In fact, computer science is inherently linear algebra, so it's really foundational to those scientific advances.

One relatively recent example that really inspired me was the first real photo that scientists were able to capture of a black hole—this mysterious remnant of giant stars that lurk all over the universe. It is the way the scientists used creativity and math to solve the problem that was so fascinating. You see, these black holes are so distant that there's no single telescope that is large enough to be able to actually see them. The scientists came up with this clever idea: creating a network of small telescopes distributed all across the globe that were synchronized to capture and focus on the same object at the same time, creating a giant virtual telescope.

Now, the aperture of this giant virtual telescope is nearly the same size as the diameter of the Earth. With that in place, the scientists and engineers were able to capture all the bits and pieces of data and put it all together into the first image of a black hole that is 53 million light-years away, which is 318 quintillion miles away. Now that's an impressive use of creativity and math!

[Music] In the future, in order to add innovation, students are going to need skills such as creative problem-solving—so not looking at things from the same perspective, being able to ideate, so come up with new ideas, and divergent thinking, right? The ability to come up with ideas that are drastically different from each other. Beyond creative problem-solving, students will also need to show adaptability, so the ability to pivot as the world and constraints around us kind of pivot.

The STEM field is constantly evolving, and it's growing as we gain more knowledge. So students' ability to be creative and adapt as the field adapts will be critical for success and for the ability to innovate as we move forward. Communication skills are always going to be essential for furthering innovation. This is because if you want to make a scientific advancement, you have to have a lot of people on your side. You have to have funding bodies, other scientists, and people interested in what you're doing.

So this means you have to have the communication tools to communicate with all of those different areas of people. Some different ways that you can learn to communicate with them are through things like presentations, visual aids, and videos. When you're preparing for communication tools of the future, it's quite difficult to know what those will be. So if we think back to 10 years ago, we didn't have things like TikTok, which is now a huge avenue for communicating things to young people.

That is something that we've had to adapt to and to learn and tailor our communication down this new area of media. So having versatility—if students are able to take their skills that they have and apply them to new areas of communication, they'll be prepared for the communication tools of the future.

There are so many ways that you can expand your creative and math skills without even really realizing that you're doing it. Like for me, I'm a big board game fan, and I realized that there are so many games that involve math and learning how to solve problems. Sometimes, when you're cooking— I love to bake—and so I feel like I'm constantly using fractions and learning how to do proportions, just because I'm doing things that I love.

So I feel like the best way to expand your mathematical and creative skills is just doing what you love to do because probably it has some kind of math in it and some kind of creativity. Try to connect what you're learning to your real life. It's really easy to be in the classroom and think that it's siloed and it's orthogonal from the world around you.

The more we can connect what we're learning in the classroom to our real life—either via sports, entertainment, politics, news—whatever, the connection that you make between math and your real life will really help you appreciate the skills and the methods and find ways to transfer them outside of just the classroom alone.

[Music] One of the newest ways of thinking about problem-solving for me is something that my math professor would tell me. He would say, "Don't be afraid to be stuck." I think that a lot of the time, when we are doing math and we get stuck, it's like sometimes it can feel like, "Wow, this is a reflection of me and my mathematical abilities. Wow, maybe I shouldn't be doing math." But really, a lot of the time, it's just an indication that you need to spend more time doing the math or figuring out what the problem is exactly.

If you haven't gotten stuck yet, then I mean, you probably will get stuck at some point. So being stuck is just a part of math, and it's kind of learning how to know what to do when you are stuck. This is a really big part of being creative in math and being able to solve problems in the future. One example that I often use is that I often try to solve problems both in the traditional algebraic way, but I also try to visualize problems in 2D and 3D space to solve them more visually.

So I think the more ways that you can figure out how to solve a problem, the more ways you can eventually sort of "save" in your toolbox and use later on to solve other problems. There are lots of different tools and resources, like apps and puzzle games, that are going to help you think about problems in new ways and help develop that critical thinking that you need to be able to apply your skills to a lot of different areas.

Sometimes, even starting at the answer and working backward through the problem can help you see a different way of getting to the answer. Students can combine new ways of thinking about problem-solving by trying to look at it from different angles. Anytime you approach a problem, if you're just looking at it from your perspective, you're not going to get a holistic view of the solution space.

So try to have perspectives and look at the problem from multiple angles to understand all the ways in which it could be viewed. The more holistically you view a problem, the more paths you look at, the more efficient and effective you're going to be at solving it.

[Music] One of the most interesting fields to me is the field of robotics and the different ways machine learning will impact our society. Robotics combines lots of math, lots of science, lots of technology, but also socio-economic factors such as human and robot trust—how humans feel about robots, how they trust them—and human-robot teams in the workplace—how humans and robots work together to accomplish a task.

Creativity will be hugely important here. Creativity is not only going to be important in designing the robots; they are very intricate, very complex systems and will require creativity to know exactly how to design them to do their jobs, but also how to integrate them into our everyday lives, which is a totally different facet of creativity.

It's actually a new way of thinking because it hasn't really been done yet. Even though there are robots around us and we've seen them—like you've got the Roomba, which hoovers your living room—really where we're heading is for robots to be everywhere and to be a really integral part of our society. So preparing for that change and using creativity to figure out the best way to do that will be a really important step in innovation in the future.

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