Unlocking the Power of Mathematics: A Conversation with Ben Orlin

Mathematics can often seem intimidating or inaccessible to many people. But according to mathematician and author Ben Orlin, math has the potential to be deeply engaging and even fun when approached with the right mindset. In a wide-ranging conversation, Orlin shares his insights on how to unlock the power and beauty of mathematics.

Viewing Math as a Language

One of Orlin's key ideas is to think of mathematics as a language - one with its own vocabulary, grammar, and ways of expressing ideas. He explains:

"Mathematics is both a set of ideas and a set of linguistic inventions for talking about those ideas and you've kind of got to learn them both in parallel you got to move back and forth between them as you go."

By framing math in this way, it can start to feel more approachable. Just as we learn to read and write in our native language, we can learn to "speak" and understand the language of mathematics.

Orlin notes that the equal sign is a pivotal concept in this linguistic view of math:

"The equal sign I see as kind of the pivot here because you need to stop seeing it as kind of the call to action or call like a drum roll preceding the answer and you need to see it as as sort of the Workhorse verb of mathematical language which is just it's it's the to be verb it's is equal to."

Rather than seeing an equation as a command to perform a calculation, we can view it as a statement expressing that two things are equivalent. This shift in perspective can make algebra feel less alien.

Embracing Curiosity and Wonder

Another key to unlocking math's potential is tapping into our natural sense of curiosity and wonder. Orlin argues that humans have an innate fascination with numbers, patterns, and shapes - we just need to awaken it:

"People have a fascination with number and with pattern and with shape and the fact that all those things turn out to be related you know that numbers are a way of talking about patterns and shapes can be a language of number and number can be a language of shapes like that's cool that's weird that's that's a weird facet of this existence we happen to find ourselves in."

He suggests that even if only a small percentage of math lessons explicitly focus on sparking curiosity and wonder, those moments can be incredibly impactful:

"Not every day of your life is equally impactful and not every day of your math education is equally impactful so those days even if it's not 90% of days when you're seeing something Vivid and electrifying and and glimpsing the patterns of the cosmos it doesn't have to be 95% of days if you do that on 5 per of days that's actually that's pretty solid that's better than we tend to do in math education."

Finding the Puzzles in Math

Orlin recommends framing mathematical concepts as puzzles or games to make them more engaging. He notes that many people happily do Sudoku puzzles every day, which are essentially systems of linear equations in disguise.

By presenting math problems as interesting puzzles to solve rather than rote exercises, we can tap into people's natural problem-solving instincts. Orlin gives an example of how this might work with quadratic equations:

"You can frame problems in in quadratics factoring problems or or solving a quadratic equation as a interesting oneoff puzzle right you can pick one that has just the right features where it's like oh you can almost guess what those numbers are if you can guess what the first one is you can maybe figure out the second one."

This puzzle-based approach can help students feel a sense of accomplishment and power when they solve a tricky problem.

The Power of Math

Indeed, Orlin argues that one of the most compelling aspects of math is the sense of power it can provide:

"What students love in math is when they feel powerful when they feel capable...The power of math is not your power to out compete someone it's your power to seize control over a weird question and pin it down and find an answer."

Rather than seeing math as a competition, we can view it as a tool that empowers us to understand and solve complex problems. This shift in perspective can make math feel more personally meaningful and rewarding.

Making Abstract Concepts Concrete

One challenge in teaching math is helping students grasp abstract concepts. Orlin suggests using concrete examples and experiences to build up to more abstract ideas:

"Often what students need is experience of those concrete particulars that are going to generalize you know leaping straight into generalities just doesn't really get you anywhere it means that you kind of wind up pushing symbols around a page."

He gives the example of using dice to teach probability - starting with physical dice that students can roll before moving to more abstract probability calculations. This grounds the math in tangible experiences.

Connecting Math to Other Disciplines

Orlin also highlights how math intersects with other fields in fascinating ways. He notes how civilizations throughout history have used mathematics for practical purposes like agriculture and astronomy. Understanding these connections can make math feel more relevant and meaningful.

He also discusses the deep links between math and music, referencing the famous quote attributed to Leibniz: "Music is the soul calculating without knowing that it calculates."

Exploring these interdisciplinary connections can reveal the hidden mathematical patterns underlying many aspects of our world.

Embracing Curiosity and Obsession

When asked what two ideas he would want to instill in everyone, Orlin emphasizes curiosity and obsession:

"First be curious right like ask questions no more...The world is so complex there's so much one could be curious about it can almost be like it's just so much noise you just shut down you're like I don't know there's too many questions I have no idea how any of this works so I'm just going to give up but if you can just kind of carve off piece and just be curious and keep asking and keep asking and like okay well I didn't get an answer there but you know I'm gonna come back tomorrow and ask more questions."

And on obsession:

"Be obsessive about what you're making what you're building...The best moments of my creative work right the the moments when I feel like I'm making the best things that I can make is is when I vanish into them."

By cultivating curiosity about the world around us and allowing ourselves to dive deep into topics that fascinate us, we can unlock new realms of understanding and creativity - in mathematics and beyond.

Conclusion

While mathematics can seem daunting, Orlin's insights reveal how we can make it more accessible and engaging. By viewing math as a language, tapping into our sense of wonder, framing concepts as puzzles, and connecting math to other disciplines, we can start to unlock its power and beauty.

Ultimately, embracing curiosity and allowing ourselves to become obsessed with interesting problems may be the key to truly appreciating mathematics. As Orlin's perspective shows, math doesn't have to be a dry, abstract subject - it can be a thrilling journey of discovery that reveals the hidden patterns shaping our world.

Article created from: https://www.youtube.com/watch?v=o4GgOBeXISk