January 13, 2020

# Exploring Curiosities, The Beauty of Calculus, and a Love of Math – Steven Strogatz on The Knowledge Project

Check out The Knowledge Project Episode Page & Show Notes

#### Key Takeaways

- Advice for teachers & professors:
- From the movie Stand and Deliver:
**“Students will rise to the level that the teacher expects, and so if the teacher expects something really hard, kids don’t even know it’s impossible. They’ll try.”** **Don’t try to cover the material, try to uncover it**– instead of insisting on covering the full curriculum, teachers should teach with a more exploratory mindset, without an end destination**Make your classroom a safe space for confusion**

- From the movie Stand and Deliver:
- Calculus plays a crucial role in GPS technology, as well as measuring how our immune systems interact with viruses
**By becoming knowledgeable in a variety of disciplines, you can apply mental models from different fields to your own, giving you a leg up on the competition**

#### Intro

- Steven Strogatz (@StevenStrogatz) is a professor of applied mathematics at Cornell University and the author of five books, including his latest,
*Infinite Powers**C*heck out his website

- Host – Shane Parrish (@ShaneAParrish)

#### A Pivotal Moment

- Back when Steven was a sophomore in high school, his math teacher presented a geometry problem to the class that he’d never seen a student be able to solve (one that the teacher, himself, didn’t know how to solve either)
- The problem: If the angle bisectors of a triangle (the two lines that bisect the two angles of a triangle) are congruent (the lines are equally long), prove the triangle is isosceles
- Well, Steven was intrigued (to say the least):
**“I worked on that problem a lot. I spent a day or two, and I still couldn’t do it. Then, days became weeks, and weeks became months. I think I spent about maybe six months on this question, trying things, getting stuck, trying other things, getting stuck. Sometimes, it would come close to working out, but I could never get the argument to go all the way through. And my friends would get annoyed with me, saying things like, ‘Come on, let’s go to the movie.’ ‘No, I feel thinking about the angle bisectors.'”**–*Steven Strogatz*- Ultimately, Steven discovered a proof, and, after showing his teacher, received praise that’s stuck with him to this day

#### 🎧 The Impact of a Great Teacher

- Steven recalls a line from the movie Stand and Deliver which he always tries to remember:
**“The students will rise to the level that the teacher expects, and so if the teacher expects something really hard, kids don’t even know it’s impossible. They’ll try.”**- Steve adds: “I try to do that myself with my students” (particularly with freshman)

#### It Didn’t Come Easy

- In college, Steven didn’t receive the best math grades:
- “I could have easily been weeded out, except I loved the subject so much that I stuck with it, even though I was one of the weakest math majors in my cohort. I just loved it more than most.” –
*Steven Strogatz*

- “I could have easily been weeded out, except I loved the subject so much that I stuck with it, even though I was one of the weakest math majors in my cohort. I just loved it more than most.” –

#### Why do most people find math dull and dry?

**1) The average person didn’t have positive experiences in math classes throughout their youth**- Most people saying something like, “I did like math until…” (we got to calculus, algebra, etc.)

**2) The subject is wrongly taught as a “tower” (each thing builds on the topic before it)**- “The reality is that math is a web, not a tower. You can jump in at different points in the network of ideas and then find your way around from there.” –
*Steven Strogatz*

- “The reality is that math is a web, not a tower. You can jump in at different points in the network of ideas and then find your way around from there.” –
**3) Teachers insist on covering EVERYTHING in the curriculum**- (16) This relates to a line Steven remembers:
**“Don’t try to cover the material, try to uncover it”**- Steven, instead, recommends teachers/professors teach courses with a more exploratory/problem-solving mindset, without an end destination

- (16) This relates to a line Steven remembers:

#### Make a Safe Space for Mathematical Confusion

- As a professor of mathematics, one thing Steven always tries to do:
**“I want to make a space that’s safe for mathematical confusion, meaning, nobody’s going to feel stupid here. We’re all confused. Confusion is the normal state of affairs when you’re trying something really hard and when you’re exploring the unknown. So it’s a safe space in the sense that you can trust us, that we’re all on the same team trying to figure this out together, and don’t worry about looking stupid.”**– Steven Strogatz

- This becomes even more important in the cutting edge areas of mathematics, science, etc.
- In these domains, no one has the answers! They’re something you can look up.

- Something else to keep in mind:
**“When you’re collaborating, it really helps to be vulnerable and to have a safe enough relationship with your collaborators that you can say, ‘I don’t get this. Could you go over that again?'”**–*Steven Strogatz*

#### How can parents get their kids excited about math?

- First off,
**avoid passing on your own anxieties about math to your kids**- “If a parent started to like math and felt more secure, that would be a big help” –
*Steven Strogatz* - Resources for parents looking to improve their math skills:
- Give Steven’s 15-week New York Times series on math a read (which later grew into his book,
*The Joy of X*) - YouTube is a golden source of math-related resources (check out the videos from 3Blue1Brown and Mathologer)
- Khan Academy

- Give Steven’s 15-week New York Times series on math a read (which later grew into his book,
- Building off the above:
- (37:20)
**“The best teachers now have unlimited reach. The internet has enabled it. Before, you were lucky if you were to get the best math teacher in your community. Now, you can access, by and large, the best math teachers in the world.”**–*Shane Parrish*

- (37:20)

- “If a parent started to like math and felt more secure, that would be a big help” –
- Second,
**avoid being afraid to admit you don’t know something**- “If you don’t know something, why are you trying to pretend? You’re going to get found out anyway.” –
*Steve Strogatz*

- “If you don’t know something, why are you trying to pretend? You’re going to get found out anyway.” –
- In general:
- “There are all kinds of different negative reactions when it comes to math. Some people feel ego deflation; they really feel like they’re stupid. Other people can do math, but they don’t see any point to it; they think it’s boring. And then there are others who find it exciting. There are challenges for parents for all three types of kids: the bored child, the depressive or distraught child who has tremendous math anxiety, and the kid who wants to do more math but is limited by the environment.” –
*Steve Strogatz*

- “There are all kinds of different negative reactions when it comes to math. Some people feel ego deflation; they really feel like they’re stupid. Other people can do math, but they don’t see any point to it; they think it’s boring. And then there are others who find it exciting. There are challenges for parents for all three types of kids: the bored child, the depressive or distraught child who has tremendous math anxiety, and the kid who wants to do more math but is limited by the environment.” –

#### Calculus – The Greatest Idea of All Time

**“Calculus is one of the greatest ideas of all time. I would say it ranks right up there with relativity theory from Einstein, with quantum theory of the atom, with evolution… It’s just had an enormous impact on the history of the world.”**–*Steven Strogatz*- Calculus = the mathematics of change (AKA how to quantify things that change)
- “It’s the first part of mathematics that can cope with the dynamics of the world… Calculus is the math for describing a world in flux.” –
*Steven Strogatz* - For example:
- The change of something’s location (throwing a ball, the planets moving around the sun, etc.)
- The changing concentration of a virus in the bloodstream after taking a drug (AKA how the immune system interacts with a virus)

- “It’s the first part of mathematics that can cope with the dynamics of the world… Calculus is the math for describing a world in flux.” –

#### Calculus’ Role in GPS Technology

**“GPS is a wonder of calculus. It has so many different aspects of calculus build into it”**–*Steven Strogatz*- Examples include:
- The way your GPS acquires signals from overhead satellites
- The way satellites estimate distances
- Fun fact: Satellites calculate distance by precisely measuring the time it takes for a signal to travel to the GPS receiver. For this reason, satellites need to keep incredibly accurate time – they even have onboard atomic clocks. But things get complicated…
- Due to relativity theory, time slows/speeds up based on how fast you’re moving (and satellites are moving fast enough that Einstein’s theory of relativity applies to them in a significant way)

- Fun fact: Satellites calculate distance by precisely measuring the time it takes for a signal to travel to the GPS receiver. For this reason, satellites need to keep incredibly accurate time – they even have onboard atomic clocks. But things get complicated…

- Examples include:

#### Comparing the Scientific Fields

- The first scientific field to make substantial progress: Astronomy
- You might find this surprising given the moons, stars, and planets are so far away – why wasn’t something like biology mastered first?
- The reason: Astronomy is filled with constants (everything is repetitive and regular), and things move quite slowly. Compare this to biology – the processes in the body move extremely fast, everything is on such a small size-scale, and there are lots of moving parts.

- You might find this surprising given the moons, stars, and planets are so far away – why wasn’t something like biology mastered first?
- Comparing biology and physics:
- In physics, everything is constant:
**“Any two electrons anywhere in the universe are absolutely indistinguishable. There is no diversity of sub-atomic particles… Every electron is completely the same in every respect as every other electron.”***– Steven Strogatz*

- In biology, there’s enormous diversity – everyone has different genes, etc.

- In physics, everything is constant:

#### Is there a soul?

**“It’s all chemistry and physics. I don’t believe in any vital spirit, or soul, or anything like that. I’m sure some people do, but to me, it’s all material… I don’t think there’s anything there but atoms and sub-atomic particles configured in increasingly subtle ways.”**–*Steven Strogatz*

#### On Choosing What to Work On

- The first choice you have in the academic domain (as researcher or PhD candidate): What to work on
- Here’s what you should think about:
- Getting a PhD is all about discovering something new and interesting
- You should work in an area where you have a comparative advantage
- Ask yourself: “What is it that I bring to the table that might give me an edge, and what subject area would best bring this out?”

#### Strategic Quitting

**“The thing your college or high school coach tells you, ‘Don’t be a quitter.’ I say, Yes, do be a quitter. Sometimes you have to quit when something’s not panning out.”**–*Steven Strogatz*

#### Stay Broad

**By becoming knowledgeable in a variety of different disciplines, you can apply mental models from different fields to your own, giving you a leg up on the competition***Scott Adams said something similar in these Podcast Notes from his appearance on The Knowledge Project*- “I’m interested in pop culture. I’m interested in science. So, I think about weird things. Sometimes they’re really important and relatively easy problems waiting for a mathematician to look on.” –
*Steve Strogatz*

- One way Steven embodied the above: Applying the 6 degrees of separation theory to the way crickets chirp (read about it here)
- The resulting scientific paper is now among the 100 most widely cited papers of all time

#### Ponder This

- 🎧
**“A great discovery that no one appreciates is not really a great discovery because science is a social enterprise. It’s not enough to do the work, you have to communicate and help people understand why it matters.”**–*Steve Strogatz*