Steven Strogatz @stevenstrogatz Twitter profile

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Steven Strogatz

@stevenstrogatz

3 years

My older daughter loves sharing math memes with me. Here’s the latest:

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Steven Strogatz

@stevenstrogatz

4 years

Sad but true

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Steven Strogatz

@stevenstrogatz

3 years

Latest math meme from my older daughter

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Steven Strogatz

@stevenstrogatz

1 year

A great mathematician named Madhava, working in Kerala, India, discovered the power series for sin(x) in the 1300s, hundreds of years before Newton, Leibniz, Gregory, Taylor, et al. In this video, master teacher @garyrubinstein shows how Madhava did it:

Madhava sine series derivation

In the 1300s an Indian mathematician derived what is now called the Taylor series for sine. But Taylor was hundreds of years later. See how Madhava anticip...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

2 years

A one-page proof of the irrationality of pi.

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Steven Strogatz

@stevenstrogatz

5 years

My daughter just calculated her first derivative!

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Steven Strogatz

@stevenstrogatz

10 years

Proof by Clementine: the surface area of a sphere is 4 pi r^2 (trace around widest part of clementine 4 times) http://t.co/Bxj2v6wpAO

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Steven Strogatz

@stevenstrogatz

2 years

Finally got around to watching “Spider-Man 2”. Recognize any of his textbooks? 🙋‍♂️

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Steven Strogatz

@stevenstrogatz

3 years

“Calm down, Pythagoras, calm down” (ht William Dunham)

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Steven Strogatz

@stevenstrogatz

2 years

Students taking a first course in nonlinear dynamics and chaos (or anyone curious about the subject): Videos of lectures are freely available. Hope you enjoy them!

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

5 years

The number of minutes of daylight is increasing at its maximum rate today. Happy max derivative day, everybody!

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Steven Strogatz

@stevenstrogatz

5 years

From one of my daughters

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Steven Strogatz

@stevenstrogatz

4 years

This book by Purcell was the best textbook I read as an undergraduate. It was so intellectually exciting, and had such fantastic pedagogy! I’m using relevant parts of it for my students this semester in multivariable calculus.

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Steven Strogatz

@stevenstrogatz

3 years

The doge rule for derivatives:

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Steven Strogatz

@stevenstrogatz

3 years

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Steven Strogatz

@stevenstrogatz

2 years

Now that I’m back from my trip, I’ve got access to my full wardrobe.

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Steven Strogatz

@stevenstrogatz

2 years

This just came in the mail today. Anything by John Stillwell is worth reading, so I’m really looking forward to dipping into his latest.

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Steven Strogatz

@stevenstrogatz

2 years

An elevator in the physics building at UC Santa Barbara conveniently has an accelerometer in it. I couldn’t resist going up and down a few times just to watch the changes in the effective strength of gravity.

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Steven Strogatz

@stevenstrogatz

1 year

You may know Prof. Gil Strang's famous book "Linear Algebra and Its Applications," or you may have watched his Linear Algebra (18.06) lectures at @MIT on YouTube. Gil's final lecture will be live streamed tomorrow at 11 am EST. Join the celebration at

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Steven Strogatz

@stevenstrogatz

4 years

My introductory course on Nonlinear Dynamics and Chaos is free online. Could be useful for students, teachers, and lifelong learners (or anyone needing a distraction). Prerequisites: basic calculus and physics. via @YouTube

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

4 years

A book and a letter that changed my life. After I read The Geometry of Biological Time, I wrote to its author and asked if I could come work with him. His reply, scrawled in his characteristic magic marker, led to his becoming my most important mentor.

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Steven Strogatz

@stevenstrogatz

1 year

Tomorrow morning at 9 am, I'll meet a new group of students in my annual course on nonlinear dynamics and chaos. After 34 years of teaching, I still get nervous before the first class -- and I'm feeling jumpy right now 😳 To all teachers and students: Have a great semester!

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Steven Strogatz

@stevenstrogatz

6 months

The third edition of my textbook, Nonlinear Dynamics and Chaos, was published today. You can preview the first 68 pages on Google Books, or take a look at the preface below to see what's new. The main new thing is a chapter on the Kuramoto model! Hope you enjoy it.

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Steven Strogatz

@stevenstrogatz

2 years

Seen in the Math Department lounge

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Steven Strogatz

@stevenstrogatz

4 years

In multivariable calculus, we often ask students to sketch surfaces in 3D but rarely teach them *how*. I found these helpful lessons in Thomas and Finney, Calculus and Analytic Geometry, alternate 9th edition, and plan to share them with my students. (1/2)

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Steven Strogatz

@stevenstrogatz

3 years

John von Neumann, a young Richard Feynman, and Stan Ulam. Three of the most original minds of the 20th century. (ht @ananyo )

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Steven Strogatz

@stevenstrogatz

2 years

Just started teaching residue theory. Fun!

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Steven Strogatz

@stevenstrogatz

4 years

@3blue1brown Her question is very good, and the answer might surprise some of you: in Al-Khwarizmi’s classic book (often regarded as the first algebra textbook), the main application of algebra is to problems stemming from Islamic inheritance law. Examples here:

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Steven Strogatz

@stevenstrogatz

4 years

Students taking a first course in nonlinear dynamics and chaos: My videotaped lectures are freely available on @YouTube here. Hope you find them useful. Prerequisites are elementary calculus and physics, and a little linear algebra.

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

1 year

Today in my undergraduate nonlinear dynamics class, one of my students asked to see a proof of the Poincaré-Bendixson theorem. Here's a handout of the proof that was shown to me when I was first learning about nonlinear differential equations, back in 1982.

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Steven Strogatz

@stevenstrogatz

4 years

Today was my first day of class, and I zoomed with the 200+ students in my "multivariable calculus for engineers" course. We had an unexpectedly wonderful session, super interactive. As you can see, I'm still on a high from it! And I want to share what worked so well... 1/n

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Steven Strogatz

@stevenstrogatz

7 years

RIP #MaryamMirzakhani . To learn about her math and life, this piece by @EricaKlarreich is a fine place to start.

A Tenacious Explorer of Abstract Surfaces | Quanta Magazine

Maryam Mirzakhani, who became the first woman Fields medalist for drawing deep connections between topology, geometry and dynamical systems, has died of cancer at the age of 40. This is our 2014…

www.quantamagazine.org

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Steven Strogatz

@stevenstrogatz

6 years

Happy to announce the birth of my new book, Infinite Powers. Available for pre-order now. Due out in April in US & UK

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Steven Strogatz

@stevenstrogatz

4 years

Today’s my birthday. In a few weeks, my wife will celebrate hers and we will be twin primes, 59 and 61. After that we’ll have to wait 12 years for the next occurrence: 71 and 73. And after that, a long slog and a lotta luck needed to get to 101 and 103.

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Steven Strogatz

@stevenstrogatz

6 years

Students, teachers, or anyone curious about nonlinear dynamics and chaos may want to watch my free lectures online

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

3 years

I’ve started reading this marvelous new book by Tristan Needham. It’s passionate and filled with geometrical insight, just like his earlier masterpiece VISUAL COMPLEX ANALYSIS.

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Steven Strogatz

@stevenstrogatz

3 years

My colleague Jim Sethna has written a wonderfully modern, interdisciplinary, and *free* textbook on statistical mechanics. He explains the big ideas and includes many cool exercises and applications.

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Steven Strogatz

@stevenstrogatz

5 years

My latest piece for @nytimes @NYTScience , on the math question that went viral a few days ago:

The Math Equation That Tried to Stump the Internet (Published 2019)

Sometimes BODMAS is just PEMDAS by another name. And no, the answer is not 100.

www.nytimes.com

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Steven Strogatz

@stevenstrogatz

3 years

Dirac and Feynman. The body language of each is so characteristic of who they were.

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Steven Strogatz

@stevenstrogatz

11 months

I'm teaching complex analysis right now. One of my students, Jackson Fellows, made this interactive tool to visualize complex functions w = f(z) as mappings from the z-plane to the w-plane. It currently supports +, -, *, /, (), i, exp, sin, and cos.

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Steven Strogatz

@stevenstrogatz

3 years

“Math Person” is a free verse poem by high school student Julia Schanen. Rather than try to describe it, let me just urge you to read it. It will take you a few minutes, and it will move you.

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Steven Strogatz

@stevenstrogatz

4 years

In movies, mathematicians are always writing on windows. In real life, these markings were made by my dog’s nose.

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Steven Strogatz

@stevenstrogatz

5 years

I met a remarkable boy named Zameer yesterday. He is 7, and we had fun doing math together. He started by showing me a multiplicative magic square he invented. Pretty soon we were discussing the positive minimum of the gamma function. via @YouTube .

Zameer doing math with Steven Strogatz

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www.youtube.com

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Steven Strogatz

@stevenstrogatz

7 years

My lectures on nonlinear dynamics and chaos are free online. Maybe useful for students taking a first course:

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

4 years

A lot of mathematical seminars have moved online. Here’s a partial list:

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Steven Strogatz

@stevenstrogatz

3 years

Nothing original here, just an easy visual way to sum an infinite geometric series.

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Steven Strogatz

@stevenstrogatz

5 years

While waiting for my differential equations test to begin last night, one of my students (Leina Peterson) showed me a study sheet she had made for her materials science course. #breathtaking

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Steven Strogatz

@stevenstrogatz

5 years

This is why they tell you not to read your own book reviews. Thanks Howard – could you suggest a book where I could learn more about “chaos theory”?

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Steven Strogatz

@stevenstrogatz

2 years

Why do so many people get Monty Hall problem (also known the three doors problem) wrong? Steven Tijms explores both the math and the psychology in this illuminating article:

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Steven Strogatz

@stevenstrogatz

6 years

Mandelbrot pancake

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Steven Strogatz

@stevenstrogatz

6 years

Fibonacci was intimately familiar with Indian math, and “his” sequence was well known to Indian linguists and poets

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Steven Strogatz

@stevenstrogatz

4 years

When I was a college student, my quantum mechanics professor (Jim Peebles) used to delight us with his little jokes. I compiled a list of some of his witticisms at the time, and an old friend of mine just reminded me of it.

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Steven Strogatz

@stevenstrogatz

2 years

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to a Fields Medal.

June Huh, High School Dropout, Wins the Fields Medal | Quanta Magazine

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

www.quantamagazine.org

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Steven Strogatz

@stevenstrogatz

4 years

Oh, the pleasures of teaching Melnikov’s method! Drawing the manifolds in real time is very stressful, but fun

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Steven Strogatz

@stevenstrogatz

5 years

Students taking a first course in nonlinear dynamics and chaos: My videotaped lectures are freely available on @YouTube here. Hope you find them useful. Prerequisites are elementary calculus and physics, and a little linear algebra. via @YouTube

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

6 years

Does this really warrant a graph?

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Steven Strogatz

@stevenstrogatz

3 years

My older daughter is now inundating me with math memes. Since you guys seem to like them (I’ll admit, I do too!), here are a few more.

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Steven Strogatz

@stevenstrogatz

2 years

"After shocking the mathematics community with a major result in 2013, Yitang Zhang now says he has solved an analogue of the celebrated Riemann hypothesis." (The analogue is called the Landau-Siegel zeros conjecture.)

Mathematician who solved prime-number riddle claims new breakthrough

Nature - After shocking the mathematics community with a major result in 2013, Yitang Zhang now says he has solved an analogue of the celebrated Riemann hypothesis.

www.nature.com

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Steven Strogatz

@stevenstrogatz

1 year

See below for the kind of interaction on Twitter that I wish we had less of here.

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Steven Strogatz

@stevenstrogatz

3 years

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Steven Strogatz

@stevenstrogatz

2 years

Today in my complex analysis class, we're going to discuss the following infinite series. Does it converge? If so, can you evaluate it in terms of elementary functions?

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Steven Strogatz

@stevenstrogatz

3 years

Leftover napkin from the 60th birthday party that my wife threw for me a couple years ago

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Steven Strogatz

@stevenstrogatz

3 years

I wish I had taken Abstract Algebra from @mattmacauley when I was in college. Here’s how he teaches it: . In contrast, when I asked my teacher what I should think about when I think about groups, he said, “Think about the axioms.”

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Steven Strogatz

@stevenstrogatz

3 years

Quarantine math workout

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Steven Strogatz

@stevenstrogatz

5 years

Cocktail party napkins at our house

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Steven Strogatz

@stevenstrogatz

2 years

I remember being bewildered by "compactness" as a first-year college student and wish I'd had access to this article back then. Students and teachers of advanced calculus, real analysis, and point set topology may find it helpful or even illuminating.

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Steven Strogatz

@stevenstrogatz

8 years

The path of the sun, when you take a picture at the same time each week of the year

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Steven Strogatz

@stevenstrogatz

4 years

For anyone taking a first course in nonlinear dynamics and chaos this semester, you might find these lectures helpful. The prerequisites are introductory physics, and some multivariable calculus and linear algebra.

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

1 year

"How would you explain the concept of eigenvectors to a child?" asks @JayDeep_1729 . A few years ago I tried to do something like that – to explain eigenvectors intuitively, in five minutes, with no pictures, just words.

Steven Strogatz explains how he teaches eigenvectors and eigenvalues.

This is how a great teacher makes concepts intuitively accessible.http://teachbetter.co/podcast.htmlhttps://itunes.apple.com/us/podcast/the-teach-better-podc...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

3 years

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Steven Strogatz

@stevenstrogatz

4 years

Happy Valentine's Day, everybody!

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Steven Strogatz

@stevenstrogatz

3 years

The origin of the term “random walk” (ht @dan_rockmore )

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Steven Strogatz

@stevenstrogatz

6 years

Students taking a first course in nonlinear dynamics and chaos may find my lectures useful. Free online at

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

2 years

Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani (2020) will begin airing on U.S. public television stations starting in March 2022 in celebration of Women's History Month. Broadcast schedule: . Trailer:

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Steven Strogatz

@stevenstrogatz

2 years

In class today I gave the usual argument (involving drawing a bridge between two closed contours) to justify why the integral of f stays the same when we deform one contour into another through a region where f is analytic. My student Sylvan found a neat alternative argument!

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Steven Strogatz

@stevenstrogatz

1 year

Just finished my first class with a "dynamicist's view of the world". There's a lot to quibble about with this picture, but it helps students see where we're headed. We are going to live below the red line, in the nonlinear world, and march from n=1 to n=3.

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Steven Strogatz

@stevenstrogatz

4 years

What math should we be teaching in high school? Data science? Calculus? Computing? Is it time to rethink the algebra/geometry/algebra sandwich? Dan Rockmore discusses the issues in this piece featuring Steven Levitt, @joboaler , and David Coleman.

Should high schools teach data science instead of calculus?

High school math curricula are designed to prep and herd students towards calculus. Some mathematicians think this path is outdated

www.salon.com

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Steven Strogatz

@stevenstrogatz

5 years

Free and open-source textbooks on calculus, linear algebra, differential equations, real analysis, abstract algebra, combinatorics, and introduction to proof -- a partial list, helpfully compiled and curated by Dana Ernst @danaernst .

Free and Open-Source Textbooks

Mathematics, Teaching, & Technology

danaernst.com

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Steven Strogatz

@stevenstrogatz

7 years

My lectures on nonlinear dynamics and chaos are free online here. Maybe useful to students taking a first course

Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. ...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

2 years

In complex analysis, I'm teaching my students about "the argument principle" now. It provides info about where the zeros of a function f(z) are. Here's a toy example, using the function w = f(z) = (z-a)(z-b), where the zeros a and b are located at the black points shown below.

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Steven Strogatz

@stevenstrogatz

2 years

Is mathematics invented or discovered? Read what Kurt Gödel had to say. Here's the text of his 1951 Gibbs Lecture (along with an introductory note) in which Gödel argues for Platonism in the philosophy of mathematics, as in the passage excerpted below.

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@stevenstrogatz

3 years

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@stevenstrogatz

8 years

Hear me try to explain eigenvalues & eigenvectors intuitively, without visuals, in 5 minutes, while clarifying why they matter. Ready? Go!

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Steven Strogatz

@stevenstrogatz

1 year

Today in nonlinear dynamics we discussed some simple flows on a torus and made connections to number theory, knot theory, and real analysis. One student said he liked seeing all that "intersectionality". (You can see a lecture about these ideas here: )

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Steven Strogatz

@stevenstrogatz

3 months

Here's a graph of x^n/n! for n = 1 to 20. Can you explain why the curves look almost evenly spaced and have such similar shapes? What's the sideways spacing between them?

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Steven Strogatz

@stevenstrogatz

2 months

This essay is charming and insightful, but it doesn't give any hint about how to *make* discoveries. For that, I would recommend this free PDF of a book by Professor Jack Oliver, one of the discoverers of plate tectonics.

Scholarship for PhD

@ScholarshipfPhd

2 months

The importance of stupidity in scientific research

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Steven Strogatz

@stevenstrogatz

3 years

Just to be on the safe side…

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@stevenstrogatz

4 years

Alissa Crans recently sent me a postcard featuring this gorgeous image. Can any of you decode it? I see that solid squares correspond to prime numbers. But what explains the color scheme and number of sub-rectangles in the entries for the composite numbers? #overthinking

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@stevenstrogatz

5 months

This onion is connected, but not simply connected

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@stevenstrogatz

5 years

Another rejection letter I'll always cherish is the following. (I had I invited myself to visit Dr. Crick – whose work on DNA topology I greatly admired – and was rebuffed in the gentlest way.) #nothing_ventured_nothing_gained

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@stevenstrogatz

4 years

Maybe everybody else knows this, but I had no idea the roof of the Sydney Opera House was fashioned from a single sphere! Learn the backstory of “the Spherical Solution” here:

Eddie Woo

@misterwootube

4 years

@mathyawp @stevenstrogatz @Math4HF @yalepress The spherical solution for the @SydOperaHouse is one of the most beautiful pieces of mathematics in the world. 💛 Francis, huge congratulations on your international release of @Math4HF !!

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Steven Strogatz

@stevenstrogatz

3 years

Today is Ramanujan’s birthday. If you have never read this remembrance by his collaborator G.H. Hardy, you must read it now. (After watching THE MAN WHO KNEW INFINITY, I hear Jeremy Irons’s voice in every line.)

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Steven Strogatz

@stevenstrogatz

4 years

Here is the math, assuming 5% prevalence of antibodies in the population, and a 90% accurate test. Under these assumptions, the test gives the wrong result about 68% of the time among the people who test positive for antibodies.

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@stevenstrogatz

3 years

28 books I've recommended here on Twitter (mostly about math, but not all...)

40 books Steven Strogatz recommended

(Updated 2024) The most up to date and comprehensive list of 40 verified book recommendations from Steven Strogatz. Includes quotes and sources.

www.readthistwice.com

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@stevenstrogatz

4 years

Here’s my attempt to explain in plain words what eigenvectors are and why they matter, in five minutes, with no visuals. Ready? Go!

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Steven Strogatz

@stevenstrogatz

2 years

The Most Important Algorithm Of All Time - ⁦ @veritasium ⁩ on the Fast Fourier Transform (including a story I had not heard before, the connection between the FFT and the nuclear arms race).

The Remarkable Story Behind The Most Important Algorithm Of All Time

The Fast Fourier Transform is used everywhere but it has a fascinating origin story that could have ended the nuclear arms race. This video is sponsored by 8...

www.youtube.com

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Steven Strogatz

@stevenstrogatz

3 years

I'm teaching a course on asymptotics and perturbation methods, and thought it might be fun to share the lectures on @YouTube . Here's lecture 1, which introduces the idea of asymptotic expansions. (For more about the course, see the rest of this thread.)

Asymptotics and perturbation methods - Lecture 1: Asymptotic expans...

This is the introductory lecture in an applied math course on asymptotics and perturbation methods, offered by Prof. Steven Strogatz at Cornell University in...

www.youtube.com

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@stevenstrogatz

5 years

I've long worried about this, and it is starting to happen: Some students aren't sure which way is "clockwise" anymore. (The screenshot below is from a student's answer on a test I just gave, in which the word "counterclockwise" was used.) #DeathOfAnalog

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@stevenstrogatz

4 years

What's a Tensor? - Dan Fleisch explains them here in 12 minutes using household objects. The result is a clear, intuitive, highly physical (as opposed to mathematical) view of tensors. More than 2 million people enjoyed it! via @YouTube

What's a Tensor?

Dan Fleisch briefly explains some vector and tensor concepts from A Student's Guide to Vectors and Tensors

www.youtube.com

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@stevenstrogatz

2 years

Nick Trefethen, professor of numerical analysis at @UniofOxford , explains what the concept of resonance can teach us about dribbling. Watch out, @StephenCurry30 !

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