A visualization showing how three mathematical concepts translate into simple objects in nature.

Mathematical equations are like sonnets says Keith Devlin. What most of us learn in school, he says, doesn’t begin to convey what mathematics is. And technology may free more of us to discover the wonder of mathematical thinking — as a reflection of the inner world of our minds.

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## Guests

is executive director of H-STAR, the Human-Sciences and Technologies Advanced Research Institute at Stanford University. His books include *Introduction to Mathematical Thinking* and *Life by the Numbers*.

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## About the Image

Staff at the Eden Project get to have their first view of the biggest rainforest in captivity from Eden's new Rainforest Lookout on September 6, 2010 in St Austell, England. The aerial platform — which is higher than the Tower of London at the top of the 55-meter-high biome, the largest greenhouse in the world — allows visitors to the Eden Project the chance to look down on the tropical canopy in a way they could never have before. The Rainforest Biome is the larger of Eden's two covered biomes at 100 meters wide, 300 meters long, and 55 meters high and contains thousands of tropical plants including banana trees, coffee, rubber plants and giant bamboo. The aerial platform, which opened to the public this month is the latest attraction to the Cornish tourist spot which gets over 1 million visitors a year.

## Reflections

### Calvin is more correct about

Calvin is more correct about math as a religion than he imagines. That Keith Devlin discovered the wonders of math at the top of a tree that allowed him to escape the confines of the forest (the Garden of Wholeness of which we are an integral part) demonstrates the veracity of Calvin's thinking.

In my youth, I literally climbed to the top of a tree on top of a Colorado mountain with its base at 12,000 feet elevation and "saw God". What we see or experience at those airy heights is NOT the truth of the world in which we are immersed, but the abstractions from that world that are poor approximations of the real thing.

Both mathematics and religions are such abstractions - mental metaphors for the world of dust and moonbeams - beautiful in its perfection, perhaps, but only a substitute for, and evasion of, the real world of which we're made.

### I have been listening to him

I have been listening to him on NPR for a long time and while NOT being a math maven, I did enjoy the talk. Thanks, yet again!

### Good morning Dr. Devlin,

Good morning Dr. Devlin,

First I trust that this message finds you contented; having food (nutrition) and cover (clothing and shelter). I woke up to your voice on the 6 am, 9/22/2013, 90.7 WMFE interview on Joy of Math with Ms. Krista Tippett. Your point of view of mathematical thinking is interesting and different especially your connection of music to math. I like your effort in massively open online courses (MOOC). Many could be edified in traditional courses, who cannot enter a fee for education university.

I could not miss your passing comment to Ms. Tippett about language and evolution of humankind. Your statement of 50,000 years did not elude my hearing. What is your evidence for the number for the age of language? You spoke of the origins of language as if it was a mystery and having evolved from some unknown source. Why is your conclusion so uncertain? Have you not read that the multiplicity of languages were an intervention of one called God Genesis 11:1, 6, 7, 9 (King James Version)? The earth was of one language before the noteworthy event Genesis 11:1 (King James Version).

Your leadership in a correct direction on the subject of language can be tremendous because of your credentials; your association with a prominent and well known seat of higher learning – Stanford; and the strength of your independent viewpoint.

Please respond with your thoughts, and your research on my challenge to your view of language and its origin.

### There is a lot more

There is a lot more mathematics to the learning process than one might naively expect.

Everyone has heard of the fabled "learning curve" but such notions are more than a poetic metaphor. Have you ever wondered what is encoded in the *curvature* of a learning curve?

See Cognition, Affect, and Learning for some surprising insights into the hidden mathematics of a learning curve.

### Al Islam is mathamatics (a

Al Islam is mathamatics (a thinking pattern) and mathamatics is Al Islam and it can be proven in no limit of time. I learned that from Elijah Muhammad in 1972.

"Say He Allah is One" Quran Chapter 112

I thoroughly enjoyed Dr. Devlin's exposition and intend to read his treatises in the future. Insha Allah ( Allah willing)

### Joy of Math. Every Sunday

Joy of Math. Every Sunday morning we listen to On Being and then discuss what we've heard and how it relates to our lives. I was excited to hear about mathematics "as a reflection of the inner world of our minds" and mathematics as seeing "patterns." I felt the interview didn't really follow through on those. Yes, music has patterns but what are other examples of mathematical patterns in life? I would have appreciated examples that would help me "see" in this different way. Interesting that people were singing the equations, but were the notes/tune chosen to specifically create the pattern of the equation they were singing about? How does that relate to my life and the inner workings of my mind? And I would have appreciated examples of how mathematics is a reflection of the mind. Keith said language and mathematics are of the same origin but he didn't explain that. To someone who doesn't see the world the way he does, I have no idea what that meant. The first 14 minutes were about how schools and people don't use use or teach math to its fullest potential. We know that. Thanks for the many, many good programs that I often encourage friends and clients to listen to, but this won't be one of them.

### Was delighted to learn about

Was delighted to learn about MOOC, hear a mathematician say that quantification is limited, and learn about The Language of Mathematics:Making The Invisible Visible...I ordered 2 copies last night ...one for my son and one to help supplement my work as a middle school teacher. Thanks

### The Joy of Math:

The Joy of Math:

We need to see a follow-up segment on MOOC since the joys of math segment into the joys of MOOC was quite disturbing.

This is a quick synopsis of Stanford University and education.....they were leaders in the education reform of the late 1980s that took text books out of the classrooms because it stifled creativity and stopped rigor in grading and moving students up because all that hurts children's feelings. The same reform had teachers allowing calculators in teaching math. This wasn't optional and teachers fought against this and for quality education just as they are fighting the reforms by the same institutions responsible for that disaster of reform. I know you all know this so I'm just setting the stage.

Stanford used that education reform to make all kinds of money writing and selling these new enlightened lessons in lieu of textbooks. Stanford is now a corporation as it has for decades been patenting and profiting off of these education reform policies. That education reform policy gave us students who graduated not able to read and do math.

Now we are having an education reform that has these same institutions with Stanford in the lead taking students online and exposed to canned lessons written by hand-picked professors. What could go wrong with that? We all know this reform is about ending completely democratic education in America and creating an autocratic capture of information from K-college and MOOC leads the way. The idea that MOOC was created to be this great free access education ....the great equalizer....is much like the Great Leader appearing on the Korean news stating THERE IS FOOD IN GROCERY STORES so you can't be hungry. I must say that the guests suggestion of liking the image of looking out from the computer screen as being intimate education just as startling as the Great Leader.

The intent with MOOC is to eliminate the diversity of learning and the bedrock of democratic activity. We need to look at the MIT decision last year to stop all large lecture hall computer lessons because of the obvious fact that students spent the time surfing the web and not following the lessons online to know this online course/lesson holds no value in achievement....it simply is being used to further capture a democratizing structure and make lots of money. Indeed, they are now trying to figure out how much to charge for these and how professors will be chosen.

The point is that we have public media in order to provide programming that is public interest. What I just outlined would be the public interest piece of what was an advertisement for a profit-making adventure. To have it imbedded in a show on morality and ethics....truly bizarre. I'm sorry for you!

### Please say on your Sunday

Please say on your Sunday morning 7 am broadcast (NYC) when the program will be rebroadcast; Sunday night, what time? It seems to be nowhere posted on the website. Also, I CANNOT STAND those soupy musical interludes between segments; part of the intellectual degeneration of NPR, everywhere. Why do you have to do this repeatedly, interrupting the most profound thoughts with mood music and advertising? It is an insult to an intelligent audience and a waste of time. Such a disappointment for such a fine program as On Being. It is ubiquitous now at NPR and a vulgarization of its mission. Victoria Southwell

### Yes, but it takes several

Yes, but it takes several years of study to understand Euler's identity. It's kind of like e=mc2. Or Newton's gravitational equation, why should it be so? But it is. Euler has another larger identity which connects addition and multiplication which is also tremendous and completely unexpected.

Pythagoras goes a lot farther - he felt that idea and form were God and generated all other realities. It's kind of form and beauty as God. This is a pre-Christian pagan religion.

Numbers are part of the natural, created world, in the realist sense or not. And any part of the created world turns out to be beautiful.

Right, mathematics or science or reason by itself, without the tempering of human considerations, make perfect sense, but lead to disaster.

"God is a mathematician." Einstein

Wonderful to see a gifted mathematician!

### There is a book about Greek

There is a book about Greek religion titled 'God as form' which describes how form can be seen as generating all else in Pythagoras. It's an emphasis on beauty, and it seems to me that it's the default metaphysical background of our public schools.

### Wow, this program opened my

Wow, this program opened my eyes to let some new ideas in. Thank you O

### 1-i have listened to ONBEING

1-i have listened to ONBEING programs for several years on

KUT austin,tx.. when i happened to wake early 600am on sunday mornings it was so exciting to be mentally challenged on deeper

aspects of spirituality interviewing leading thinkers...

2--this seeming NEW DIRECTION of deep analysis of physics and mathematical persons connected with spirituality and philosophy is major contribution to the search for meaning in this new century.

### I was disappointed to hear Ms

I was disappointed to hear Ms. Tippett begin her interview by saying she is "congenitally bad," or words to that effect, at math. People with certain disabilities may be congenitally bad at math--or French or cooking or volleyball--but I believe the rest of us are limited only by our willingness to do the work. I'm 70 years old, a retired professional writer, and for the past three years I've been studying calculus (actually, pre-calculus, since I had some brushing up to do) at various places on line. I'm getting better at it, maybe even good.

### You, too, eh?

You, too, eh?

To the idea that some people are inherently math-talented while others are "congenitally bad at math", a great discussion of this phenomenon-or-myth can be found at http://qz.com/139453/theres-one-key-difference-between-kids-who-excel-at-math-and-those-who-dont/

### I love the line in which he

I love the line in which he states "technology may free more of us to discover the wonder of mathematical thinking" We can certainly hope so! Freedom of thought and freedom of travel! Best wishes!

### Good day Professor Devlin,

Good day Professor Devlin,

I found you through your Stamford online math class. After watching two of your utube videos I am convinced you will go down in history as the most extraordinary mathematicians in this century. You are improving the world, and you certainly changed my perspective on math, which has always been full of fear. I look forward to learning eveything I can from you for as long as I live.. I am deeply humbled and grateful to you. Blessings and eternal thanks!

### "Mathematics is a lense

"Mathematics is a lense through which you look at the world. But in a deeper sense, it's a mirror through which you look at yourself."

I find it somewhat ironic that this week's On Being, about the mathematican Keith Devlin, is how numbers apply to spiritual understanding. Just two weeks ago I was thinking hard about what numbers actually are. They represent nothing tangible physically. I came to the conclusion that numbers have literally know physical meaning. Yet, numbers mean so much to people. They mean everything. How we see and interpret the world is entirely grounded in how we understand numbers. At the same time though, we make these connections and we use these numbers without even realizing it. Our connection to them, is inherent regardless of what level of numerical education we possess. Numbers are a metaphysical representation through which we intrepret both the physical and the spiritual. As Devlin says, it is a way we look at the world but also a way we reflect upon ourselves.

I think his study is particularly fascinating, specifically how he views his online class, which has thousands of students throughout the world as more personal than a lecture in a classroom. He says it is because he speaks more directly to the student who must tune in online and see his lecture rather than divide his attention and their through everyone in the classroom. I think this also applies to how he says our understanding of mathematical knowledge must catch up to our technoloy for to really appreciate the connections it makes between the way we are, the way others are, and the way the universe is. After all, through mathematics we can see the world through a lens, but also look at a mirror into ourselves.

### Hello Krista and gang,

Hello Krista and gang,

I very much so enjoy your shows. I listen with enthusiasm. Podcasts allow me to listen out of order and here i am in 2014 listening to this conversation on Math. I would challenge you Krista to re-evaluate your understanding of your inability to do math. As white women we were told to be nurses, teachers and wives until the mid 80's in urban centers and likely mid 90's in rural. Middle class girls were fostered into quiet activities like reading and writing journals. Boys into athletics and certainly we were surrounded by white male faces in math, science and chemistry.

That like anything else takes generations to undo.

How would you know if you were good at math?

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