“Persistence is a great substitute for talent.”—Steve Martin

I think education is one of the most important subjects in desperate need of a real Copernican revolution. Salman Khan is laying the groundworks.

Might seem irrelevant at first, but the fact that our brain can make sense of any signals we feed to it, corroborates the idea that our intelligence is much more malleable than we think it is. In this talk you'll see that they let a deaf man understand words through vibration patterns on his back. "The brain just figures out what to do with it."

Warning this will be a fair bit of text, but it is 100% worth reading.


While working through the course "Learning how to learn" on Coursera by Barbara Oakely and Terrence Sejnowski (If your interested in machine learning Terrence Sejnowski is the person who with Dr Geoffrey Hinton showed that simple neural networks could be made to learn tasks of at least some sophistication and with Hinton also discovered the Boltzmann machine / pioneered the application of learning algorithms to difficult problems in speech and vision) . Part of the course consists of interviews with experts of learning and people who wern't conventionally gifted. 


One of the interviews is with Dr. Robert Gamache who has been named by Thomson Reuters as one of the world's most influential scientific minds for 2014. From the interview

"Dr. Gamache is also clearly a very active researcher. Of the list of the ten most cited publications by the University of Massachusetts Lowell faculty compiled in 2011, he was a coauthor on five of the ten, including the top three papers

... 

First, let me say that I'm dyslexic and as a child I had. Really a lot of trouble learning English, spelling, grammar, reading. I still have trouble reading. I'm a little bit slower than most people, especially with the precision needed for reading scientific articles

...

when I was an undergraduate, there was not a lot of research on how we learn, and the things I did, I just stumbled upon them. Now they are backed by research, and you, you show a number of these things in your book and I can attest that they work. So when I was an undergraduate I was taking physical chemistry in my third year and I became fascinated with the fact that you could take equations, you could take simple rules of physics. And with that, you could derive other equations. And what I did is I started doing every problem in the textbook. At first, it was a little difficult but with time, I could do problems as fast as I could look at them. So, I noticed that problem solving in other courses at the same time became easier. It was later in graduate school that I found that there was research and this repetition actually hard-wires your brain. So in my case, I hardwired my brain to solve problems. Precisely. I, I think it's almost like again, like learning an instrument. By practicing continuously, you can bring those, those parts of a melody to mind instantly, and, and play them and fit them together in new ways more easily, and that can be a very effective technique for learning.

...

And the, the early, early stages of that meant I had a lot of studying to do. So, I would come home from a full day at work, and I would immediately sit down at my desk. And start studying some more. And often I would get stuck on, on concepts or stuck on problems then I had to take a break for dinner or a few times I had friends come over just to say hello. And what I found was while eating dinner and conversation, suddenly the answer would just pop up in my mind. And at the time, I would run off and write it down like I was going to lose it if I didn't do it immediately. But the gears are always turning in the background. My wife used to joke that I had two brains. Now when I get stuck, I deliberately take a break and try to do something just to relax, you know, almost thoughtless, it can be as simply as bouncing a tennis ball off the wall or something like that. After five to ten minutes, I tend to go back to the problem with the answer. And sometimes, I have to sleep on it. There are many mornings when I wake up and suddenly, I have the answer in my brain." 

A link to the interview as a youtube video is as follows 

A phenomenal collection of essays entitled “Living Proof: Stories of Resilience Along the Mathematical Journey”, from the AMS AND MAA. The stories are organized around common themes in the experiences. Part I is about math getting hard and people hitting a wall. Part II is about struggling to belong in math (and is particularly well aligned with the goals of this blog). Part III is about persevering through and overcoming difficulties. And Part IV is about the sometimes challenge of integrating our mathematical identities with the rest of our lives.

www.ams.org/about-us/LivingProof.pdf

Cal Newport: "Follow Your Passion" Is Bad Advice

Innate Ability in Math? I don't think so
Stanford professor Margot Gerritsen: gerritsn.people.stanford.edu/wzzn-innate-ability-math-i-dont-think-so

Mentions the nature versus nurture debate, and contains other helpful insights.

Why Late Bloomers Are Undervalued | Rich Karlgaard | TEDxFargo