But mathematicians also star in some of the most dramatic stories in science. The lone, unrecognized genius laboring away on a groundbreaking theory over many years is more fiction than fact for most of modern science—but not in mathematics. Andrew Wiles’ 1995 proof of Fermat’s last theorem, which had defied all efforts to prove it for more than 300 years, was made all the more dramatic by the secrecy with which it was conducted. But Wiles was already ensconced in the elite circles of mathematics when he did his work.
Not only did Zhang work in relative secrecy, he was also a complete unknown. He had found work as a lecturer at the University of New Hampshire (UNH) in 1999, eight years after he finished his Ph.D., with the help of connections at his undergraduate institution, Peking University. Then, in April of this year, Zhang announced a proof that cracked open a century-old problem in mathematics, called the twin prime conjecture. “It was like climbing Everest,” says Ayalur Krishnan, a math professor at CUNY’s Kingsborough community college.
(tip of the hat to Frank)
Explaining something technical is a real challenge. Here Margot Geeritsen talks about a great piece of applied math - the Navier-Stokes equation. If you have seen a bit of calculus you should be ok with it and learn why this is so useful. A nice job and she uses a real chalkboard...
Elliptic curve cryptography (ECC) is one of the most powerful but least understood types of cryptography in wide use today. An increasing number of websites make extensive use of ECC to secure everything from customers' HTTPS connections to how they pass data between data centers. Fundamentally, it's important for end users to understand the technology behind any security system in order to trust it. To that end, we looked around to find a good, relatively easy-to-understand primer on ECC in order to share with our users. Finding none, we decided to write one ourselves. That is what follows.
Be warned: this is a complicated subject, and it's not possible to boil it down to a pithy blog post. In other words, settle in for a bit of an epic because there's a lot to cover. If you just want the gist, here's the TL;DR version: ECC is the next generation of public key cryptography, and based on currently understood mathematics, it provides a significantly more secure foundation than first-generation public key cryptography systems like RSA. If you're worried about ensuring the highest level of security while maintaining performance, ECC makes sense to adopt. If you're interested in the details, read on.
You run into a bit of this - people under forty tend to have tatoos these days and there is a subset who are invovled in science, math and technology. Carl Zimmer has been cataloging some of them for years and has about 300 posted at his site at The Loom (which is now hosted by National Geographic).
I selected this one as it would be my choice if I had a tatoo - the most beautiful mathematical expression I can think of...
Comments by Carl Wieman appearing in the Fall 2012 issue of the National Academy of Sciences Issues publication. Some interesting point and good fodder for discussion. Some of what he prescribes sounds like the Finnish system.
Science, technology, engineering, and mathematics (STEM) education is critical to the U.S. future because of its relevance to the economy and the need for a citizenry able to make wise decisions on issues faced by modern society. Calls for improvement have become increasingly widespread and desperate, and there have been countless national, local, and private programs aimed at improving STEM education, but there continues to be little discernible change in either student achievement or student interest in STEM. Articles and letters in the spring and summer 2012 editions of Issues extensively discussed STEM education issues. Largely absent from these discussions, however, is attention to learning.
This is unfortunate because there is an extensive body of recent research on how learning is accomplished, with clear implications for what constitutes effective STEM teaching and how that differs from typical current teaching at the K-12 and college levels. Failure to understand this learning- focused perspective is also a root cause of the failures of many reform efforts. Furthermore, the incentive systems in higher education, in part driven by government programs, act to prevent the adoption of these research-based ideas in teaching and teacher training.
A new approach
The current approach to STEM education is built on the assumption that students come to school with different brains and that education is the process of immersing these brains in knowledge, facts, and procedures, which those brains then absorb to varying degrees. The extent of absorption is largely determined by the inherent talent and interest of the brain. Thus, those with STEM “talent” will succeed, usually easily, whereas the others have no hope. Research advances in cognitive psychology, brain physiology, and classroom practices are painting a very different picture of how learning works.
We are learning that complex expertise is a matter not of filling up an existing brain with knowledge, but of brain development. This development comes about as the result of intensive practice of the cognitive processes that define the specific expertise, and effective teaching can greatly reduce the impact of initial differences among the learners.
This research has established important underlying causes and principles and important specific results, but it is far from complete. More research is needed on how to accomplish the desired learning most effectively over the full range of STEM skills and potential learners in our classrooms, as well as how to best train teachers.
What is learning STEM?
The appropriate STEM educational goal should be to maximize the extent to which the learners develop expertise in the relevant subject, where expertise is defined by what scientists and engineers do. This is not to say that every learner should become a scientist or engineer, or that they could become one by taking any one class, but rather that the value of the educational experiences should be measured by their effectiveness at changing the thinking of the learner to be more like that of an expert when solving problems and making decisions relevant to the discipline. As discussed in the National Research Council study Taking Science to School, modern research has shown that children have the capability to begin this process and learn complex reasoning at much earlier ages than previously thought, at least from the beginning of their formal schooling. Naturally, it is necessary and desirable for younger children to learn less specialized expertise encompassing a broader range of disciplines than would be the case for older learners.
I'm also a believer in going well beyond STEM and moving to a more effective and broader education .. but interesting points.