The formula of the winter: 5:4:2.5

From the brilliant post THE WONDROUS MATHEMATICS OF WINTER in The New Yorker blog, by :

There’s the snowman: the human form given in three spheres. It is a sort of absurdist abstraction: the top sphere makes sense, and we can stretch to consider the middle one to have captured the salient properties of those of us with more orbic midsections. But I don’t know what to make of the bottom sphere. There may be some work to do here, which Euclid or Archimedes might have gotten to if it had snowed more often in Greece. The ratios of the spheres matter. A stack of three equally sized white spheres might read as tennis balls in a sleeve or cocktail onions on a toothpick. After considerable investigation, I have discovered that if the proportions of the diameters are 5:4:2.5 (from bottom to top) then the form unambiguously reads as a snowman, with or without carrot, coal, sticks, scarf, or hat. We have then a stack of three white spheres that signify archetypal “winter” quite clearly. I challenge you to signify any other time of year with such simple geometry.


Read more, including including Gregory Buck’s musings on how winter is the Platonist’s season, and why being a mathematician is like being stuck in a blizzard.


A new revisionist movement?

A conference 21st Century Mathematics, 22-24 April 2013, Stockholm will discuss some challenging   questions:

[…] In the 21st century, humanity is facing severe difficulties at the societal (global warming, financial stresses), economic (globalization, innovation) and personal levels (employability, happiness). Technology’s exponential growth is rapidly compounding the problems via automation and off-shoring, which are producing social disruptions. Education is falling behind the curve, as it did during the Industrial Revolution. The last profound changes to curriculum were effected in the late 1800’s as a response to the sudden growth in societal and human capital needs. As the world of the 21st century bears little resemblance to that of the 19th century, education curricula are overdue for a major redesign. […]
1. What should the goal of mathematics be in the 21st century?
a. What are the reasons for teaching mathematics? (as a tool, to train abstract thinking, to train logic and reasoning, the ability to argue/as a way of expression?)
b. How have the goals of mathematics drifted over time? (Priest class– logic, merchant class–accounting, trade class– measurement and geometry, and how this changed after the industrial revolution)
c. How does the present system achieve or fail to achieve these goals?
d. What is the role of Higher Ed accreditation in perpetuating the status quo?
e. What branches of mathematics matter to the widest number of professions? Are they adequately represented in the curriculum?
f. What is “math for the real-world”? How do most professions use Maths? What could they use they are not learning?
2. What are the best practices curricula from around the world? How do these succeed or fail to achieve the needs and possibilities of the 21st century?
a. When should math be a separate topic, vs just-in time practice embedded in other disciplines such as Robotics?
b. In reverse and for instance, should financial literacy be part of Mathematics?
c. When should we continue leading in formalism, vs transpose and lead with examples and applications to guide students into formalism?
d. How do we inject skills (Creativity, Critical Thinking, Communication, Collaboration) into math knowledge acquisition?
e. How do we inject Character attributes (perseverance, ethics etc) into math knowledge acquisition?

The question that is not asked is why “New Math” reforms of 1960s and 1970s almost universally failed.


Lincoln talks about Euclid

[reposted, with additions, from 22 November 2012]

A clip: Lincoln talks about Euclid,

from Steven Spielberg’s Lincoln. In the title role:Daniel Day-Lewis. Screenplay: Tony Kushner.

The film suggests that Lincoln was using mathematical concept of transitivity as a guiding principle of political consensus-building.

A more detailed discussion of political aspects can be found in ‘s post on Huffington Post blog, and a remarkably interesting criticism (by Christopher S. Morrissey) in The Catholic World Report:

 […] screenwriter Tony Kushner portrays Lincoln’s pursuit of the Thirteenth Amendment as flowing, not from Christian charity, but from mathematical reasoning analogous to the abstractions Lincoln read about in Euclid’s Elements.

“Euclid’s first common notion is this,” says Lincoln in the film, “Things which are equal to the same thing are equal to each other. That’s a rule of mathematical reasoning. It’s true because it works. Has done and always will do. In his book, Euclid says this is ‘self-evident.’ You see, there it is, even in that 2,000-year-old book of mechanical law. It is a self-evident truth that things which are equal to the same thing are equal to each other.”

The scene is a fiction. The truth is more interesting. Lincoln himself actually said this: “One would start with confidence that he could convince any sane child that the simpler propositions of Euclid are true; but, nevertheless, he would fail, utterly, with one who should deny the definitions and axioms. The principles of Jefferson are the definitions and axioms of free society. And yet they are denied, and evaded, with no small show of success. One dashingly calls them ‘glittering generalities’; another bluntly calls them ‘self-evident lies’; and still others insidiously argue that they apply only ‘to superior races.’” (6)

Difficult as it is to teach someone mathematics (and to apply its self-evident truths in a process of reasoning), it is even more difficult to teach and apply the truth of the Declaration of Independence about human equality (“that all men are created equal”).

TIMMS 2011 International Results in Mathematics

Some results of TIMMS 2011 International Results in Mathematics are published and generated some media response. However, it is too early to have a serious discussion of the report. At the moment, the data released is very crude; for example, there are no problems and no way to choose illustrative examples. So we suggest to wait until one can

see how different countries perform on specific released problems – in January or February 2013, according to TIMMS’ schedule.

Mathematics graduates from 2011: Type of work for those in employment

From What do graduates do? published by Higher Education Careers Services Unit:

39.9% Business and Financial Professionals and Associate Professionals
9.9% Retail, Catering, Waiting and Bar Staff
8.0% Other Occupations
8.0% Information Technology Professionals
7.4% Education Professionals
6.1% Other Clerical and Secretarial Occupations
6.0% Commercial, Industrial and Public Sector Managers
4.4% Numerical Clerks and Cashiers
3.2% Marketing, Sales and Advertising Professionals
2.6% Other Professionals, Associate Professional and Technical
1.3% Arts, Design, Culture and Sports Professional
1.1% Engineering Professionals
0.8% Social &

Welfare Professionals
0.7% Scientific Research, Analysis & Development Professionals
0.5% Health Professionals and Associate Professionals
0.2% Legal Professionals
0.1% Unknown Occupations