### History of Science, Environmental & Science Education

by Edward Hessler**A Mathematical Breakthrough**

It was on this day, November 25, 1915 that Albert Einstein presented his famous General Relativity field equations at a lecture at one of the hotbeds of European physics, the University of Gottingen. Just a few years later, Gottingen was one of three centers for the study of physics and quantum mechanics.

*Video By Jubobroff (Own work)

[CC BY 3.0 (http://creativecommons.org/licenses/by/3.0)],

via Wikimedia Commons

It is easy to forget how mathematical this breakthrough was. Einstein worked and corresponded with some of the best mathematicians on the continent for several years. It was not born overnight in a flash of inspiration.The geometrical ideas were deep and difficult, not at all intuitive. At times Einstein struggled with them.

**Marcelo Gleiser on Einstein's Theory**

Marcelo Gleiser, a theoretical physicist and cosmologist at Dartmouth College who also writes for 13.7 at NPR wrote about this anniversary today. I was so glad he couldn't resist writing the equation down and even happier when he asked us to look at it. What's on the right side; what's on the left side. This not only draws attention to the equation but is a way of asking us to think about it.

I've a friend who teaches college physics. He uses this strategy of asking students this kind of question fairly often, at least in classes I've observed because most students want to "plug and chug," especially under the heat of a test but also when dealing with problem sets. They want to get it over and move on. But mathematics is more than computing. It is used in formulas and equations to summarize--organize data--as well as reveal relationships.

To do this requires, especially when you are stuck, to ask "What will happen if..?" kinds of questions. Suppose you move something from one side of an equation to the other or in a formula using fractional components, move something from top to bottom or vice versa? Change the value of a quantity? Sometimes I've seen my friend simply ask "what's on top; what's on bottom?" (what it means) and to describe what a change in a quantity or a reversal of a quantity does to the mathematical representation or simply to ask what the symbols stand for. The idea is not only to understand the tool but also the concept(s).

Gleiser's essay may be found here.

**NASA: Beyond Einstein Program**

Image from Amazon.com |

Happy Birthday General Relativity!

PS#1--This just in. The NAS Press "messed-up" which means that the PDFs are not free as previously advertised. NAS Press makes the offer free until November 30, 2015.

PS#2. Each Thanksgiving, Sean Carroll, a theoretician at CalTech posts about an equation (Riemann geometry this year) to be thankful for. Carroll includes a link to a video, "E=MC^2...How Einstein's Theory of Relativity Changed Everything," in which he and Jeffrey Bennett are interviewed by Mat Kaplan. Carroll and Bennett focus on general relativity in their research in physics.

PS#3. And speaking of "mess-ups." Einstein delivered his talk on general relativity in Berlin at the Prussian Academy,

**not**Gottingen as I shouted from the roof-top!

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