Good book! Here's a few notes from me and Farnham Street:

http://pandawhale.com/post/31877/in-pursuit-of-the-unknown-17-equations-that-changed-the-world

E = mc² is a simplification of the full law E² = p²c² + m²c^4

E: system energy, p: impulsion, c: light speed, m: system mass

I don't understand why it is never mentioned.

E = mc² is only true for static mater.

Now if you take a photon, the mass m=0 --> E = 0!? but photon is energy, how could E = 0!?

Because E = mc² is not relevant for photons, it's not mater, nor static!

Now, If we take E² = p²c² + m²c^4 with m = 0, we get E = pc, and this one is true. : )

So yeah let's stop displaying E = mc² as a general fundamental equation, it's an approximation.

It's the approximation most civilians can remember.

It was popularized by the television series The Twilight Zone.

But you're right, photons do not have zero energy.

Yep, popularizing is hard, but essential, very high responsibility.

Some auto-proclaimed popularizers don't realize it and just look for fame through the mystic/magic image sciences have among the average population, that upsets me, a lot. ^_^

Yes, and people see signs in things that are completely random and circumstantial.

People believe what they want to believe. It is maddening to the rational mind!

In 2013, mathematician and science author Ian Stewart published a book on 17 Equations That Changed The World. 

This convenient table on Dr. Paul Coxon's twitter account by mathematics tutor and blogger Larry Phillips summarizes the equations:

Personally, I think this Infographic says it best.

Aha! So that's how he figured it out!!

More about this:

http://pandawhale.com/post/70278/17-equations-that-changed-the-course-of-history-by-ian-stewart