The 17 Equations That Changed The Course Of History

[jakeXT]

Mathematics is all around us, and it has shaped our understanding of the world in countless ways.

In 2013, mathematician and science author Ian Stewart published a book on 17 Equations That Changed The World. We recently came across this convenient table on Dr. Paul Coxon's twitter account by mathematics tutor and blogger Larry Phillips that summarizes the equations. (Our explanation of each is below):

Read more: http://www.businessinsider.com/17-equations-that-changed-the-world-2014-3

Ian Stewart claims that the Black-Scholes equation changed the world. Does he really believe that mathematics caused the financial crisis?

"It was abuse of their equation that caused trouble, and I don't think you can blame the inventors of an equation if somebody else comes along and uses it badly," he says.

"And it wasn't just that equation. It was a whole generation of other mathematical models and all sorts of other techniques that followed on its heels. But it was one of the major discoveries that opened the door to all this."

Black-Scholes changed the culture of Wall Street, from a place where people traded based on common sense, experience and intuition, to a place where the computer said yes or no.

http://www.bbc.com/news/magazine-17866646

[louis-t]

1. I agree with the solution to Black-Scholes.

That's the part that WE got.

[TxDemChem]

2. Ain't that the truth!

[Warpy]

3. No kidding, but nothing will throw a spanner into it more quickly

than even a tiny per transaction tax. That's why so many of us have wanted it for so long.

[hunter]

4. Some hard prison time for some of these bankers wouldn't hurt either.

I call bullshit on many of their "proprietary" algorithms. What these crooks' software actually did was cover up old fashioned insider trading and other sorts of market corruption.

[jobendorfer]

5. The first of Maxwell's Equations is given incorrectly

It should read Del Dot E = Rho / e, where e is the permitivitty.
That is, the electric field is equal to density of the enclosed charge divided by the permitivitty of the enclosed region.

J.

[Jim__]

6. In the book, Stewart notes that he's using a simpler form of the equations.

From the book:

... Maxwell used specific formulas involving the three components of the electric and magnetic fields. In the special case in which there are no conducting wires or metal plates, no magnets, and everything happens in a vacuum, the equations take a slightly simpler form, and I will restrict the discussion to this case.

This case seems to agree with the description in wikipedia:

In a region with no charges (ρ = 0) and no currents (J = 0), such as in a vacuum, Maxwell's equations reduce to:



...

[DetlefK]

7. That's boooring. You end up with equation 8 again.

[Jim__]

8. Wow! I bet Stewart didn't know *that* when he included both equations in his book.

[DetlefK]

12. One does not need to dumb it down to discuss it.

He could have said: "Hey look: Electricity has a charge but magentism hasn't! And you can create a magnetic field via an electric current! And if a magnetic field changes over time, it creates a voltage that induces a current which induces another magnetic field that tries to balance that change out!"

[Jim__]

13. Stewart's point was that Maxwell's simplified equation resolves to the wave equation.

He used the information required to clearly make his point.

[struggle4progress]

9. Perhaps Napier's logarithms did not actually satisfy equation #2 but something rather like

log(xy) = log(x) + log(y) - 161180950

[Jim__]

14. I'm not sure what point they're trying to make.

But, I've checked a few of the logs in Napier's book, The Wonderful Canon of Logarithms, and all the logs I checked satisfy:

log(xy) = log(x) + log(y).

That's really what Napier was after, so it would be surprising if it didn't work.

That article may be making a somewhat different point, but looking at Napier's book, his logs certainly appear to work in the expected way.

[struggle4progress]

15. Read the translator's preface at your link: the table of so-called "hyperbolic logarithms"

at the end of the book is clearly a table of what we now call "natural logarithms" -- which do obey log(xy) = log(x) + log(y) -- but, as the translator notes, that table was not actually in Napier's original book: in fact, those logarithms were invented by others, while the table Napier himself published is the one with the sine and logarithm headings

Napier's table, unlike a table of "hyperbolic logarithms" (that is, "natural logarithms&quot , and unlike the even more convenient table of "Briggsian logarithms" (that is, "common logarithms&quot , has the unfortunate features that log(10 000 000) = 0 -- rather than the more convenient log(1) = 0 -- and that log(x) decreases with increasing x, as you can see by inspecting Table I "Napier's Logarithms of Sines," which is the table Napier himself published

[Jim__]

16. OK, thanks. I this thought that this was his original book.

But, Stewart's book never attributes that equation to Napier.

[struggle4progress]

17. Part of it seems to be his original book, in English translation

[struggle4progress]

10. #3 is anachronistic: the limit concept is nineteenth century

Moreover, the notation df/dx is due, not to Newton, but to Leibniz, who appears to have developed calculus independently of Newton: this was a bitter priority dispute at the time

What Newton actually wrote, in his definition of "fluxions" (which have become our modern derivatives), bears little resemblance to #3

[struggle4progress]

11. Regarding #5, Euler did indeed introduce the symbol i for the square root of -1,

and he afterwards did interesting things with imaginary numbers, but complex numbers had been discovered rather earlier, and had been studied in connection with the renaissance solution of the cubic equation, and a many useful calculational rules developed prior to Euler; nor was the story over with Euler, since a full understanding of the appropriate algebraic rules requires later notions, such as that of the Riemann surface