
Mathematical Equations That Changed the World - ibsathish
https://twitter.com/paulcoxon/status/442706898370834432/photo/1
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oskarth
Interesting. But why on earth is Black-Scholes equation on that list? It's not
like Long-Term Capital Management took over the world with it. It's a fragile
model and does not deserve to be on the same list as these beautiful and
useful ideas.

~~~
auvi
Yeah I was also a bit surprised. LTCM's "Long-Term" was ~ 4 years (1994-1998)
with a total loss around $4.6 Billion. That time seems to be very small
compared to the ~ 2500 years of the list. And $4.6 Billion? It's not even one
third of WhatsApp!

~~~
justincormack
LTCM was not the only outcome of it. Pretty much of all of modern finance is.

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greenyoda
It's pretty worthless to just present a picture of these equations without any
explanation of what their significance is or how they "changed the world". The
image format is particularly bad since you can't even copy/paste the text into
a search engine if you want more information. Twitter isn't really a good
medium for presenting mathematical and scientific concepts.

~~~
cconroy
Worthless to you at this moment. Number 3 is differential calculus. That's a
big one.

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namenotrequired
Large image:
[https://pbs.twimg.com/media/BiTPlBKCMAARAAw.png:large](https://pbs.twimg.com/media/BiTPlBKCMAARAAw.png:large)

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dmunoz
For a bit of perspective about these equations:

I only have a bachelor of science degree with a major in computer science.
Mostly through my interest in physics and mathematics, and hence the electives
I took, I have a somewhat intimate familiarity with all of 1-5, 9, 13, and 14.
I have at least basic knowledge about 7, 11, and 12. I have no idea, really,
about 6 and 15-17. I'm a bit embarrassed about #15, given what I do. I have
heard good things about Shannon's original paper, so I should give it a read.
The ones I never listed fall into a half-half area, where I am aware of their
meaning, but not very familiar with them.

At the university I obtained my degree from, just as I was graduating they
were removing the requirement for computer science majors to take 6 credits in
third or fourth year mathematics courses. All that is required now is first
year calculus courses, with linear algebra and statistic in second year. The
credits are moved to electives, so interested students can still take
mathematics courses, but I feel like few of them will.

It was posted elsewhere in these comments that a proper treatment of these
equations is found in Ian Stewart's book "In Pursuit of the Unknown: 17
Equations That Changed the World". I had heard of this previously, and now
look forward to giving it a read.

Edit: To be clear about something, plenty of my knowledge of these equations
came from my choice of electives in second and third year physics courses. So,
my moaning about the removal of required mathematics credits isn't precisely
relevant.

It was one of the few major disappointments of my time at university that I
didn't get to take the proper course in electrodynamics (equations in 11). I
have always meant to obtain Griffiths' text on the subject and give it a fair
shake, and still plan to do so. Entertainingly, I looked it up quickly on
Amazon and see they released a fourth edition in 2012, which has mixed reviews
and seems to suffer from the usual publisher hijinx.

~~~
raverbashing
6 is Vertices - Edges + Faces = 2

For example, a cube: 6 faces, 8 vertices, 12 edges:
[http://en.wikipedia.org/wiki/Euler_characteristic](http://en.wikipedia.org/wiki/Euler_characteristic)

15 is this:
[http://en.wikipedia.org/wiki/Information_entropy#Definition](http://en.wikipedia.org/wiki/Information_entropy#Definition)

16 is kind of a cop out to call it "Chaos", it's one specific case, this:
[http://en.wikipedia.org/wiki/Logistic_map](http://en.wikipedia.org/wiki/Logistic_map)

17 is in Finance:
[http://en.wikipedia.org/wiki/Black_scholes_formula#Black.E2....](http://en.wikipedia.org/wiki/Black_scholes_formula#Black.E2.80.93Scholes_formula)

~~~
dmunoz
Yes, I'm capable of looking them up. I was only pointing out which equations
were hit upon during my education.

Actually, one thing your post made me realize is that I did touch upon
equation 6 in a fourth year algorithms class. I didn't know it as related to
polyhedra, as we used it in relation to vertices, edges, and faces in
complexity analysis of geometric algorithms.

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alister
This list is the basis of a book by the same author:

[http://www.amazon.com/In-Pursuit-Unknown-Equations-
Changed/d...](http://www.amazon.com/In-Pursuit-Unknown-Equations-
Changed/dp/0465085989/)

It's extremely easy to find a free PDF download of the book. I'm assuming the
free PDF has been authorized, how does one even tell these days short of
contacting the author?

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justincormack
Easy way to tell is if it is available from the author's website.

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sebastianavina
do you have a link?

~~~
justincormack
You do realise it is almost certainly unauthorised?

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cschmidt
A nice list, although I'd quibble a bit about dS >= 0 being on there. That
entropy increases is important, but the equation itself doesn't really have a
mathematical relation like the others.

~~~
alokv28
I'd replace it with S = k log(Omega), which links thermodynamics to quantum
mechanics.

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a_olt
No. 16, 'Chaos Theory' is actually called the 'Logistic Equation' and it is
used in biology to model populations. It does exhibit transition to a chaotic
regime for certain values of k, but it's improper to refer to it as 'Chaos
Theory equation'.

~~~
kartikkumar
Yep, if anything the Restricted 3-Body Problem (R3BP) should be considered the
"chaos theory equation", since it was Poincaré study of chaotic solutions in
the R3BP that led to the discovery of sensitivity to initial conditions.
Smale's horseshoe map would be another apt equation, since it succinctly
describes the dynamics of chaotic systems, through the twisting and warping of
the map. The Lorenz attractor is another important example that highlights the
concept of deterministic chaos.

~~~
ganeumann
I don't quite get how chaos theory changed the world. All of the other
equations I get (although whether Shannon's equation changed the world or
merely described the change is probably arguable.)

How did chaos theory change the world?

~~~
kartikkumar
Understanding deterministic chaos has been the cornerstone of a wide range of
fields, including physics, medicine, economics, and business. There are a
wealth of everyday applications. Control systems in the real world have to
deal with the underlying structure of the dynamics that govern how such
systems naturally behave in the feedback loop.

There are a few different resources you can find that list practical
applications of chaos theory. Here are a few that I found that I think you
will find interesting:

* [http://www.slideshare.net/anthaceorote/chaos-theory-an-intro...](http://www.slideshare.net/anthaceorote/chaos-theory-an-introduction)

* [https://www.csuohio.edu/sciences/dept/physics/physicsweb/kau...](https://www.csuohio.edu/sciences/dept/physics/physicsweb/kaufman/yurkon/chaos.html)

* [PDF] [http://math.arizona.edu/~shankar/efa/efa4.pdf](http://math.arizona.edu/~shankar/efa/efa4.pdf)

And there's plenty more!

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daeken
Interesting as this is, #13 is not "Relativity", it's the mass-energy
equivalence.

~~~
moultano
If I had to pick the single equation for relativity it would be the definition
if interval. You can derive the rest from that, and it is IMHO the most
beautiful expression of it.

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noobermin
As a grad student in physics, I'd vote for the inclusion of the Dirac equation
or Klein-Gordon (can't put the whole standard model in there) and may be the
Einstein Field Equations.

Other than that, I agree with most of the list. I haven't heard good things
about Black and Scholes, though.

EDIT: Oh, and I thought of another. No doubt: [X,P] = i h/2pi Definitely more
important than Schrodinger.

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ColinWright
See also:
[http://www.youtube.com/watch?v=KGpb3_XkEvg](http://www.youtube.com/watch?v=KGpb3_XkEvg)

Submitted here:
[https://news.ycombinator.com/item?id=7291571](https://news.ycombinator.com/item?id=7291571)
\- although no discussion.

~~~
dmunoz
> although no discussion

No surprise about that. I imagine a large portion of us completely ignore
posts directly to youtube with no context outside of the title. Personally, I
also wouldn't have shared around a video consisting only of floating images
and text with technoish music playing. Seems like that is the youtube channels
niche, though.

Interestingly, the formula for the Fourier transformation is wrong in both of
these posts. In the image, the integration is from infinity to infinity, and
in the video the limits of integration are negative infinity to negative
infinity.

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javajosh
It's really, really strange to me that F=ma is not on the list. Also very
important, but missing: Hooks law, Ohms Law, the Ideal Gas Law. The binomial
theorem and Taylor series are just as important as Fourier series, if not more
so.

A very strange, almost arbitrary list. Thumbs down.

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pge
What about e^(i*pi) = -1?

~~~
Jach
Covered by Fourier Transforms.

The equations for Nash Equilibrium and Fermat's Little Theorem are two I would
have liked to see.

~~~
nextos
Yes, I think Nash equilibrium will be way more influential in the long-term
than Black-Scholes.

~~~
aswanson
Neither one of them should be on there. Both rest upon the false assumption of
human rationality. They are delusions masquerading as mathematical truth.

~~~
consz
Black Scholes doesn't assume rational market participants.

~~~
justincormack
It does make other bogus assumptions though. Normal distributions, risk free
interest rates,...

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albertyw
Fourier Transform equation is wrong. Integral from infinity to infinity? That
doesn't make sense. It should be negative infinity.

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spitfire
Where's the simplex algorithm? Optimization has had absolutely astounding
effects on the modern world, but it's missing there.

~~~
dalke
These are equations, not algorithms.

~~~
dmunoz
Interestingly, around the same time the book these equations were originally
collected in (as pointed out in another comment, this is Ian Stewart's In
Pursuit of the Unknown: 17 Equations That Changed the World), the book Nine
Algorithms That Changed the Future: The Ingenious Ideas That Drive Today's
Computers also came out. They were actually published ~5 months apart, but I
remember them being close together on Amazon recommendations, list of other
books people viewed, etc. at the time.

I haven't read that one either. Looking at the index quickly, it doesn't look
like Simplex is in there.

~~~
dalke
To be fair, simplex doesn't really "drive today's computers", at least nowhere
near like it did the computers of the 1950s.

This list of important algorithms includes Simplex -
[http://www.koutschan.de/misc/algorithms.php](http://www.koutschan.de/misc/algorithms.php)
. Others do as well. And some do not.

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tanvach
Black-Scholes' is a big deal in economics and finance. Their innovations were
risk-neutral pricing (the r terms in the equation) and replicating portfolio
argument. These completely changed how to price all securities you see, not
just options. The idea was so radical their paper was unable to be published
for years.

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Xcelerate
In my opinion, the Schrodinger equation is by far the most important. It
provides an accurate prediction of almost all earth-scale (and smaller)
phenomena except gravity. Although I suppose some of the heavier elements
require KG or the Dirac equation to account for relativistic effects.

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iandanforth
Poorly documented functions which use single character variables. Maths
notation is great for brevity but fails utterly tests for readability and ease
of comprehension.

~~~
Jugurtha
You're trolling, right ? Are you kidding ? "Poorly documented" ? I use most of
them on a regular basis. I haven't had first hand exposure with only
Black&Scholes': But I looked the thing up when I was a freshman as I was
interested in stock prices, and was interested in Louis Bachelier, Brownian
motion. The rest is well documented through the whole Engineering curriculum.
There are a couple I haven't used in a while (Schrödinger's and relativity
(hint: Who is Poincaré)).

These "single character variables" are known for whom they matter. You can't
have brevity and delimiter-separated names. Equations taking a whole line (or
more), good luck with that.

"Maths notation is great for brevity but fails utterly tests for readability
and ease of comprehension".. Okay, clearly trolling.

Next thing you know, IEEE will hire Will.i.am or Apple fanboys as consultants
to make things "beautiful".

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NAFV_P
Where on Earth is integral calculus?

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pmtarantino
As is presented in the image, teh Second Law of Therm is an inequation.

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alexjab
well #3 has got a typo in the formula, and #5's title is kind of misleading...

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frede
#9 as well, the lower limit should be minus infinity.

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tvst
And #7 is missing a minus sign in the exponent. Otherwise the whole thing
diverges.

~~~
noobermin
I actually didn't catch that! That's hilarious.

