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Mathematical Equations That Changed the World
- namenotrequired 13y agoLarge image: https://pbs.twimg.com/media/BiTPlBKCMAARAAw.png:large https://pbs.twimg.com/media/BiTPlBKCMAARAAw.png:large
- pge 13y agoWhat about e^(i*pi) = -1?
- liquidise 13y agoWhile this relationship is profound, i'm not sure it has led to any industry or academic shifts in understanding. Every equation on this list has single handedly expanded a respective field of study by its discovery.
- Jach 13y agoCovered by Fourier Transforms. The equations for Nash Equilibrium and Fermat's Little Theorem are two I would have liked to see.
- nextos 13y agoYes, I think Nash equilibrium will be way more influential in the long-term than Black-Scholes.
- aswanson 13y agoNeither one of them should be on there. Both rest upon the false assumption of human rationality. They are delusions masquerading as mathematical truth.
- consz 13y agoBlack Scholes doesn't assume rational market participants.
- justincormack 13y agoIt does make other bogus assumptions though. Normal distributions, risk free interest rates,...
- wreegab 13y agoI thought the problem with Black-Scholes is that it didn't factor in the use of Black-Scholes by participants.
- igravious 13y agoThat's an interesting perspective. And it's a perspective that would be familiar to any student of cybernetics and social systems theory: http://en.wikipedia.org/wiki/Second-order_cybernetics http://en.wikipedia.org/wiki/Second-order_cybernetics so-called second order cybernetics. Fascinating stuff I think.
- noobermin 13y agoOne could argue that with i^2=-1 and the taylor expansion of sine and cosine and the exponential, one get's that.
- cschmidt 13y agoA 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 13y agoI'd replace it with S = k log(Omega), which links thermodynamics to quantum mechanics.
- deleted 13y ago[deleted]
- ColinWright 13y agoSee 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 13y ago> 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.
- pmtarantino 13y agoAs is presented in the image, teh Second Law of Therm is an inequation.
- spitfire 13y agoWhere's the simplex algorithm? Optimization has had absolutely astounding effects on the modern world, but it's missing there.
- dalke 13y agoThese are equations, not algorithms.
- dmunoz 13y agoInterestingly, 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 13y agoTo 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.
- iandanforth 13y agoPoorly documented functions which use single character variables. Maths notation is great for brevity but fails utterly tests for readability and ease of comprehension.
- mewwts 13y agoI'm pretty sure you're not supposed to comprehense it just by looking at it once. Maths(and physics) is not programming, and to be honest all of those ``functions'' are pretty well documented, both in books and articles online.
- Jugurtha 13y agoYou'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".
- deleted 13y ago[deleted]
- alister 13y agoThis list is the basis of a book by the same author: http://www.amazon.com/In-Pursuit-Unknown-Equations-Changed/dp/0465085989/ http://www.amazon.com/In-Pursuit-Unknown-Equations-Changed/d... 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?
- justincormack 13y agoEasy way to tell is if it is available from the author's website.
- sebastianavina 13y agodo you have a link?
- justincormack 13y agoYou do realise it is almost certainly unauthorised?
- greenyoda 13y agoIt'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 13y agoWorthless to you at this moment. Number 3 is differential calculus. That's a big one.
- a_olt 13y agoNo. 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 13y agoYep, 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 13y agoI 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 13y agoUnderstanding 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-introduction http://www.slideshare.net/anthaceorote/chaos-theory-an-intro... * https://www.csuohio.edu/sciences/dept/physics/physicsweb/kaufman/yurkon/chaos.html https://www.csuohio.edu/sciences/dept/physics/physicsweb/kau... * [PDF] http://math.arizona.edu/~shankar/efa/efa4.pdf http://math.arizona.edu/~shankar/efa/efa4.pdf And there's plenty more!
- alexjab 13y agowell #3 has got a typo in the formula, and #5's title is kind of misleading...
- albertyw 13y agoFourier Transform equation is wrong. Integral from infinity to infinity? That doesn't make sense. It should be negative infinity.
- daeken 13y agoInteresting as this is, #13 is not "Relativity", it's the mass-energy equivalence.
- moultano 13y agoIf 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.
- Jugurtha 13y agoYeah, and people think Einstein invented the "Atomic Bomb". You see it in the media, movies, popular culture, etc. Sometimes you have to talk the talk to get your message across.. And it's delta-m (the 'mass default', pardon my English).
- oskarth 13y agoInteresting. 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 13y agoYeah 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!
- deleted 13y ago[deleted]
- justincormack 13y agoLTCM was not the only outcome of it. Pretty much of all of modern finance is.
- alienfluid 13y agoThese are equations that changed the world, for better or for worse. Black-Scholes opened up a whole world of asset pricing that much of the financial system today is based on. It can be argued that it did indeed have a deep effect on the state of the world through developments in modern finance.
- xmonkee 13y agoLTCM aren't the only ones to ever use Black-Scholes. It's used millions of times every day around the world as of today. Sure, the equation isn't very sophisticated, but it's the standard model for volatility based product pricing around the world. Volatility surfaces are sometimes back calculated from market prices using the Black-Scholes equation and then plugged into various more advanced models. But the vast majority of all derivative trades (at least in the equity and FX space) are still purely based on Black-Scholes.
- dredmorbius 13y ago
- dmunoz 13y agoFor 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 13y ago6 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.E2.80.93Scholes_formula http://en.wikipedia.org/wiki/Black_scholes_formula#Black.E2....
- noobermin 13y agoAs 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.
- javajosh 13y agoIt'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.
- NAFV_P 13y agoWhere on Earth is integral calculus?
- tanvach 13y agoBlack-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.
- Xcelerate 13y agoIn 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.