What is the strangest math that turned out to be useful?
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Complex numbers. Also known as imaginary numbers. The imaginary number
iis the solution to√-1. And it is really used in quantum mechanics and I think general relativity as well.A complex number is just two real numbers stitched together. It's used in many areas, such as the Fourier transform which is common in computer science is often represented with complex numbers because it deals with waves and waves are two-dimensional, and so rather than needing two different equations you can represent it with a single equation where the two-dimensional behavior occurs on the complex-plane.
In principle you can always just split a complex number into two real numbers and carry on the calculation that way. In fact, if we couldn't, then no one would use complex numbers, because computers can't process imaginary numbers directly. Every computer program that deals with complex numbers, behind the scenes, is decomposing it into two real-valued floating point numbers.
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DES is symmetric key cryptography. It doesn't rely on the difficulty of factorizing large semi-primes. It did use a 56-bit key, though.
Public key cryptography (DSA, RSA, Elliptic Curve) does rely on these things and yes it's a 4096-bit key these days (up from 1024 in the older days).
RSA mostly uses 4096 bit keys nowadays. DSA is no longer used (or shouldn't be lol). Ed25519 uses 256 bit keys.
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Donuts were basis of the math that would enable a planned economy to be more efficient than a market economy (which is a very hard linear algebra problem).
Basically using that, your smart phone is powerful enough to run a planned economy with 30 million unique products and services. An average desktop computer would be powerful enough to run a planned economy with 400 million unique products and services.
Odd that knowledge about it has been actively suppressed since it was discovered in the 1970s but actively used mega-corporations ever since…
It's funny that you're saying this is "actively suppressed" while not naming this field or providing links for further readings.
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There have been a number of Scientific discoveries that seemed to be purely scientific curiosities that later turned out to be incredibly useful. Hertz famously commented about the discovery of radio waves: “I do not think that the wireless waves I have discovered will have any practical application.”
Are there examples like this in math as well? What is the most interesting "pure math" discovery that proved to be useful in solving a real-world problem?
Imaginary numbers probably, they're useful for a lot of stuff in math and even physics (I've heard turbulent flow calculations can use them?) but they seem useless at first
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This won't make any sense to any of you right now, but: E = md^3^
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I am pretty sure that the first thing you mentioned (multiplying being easy and factoring being hard) is the basis of public key cryptography which is how HTTPS works.
Somewhat related fun fact: One of the most concrete applications for quantum computers so far is breaking some encryption algorithms.
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A complex number is just two real numbers stitched together. It's used in many areas, such as the Fourier transform which is common in computer science is often represented with complex numbers because it deals with waves and waves are two-dimensional, and so rather than needing two different equations you can represent it with a single equation where the two-dimensional behavior occurs on the complex-plane.
In principle you can always just split a complex number into two real numbers and carry on the calculation that way. In fact, if we couldn't, then no one would use complex numbers, because computers can't process imaginary numbers directly. Every computer program that deals with complex numbers, behind the scenes, is decomposing it into two real-valued floating point numbers.
I don't think this is really an accurate way of thinking about them. Yes, they can be mapped to a 2d plane, so you can represent them with their two real-numbered coordinates along the real and imaginary axes, but certain operations with them (eg. multiplication) can be done easily with complex numbers but are not obvious how to carry out with just grid points. (3,4) * (5,6) isn't well-defined, but (3+4i) * (5+6i) is.
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How do you define "pure math discovery"?
wrote on last edited by [email protected]A math discovery unmotivated by research in other fields; just discovering math to see if it works out
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Quake, not Doom. Doom didn't use true 3D rendering and had almost no dynamic lighting.
Oops. I thought that weird approximated constant was somewhere in the doom sources... Thanks I guess for correcting me.
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It’s crazy how engaging and well done Veritasium videos are and they’re just free to watch on YouTube.
And on spotify nowadays
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There have been a number of Scientific discoveries that seemed to be purely scientific curiosities that later turned out to be incredibly useful. Hertz famously commented about the discovery of radio waves: “I do not think that the wireless waves I have discovered will have any practical application.”
Are there examples like this in math as well? What is the most interesting "pure math" discovery that proved to be useful in solving a real-world problem?
Integration.
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It's imaginary numbers. Full stop. No debate about it. The idea of them is so wild that they were literally named imaginary numbers to demonstrate how silly they were, and yet they can be used to describe real things in nature.
I'm studying EE in university, and have been surprised by just how much imaginary numbers are used
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Oops. I thought that weird approximated constant was somewhere in the doom sources... Thanks I guess for correcting me.
Here's some math-related Doom content for you: John Romero accidentally coded in the wrong digit of pi in the 10th position, and this guy explores how the game rendering changes when pi is increasingly wrong
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wrote on last edited by [email protected]
That's a perfect example of a typical interaction between a Technology Management Consultant and somebody from a STEM area.
Techies with an Engineering background who are in Tech and Tech-adjacent companies are often in the receiving end of similar techno-bollocks which makes no sense from such "Technology" Management Consultants, but it's seldom quite as public as this one.
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I'm studying EE in university, and have been surprised by just how much imaginary numbers are used
I was gonna ask how imaginary numbers are often used but then you reminded me of EE applications and that's totally true.
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It's funny that you're saying this is "actively suppressed" while not naming this field or providing links for further readings.
Donut mathematics is the name of the field; I literally named it.
The writings on it are dense and only available in Russian and Mandarin Chinese. Further I provided the name of an author on the subject.What would you call the purposeful prevention of English/French/German/etc translations of the material?
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As far as I know, matrices were a "pure math" thing when they were first discovered and seemed pretty useless. Then physicists discovered them and used them for all sorts of shit and now they're one of the most important tools in in science, engineering and programming.
Huge in 3d graphics and AI.
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60 was chosen by the Ancient Sumerians specifically because of its divisibility by 2, 3, 4, and 5. Today, 60 is considered a superior highly composite number but that bit of theory wouldn’t have been as important to the Sumerians and Babylonians as the simple ability to divide 60 by many commonly used factors (2, 3, 4, 5, 6, 10, 12, 15) without any remainders or fractions to worry about.
12 is the most based number in that respect IMO.
But then...hey, we use that for hours!
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Shoutout to Satyendra Nath Bose who helped pioneer relativity as a theoretical physicist because he didn't want to study something useful that would benefit the British.
Same thing with early studies on prime numbers
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Donut mathematics is the name of the field; I literally named it.
The writings on it are dense and only available in Russian and Mandarin Chinese. Further I provided the name of an author on the subject.What would you call the purposeful prevention of English/French/German/etc translations of the material?
The phrase "donut mathematics" was not in your earlier comment. You literally did not name it.
