What is the strangest math that turned out to be useful?
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I'd like to read up on this if you have sources
Look up Wassily Wassilyevich Leontief
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That's pretty interesting. Do you happen to have any introductory material to that topic?
I mean, it might even have applications outside of running a techno-communist nation state. For example, for designing economic simulation game mechanics.
Well Wassily Wassilyevich Leontief won a Nobel prize in economics for his work on this subject that might help you get started
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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?
Non-linear equations have entered the chat.
Chaos and non-linear dynamics were treated as a toy or curiosity for a pretty long time, probably in no small part due to the complexity involved. It's almost certainly no accident that the first serious explorations of it after Poincare happen after the advent of computers.
So, one place where non-linear dynamics ended up having applications was in medicine. As I recall it from James Gleick's book Chaos, inspired by recent discussion of Chaotic behavior in non-linear systems, medical doctors came up with the idea of electrical defibrillation- a way to reset the heart to a ground state and silence chaotic activity in lethal dysrhythmias that prevented the heart from functioning correctly.
Fractals also inspired some file compression algorithms, as I recall, and they also provide a useful means of estimating the perimeters of irregular shapes.
Also, there's always work being done on turbulence, especially in the field of nuclear fusion as plasma turbulence seems to have a non-trivial impact on how efficiently a reactor can fuse plasma.
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Sure, but 1 is a real number.
Yes, and 1 is also a complex number.
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Non-linear equations have entered the chat.
Chaos and non-linear dynamics were treated as a toy or curiosity for a pretty long time, probably in no small part due to the complexity involved. It's almost certainly no accident that the first serious explorations of it after Poincare happen after the advent of computers.
So, one place where non-linear dynamics ended up having applications was in medicine. As I recall it from James Gleick's book Chaos, inspired by recent discussion of Chaotic behavior in non-linear systems, medical doctors came up with the idea of electrical defibrillation- a way to reset the heart to a ground state and silence chaotic activity in lethal dysrhythmias that prevented the heart from functioning correctly.
Fractals also inspired some file compression algorithms, as I recall, and they also provide a useful means of estimating the perimeters of irregular shapes.
Also, there's always work being done on turbulence, especially in the field of nuclear fusion as plasma turbulence seems to have a non-trivial impact on how efficiently a reactor can fuse plasma.
A good friend of mine from high school got his physics PhD at University of Texas and went on to work in the high energy plasma physics lab there with the Texas Petawatt laser, and a lot of the experiments it was used for involved plasma turbulence and determining what path energetic particles would take in a hypothetical fusion reactor.
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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?
The math fun fact I remember best from college is that Charles Boole invented Boolean algebra for his doctoral thesis and his goal was to create a branch of mathematics that was useless. For those not familiar with boolean algebra it works by using logic gates with 1s and 0s to determine a final 1 or 0 state and is subsequently the basis for all modern digital computing
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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?
Not math but the discovery of Thermus aquaticus was seemingly useless but later had profound applications in medicine. There's a good Veritasium video on it
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Tell him I would like to subscribe to his blog
The following aren't necessarily answers to your question, but he also mentioned these, and they are way too funny to not share:
The Hairy Ball theorem
Cox Ring
Tits Alternative
Wiener Measure
The Cox-Zucker machine (although this was in the 70s and it's rumored that Cox did most of the work and chose his partner ONLY for the name.
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A good friend of mine from high school got his physics PhD at University of Texas and went on to work in the high energy plasma physics lab there with the Texas Petawatt laser, and a lot of the experiments it was used for involved plasma turbulence and determining what path energetic particles would take in a hypothetical fusion reactor.
Be honest, how many unofficial experiments were there?
You ever just start lasering shit for kicks?
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prime number factorization is the basis of assymetric cryptography. basically, if I start with two large prime numbers (DES was 56bit prime numbers iirc), and multiply them, then the only known solution to find the original prime numbers is guess-and-check. modern keys use 4096-bit keys, and there are more prime numbers in that space than there are particles in the universe. using known computation methods, there is no way to find these keys before the heat death of the universe.
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).
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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?
A brain teaser about visiting all islands connected by bridges without crossing the same bridge twice is now the basis of all internet routing. (Graph theory)
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Does this count? Because it really is wtf.
Doom absolutely counts!
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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?
The first few people to discover natural logarithms in the 1600s probably felt like they unlocked some weird pattern of the universe that repeats in a bunch of different naturally occurring settings for exponential growth or decay
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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?
If I recall correctly, one mathematician in the 1800s solved a very difficult line integral, and the first application of it was in early computer speech synthesis.
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The math fun fact I remember best from college is that Charles Boole invented Boolean algebra for his doctoral thesis and his goal was to create a branch of mathematics that was useless. For those not familiar with boolean algebra it works by using logic gates with 1s and 0s to determine a final 1 or 0 state and is subsequently the basis for all modern digital computing
Was he trying to dunk on his professors?
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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.It's used extensively in electronic circuit design (where it's called "j", as "i' already meant electronic current).
Also signal processing has i or j all over it.
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I wonder if complex numbers predate the discovery of electromagnetism
Yes, mathematicians first encountered equations which could only be solved with complex numbers in the 16th century.
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Yes, and 1 is also a complex number.
Of course, but 1 is the loneliest number.
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This talk by Freya Holmer on Quarternions is awesome and worth anybody’s time that like computer graphics, computer science, or just math.
That was a cool watch. Thanks.
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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).
thank you
