6 ms·

It would help if the article included at least one real world application in layman's terms.

mFixman 6y ago
Because you are finding the secrets of the Universe? Because math is fun? Not all work has to have a real world application ($$$). It would help if the you included at least one real world application of writing your comment.
- boomboomsubban 6y ago
  Even when math does have profound real world applications they aren't always immediately apparent. Think of how many millennia work was done on primes before they became a huge part of cryptography, though they did have some other uses along the way.
- mjcohen 6y ago
  A real world application is getting someone to respond with a real world application that would help you make money.
GordonS 6y ago
A bit of an aside, but this was always my biggest bugbear when learning maths way back when I was in school - we were never given any practical reasons of why any of it was useful. Even if you explicitly asked the maths teacher "what's it for", they could never give a useful response - it often seemed like they'd never considered this themselves. Around 13-14 years old, I got interested in building mods for Quake. When I decided to create a bot, I finally understood at least how trigonometry was useful. I won the annual mathematics prize at school that year, and I'm sure it was only because real-world use had gotten me interested.
- concreteblock 6y ago
  Big reason is that many high school math teachers don't really understand math well enough for the job.
  - concreteblock 6y ago
    To clarify, since I can't edit: This is coming from my experience as someone who has taught math to teachers getting their master's degree. It sounds mean but I wanted to emphasize that the state of early math education is not just due to poorly designed curriculum, but because there is little incentive for mathematically competent people to teach children. (Imo, of course).
    - chadcmulligan 6y ago
      The other problem in my experience (as a parent and math nerd) is that the whole math teaching area is full of people who don't know math, so coming in and having a math person teach math means you have a huge number of arguments you'd have to have. The only way I know of is to just get after school tuition and ignore the school. This is difficult though - why do I have to do maths after school? no one else does.
- Akronymus 6y ago
  For me, learning a subject in school is much harder than learning it "in the real world" precisely because I often lack the connection to it being practical or it otherwise just being taught as what instead of why. For me the connection of why it is like that makes me actually grok it, rather than forgetting it after 5 minutes.
- boomboomsubban 6y ago
  This sentiment is incredibly common, and it's strange that you then get to calculus where the real world applications are such an integral part of the subject.
- bordercases 6y ago
  There is not one way any piece of mathematics is useful, and we don't always know ahead of time what kind of mathematics is useful or not. That's why it's (a) important to know how mathematics can be built from concrete instances, like you did with your Quake Bot, and (b) that it takes a lot of practice with mathematics to know how mathematical modeling is generally done, so that you can see how incremental advances in higher mathematics might lead to breakthroughs in applied mathematics in the future. Otherwise mathematics fulfills an aesthetic sense for beauty and elegance in one's own thinking that most people's minds don't seem to support by default. There's nothing wrong with that, but it's just as valid an attitude to the subject as presuming everything should be motivated by applications at first. To those people who enjoy mathematics for its own sake, it's a form of play which might organize something important in the future, that you otherwise would have missed because you're too busy applying some other form of mathematics.
- elliekelly 6y ago
  This comment resonates with me so much. I remember learning how to program, as an adult, and having an epiphany about all those times my teachers wrote f(x) and then proceeded to write some hodgepodge of numbers and letters. No one had ever explained why I would ever need some function for x to spit out something else and so I was sort of lost from the very beginning when it came to any kind of high level math. Ditto for sets and pairs. Basically all of my math education was a complete waste until I learned a bit of computer programming and could play around with implementing the abstract concepts and relate those concepts to practical uses. Then suddenly it all made so much more sense!
- abdullahkhalids 6y ago
  As a teacher, I believe applications must be discussed - I am a physicist after all. But I remember my peers asking for applications from math teachers when we were in school, but I never saw them ask the same from art teachers. Somehow, everyone understood that drawing and coloring were just for pleasure and stroking our aesthetic sensibilities, and an application was not needed. But people rarely think of math the same way. Yet, it's all pattern recognition and creation.
  - sethhochberg 6y ago
    As a person who briefly pursued a degree in a traditional engineering discipline before finding my way back to the arts (music) and then eventually into a software career, I think the difference - at least for me - is that with the arts I've never gotten the impression that the fundamentals stop being interesting if they're still applied well. To phrase it another way: practicing scales can be boring. But playing a walking bassline is a whole lot more similar to scales than it is anything else, and one of the most fun things to do with an instrument is to jam with other people using the fundamentals you all share. I never felt the same way with math, because I never felt like math allowed me to put anything unique and of my own into the mix. Learning the same proof from a book that a million other kids taking geometry learned was much less interesting to me than transcribing a solo some musician played so that I could try to riff on the style they put into the world. Sure, yeah, there's rules in music theory too. You're expected to learn them, and get graded on them in tests if you study music academically. But I don't know of any famous mathematician who ever said something like the various Duke Ellington quotes around "if it sounds good, it IS good". In the art world, similar riffs on an existing idea are everything. In math, they're just... wrong. Or at least thats the understanding I had as a student which led me to only care about the parts of math that seemed to be directly applicable to me, or really intuitive.
    - willowfine 6y ago
      As a mathematician, I would claim that math at its best is exactly about riffing and jamming on shared fundamentals and adding your own insights. But it is often misunderstood what these fundamentals are: not the proofs or the formulas, but the elements of logical reasoning that make it possible to say with absolute certainty that given some conditions, some statement must be absolutely true. A riff on a proof in geometry isn't changing a few of the letters around to see if still works - it might instead be about changing the assumptions. In plane geometry, the angles of a triangle sum to 180 degrees. But what if we are not in the plane, but on the surface of a sphere, such as the earth? Does a triangle connecting the north pole to two points on the equator still have the sum 180 degrees? If not, can we prove something else about it? In the context of the original article, it might be something like "Can we use any parts of our proof about pentagons (5-cycles) for some other shapes? What about hexagons (6-cycles)? Or is there even any insight we can generalize so that it becomes a statement about cycles of any length?" Sadly, this is way too seldom the way math is taught. I didn't enjoy the endless calculations of long division in grade school, or the memorization of different tricks for solving trigonometric integrals in college, either. For a famous mathematician quote, how about Paul Erdös concept of "a proof from the Book" - said about math proofs that are so perfect and clear that they must be in God's celestial collection. Often, there is more than one way to prove something true - checking every example by brute force would be the most extreme - but sometimes you can discover an elegant argument that just convinces everyone who reads it that it simply must be true. That could also be thought of as riffing on a proof: Ok, you convinced me that this is true, after many boring pages of calculations - can I find a simpler way to convince myself of the same thing, and improve both our understandings?" Quanta magazine had a nice article about this as well: https://www.quantamagazine.org/gunter-ziegler-and-martin-aigner-seek-gods-perfect-math-proofs-20180319/ https://www.quantamagazine.org/gunter-ziegler-and-martin-aig...
_rpd 6y ago
This finding expands our knowledge of graphs. The classic application of graphs is logistics, but there are many, many more ... https://en.wikipedia.org/wiki/Graph_theory#Applications https://en.wikipedia.org/wiki/Graph_theory#Applications
klyrs 6y ago
I just did a search for "real-world applications of Ramsey theory" and this was the closest I got. Sorry. http://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseykings.pdf http://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseykings.pdf
einpoklum 6y ago
A research grant application maybe? :-P

Because you are finding the secrets of the Universe? Because math is fun? Not all work has to have a real world application ($$$). It would help if the you included at least one real world application of writing your comment.

boomboomsubban 6y ago
Even when math does have profound real world applications they aren't always immediately apparent. Think of how many millennia work was done on primes before they became a huge part of cryptography, though they did have some other uses along the way.
mjcohen 6y ago
A real world application is getting someone to respond with a real world application that would help you make money.

GordonS 6y ago

A bit of an aside, but this was always my biggest bugbear when learning maths way back when I was in school - we were never given any practical reasons of why any of it was useful. Even if you explicitly asked the maths teacher "what's it for", they could never give a useful response - it often seemed like they'd never considered this themselves. Around 13-14 years old, I got interested in building mods for Quake. When I decided to create a bot, I finally understood at least how trigonometry was useful. I won the annual mathematics prize at school that year, and I'm sure it was only because real-world use had gotten me interested.

concreteblock 6y ago
Big reason is that many high school math teachers don't really understand math well enough for the job.
- concreteblock 6y ago
  To clarify, since I can't edit: This is coming from my experience as someone who has taught math to teachers getting their master's degree. It sounds mean but I wanted to emphasize that the state of early math education is not just due to poorly designed curriculum, but because there is little incentive for mathematically competent people to teach children. (Imo, of course).
  - chadcmulligan 6y ago
    The other problem in my experience (as a parent and math nerd) is that the whole math teaching area is full of people who don't know math, so coming in and having a math person teach math means you have a huge number of arguments you'd have to have. The only way I know of is to just get after school tuition and ignore the school. This is difficult though - why do I have to do maths after school? no one else does.
Akronymus 6y ago
For me, learning a subject in school is much harder than learning it "in the real world" precisely because I often lack the connection to it being practical or it otherwise just being taught as what instead of why. For me the connection of why it is like that makes me actually grok it, rather than forgetting it after 5 minutes.
boomboomsubban 6y ago
This sentiment is incredibly common, and it's strange that you then get to calculus where the real world applications are such an integral part of the subject.
bordercases 6y ago
There is not one way any piece of mathematics is useful, and we don't always know ahead of time what kind of mathematics is useful or not. That's why it's (a) important to know how mathematics can be built from concrete instances, like you did with your Quake Bot, and (b) that it takes a lot of practice with mathematics to know how mathematical modeling is generally done, so that you can see how incremental advances in higher mathematics might lead to breakthroughs in applied mathematics in the future. Otherwise mathematics fulfills an aesthetic sense for beauty and elegance in one's own thinking that most people's minds don't seem to support by default. There's nothing wrong with that, but it's just as valid an attitude to the subject as presuming everything should be motivated by applications at first. To those people who enjoy mathematics for its own sake, it's a form of play which might organize something important in the future, that you otherwise would have missed because you're too busy applying some other form of mathematics.
elliekelly 6y ago
This comment resonates with me so much. I remember learning how to program, as an adult, and having an epiphany about all those times my teachers wrote f(x) and then proceeded to write some hodgepodge of numbers and letters. No one had ever explained why I would ever need some function for x to spit out something else and so I was sort of lost from the very beginning when it came to any kind of high level math. Ditto for sets and pairs. Basically all of my math education was a complete waste until I learned a bit of computer programming and could play around with implementing the abstract concepts and relate those concepts to practical uses. Then suddenly it all made so much more sense!
abdullahkhalids 6y ago
As a teacher, I believe applications must be discussed - I am a physicist after all. But I remember my peers asking for applications from math teachers when we were in school, but I never saw them ask the same from art teachers. Somehow, everyone understood that drawing and coloring were just for pleasure and stroking our aesthetic sensibilities, and an application was not needed. But people rarely think of math the same way. Yet, it's all pattern recognition and creation.
- sethhochberg 6y ago
  As a person who briefly pursued a degree in a traditional engineering discipline before finding my way back to the arts (music) and then eventually into a software career, I think the difference - at least for me - is that with the arts I've never gotten the impression that the fundamentals stop being interesting if they're still applied well. To phrase it another way: practicing scales can be boring. But playing a walking bassline is a whole lot more similar to scales than it is anything else, and one of the most fun things to do with an instrument is to jam with other people using the fundamentals you all share. I never felt the same way with math, because I never felt like math allowed me to put anything unique and of my own into the mix. Learning the same proof from a book that a million other kids taking geometry learned was much less interesting to me than transcribing a solo some musician played so that I could try to riff on the style they put into the world. Sure, yeah, there's rules in music theory too. You're expected to learn them, and get graded on them in tests if you study music academically. But I don't know of any famous mathematician who ever said something like the various Duke Ellington quotes around "if it sounds good, it IS good". In the art world, similar riffs on an existing idea are everything. In math, they're just... wrong. Or at least thats the understanding I had as a student which led me to only care about the parts of math that seemed to be directly applicable to me, or really intuitive.
  - willowfine 6y ago
    As a mathematician, I would claim that math at its best is exactly about riffing and jamming on shared fundamentals and adding your own insights. But it is often misunderstood what these fundamentals are: not the proofs or the formulas, but the elements of logical reasoning that make it possible to say with absolute certainty that given some conditions, some statement must be absolutely true. A riff on a proof in geometry isn't changing a few of the letters around to see if still works - it might instead be about changing the assumptions. In plane geometry, the angles of a triangle sum to 180 degrees. But what if we are not in the plane, but on the surface of a sphere, such as the earth? Does a triangle connecting the north pole to two points on the equator still have the sum 180 degrees? If not, can we prove something else about it? In the context of the original article, it might be something like "Can we use any parts of our proof about pentagons (5-cycles) for some other shapes? What about hexagons (6-cycles)? Or is there even any insight we can generalize so that it becomes a statement about cycles of any length?" Sadly, this is way too seldom the way math is taught. I didn't enjoy the endless calculations of long division in grade school, or the memorization of different tricks for solving trigonometric integrals in college, either. For a famous mathematician quote, how about Paul Erdös concept of "a proof from the Book" - said about math proofs that are so perfect and clear that they must be in God's celestial collection. Often, there is more than one way to prove something true - checking every example by brute force would be the most extreme - but sometimes you can discover an elegant argument that just convinces everyone who reads it that it simply must be true. That could also be thought of as riffing on a proof: Ok, you convinced me that this is true, after many boring pages of calculations - can I find a simpler way to convince myself of the same thing, and improve both our understandings?" Quanta magazine had a nice article about this as well: https://www.quantamagazine.org/gunter-ziegler-and-martin-aigner-seek-gods-perfect-math-proofs-20180319/ https://www.quantamagazine.org/gunter-ziegler-and-martin-aig...

_rpd 6y ago

This finding expands our knowledge of graphs. The classic application of graphs is logistics, but there are many, many more ... https://en.wikipedia.org/wiki/Graph_theory#Applications https://en.wikipedia.org/wiki/Graph_theory#Applications

klyrs 6y ago

I just did a search for "real-world applications of Ramsey theory" and this was the closest I got. Sorry. http://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseykings.pdf http://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseykings.pdf

einpoklum 6y ago

A research grant application maybe? :-P