Ants are the graph theory of biology.
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It's still math. There are still right answers. Especially for the combinatorics problems you do as you build up to some of the theorems.
It's just a lot of theorems are easy to state, sound reasonable but hard or unproven.
@futurebird Oh, I see. I misunderstood what you meant. Thanks.
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The "math most likely to make you mad" is continuum theory. But the math that will most reliably lead to a being fixated on it?
Graph Theory.
@futurebird it's how you get that gaunt, haunted look that Veritasium's animators like in mathematicians.
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The "math most likely to make you mad" is continuum theory. But the math that will most reliably lead to a being fixated on it?
Graph Theory.
@futurebird Yes! Graph Theory is such a darling of beauty and frustration.
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@futurebird Graph theory is good from a "not all math is about numbers" perspective. But it really isn't that approachable. That's one of two classes I dropped in graduate school. And I have papers published in graph theory.
@futurebird Geometry is probably a little more approachable and still mostly number-free but IDK that is that much better. Knot theory, maybe? That might be worse.
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* Anyone can understand some of the big questions in graph theory
* People think graph theory is "great for kids" for some reason (yeah if you want them to be obsessed with unproved theorems for their whole life)
* It's very easy to get very deep in graph theory and VERY lost. Easy to state problems with no solutions
* You just know it's all CONNECTED and it's going to drive you nuts forever@futurebird "graph theory has too many unproven theorems" actually just statistical error. average graph theorist has 0 unproven theorems. Cantors Georg, who lives in a cave & posits over 10,000 theorems a day, is an outlier adn should not have been counter
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The "math most likely to make you mad" is continuum theory. But the math that will most reliably lead to a being fixated on it?
Graph Theory.
@futurebird Graph theory is great because any time I have a problem that needs it, my mathematician colleagues will line up to help with it.
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* Anyone can understand some of the big questions in graph theory
* People think graph theory is "great for kids" for some reason (yeah if you want them to be obsessed with unproved theorems for their whole life)
* It's very easy to get very deep in graph theory and VERY lost. Easy to state problems with no solutions
* You just know it's all CONNECTED and it's going to drive you nuts forever@futurebird can confirm, am insane and graph theorist
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It's still math. There are still right answers. Especially for the combinatorics problems you do as you build up to some of the theorems.
It's just a lot of theorems are easy to state, sound reasonable but hard or unproven.
@futurebird@sauropods.win @photovotary@beige.party some like 4-color theorem has a very unsatisfyingly inelegant proof -
* Anyone can understand some of the big questions in graph theory
* People think graph theory is "great for kids" for some reason (yeah if you want them to be obsessed with unproved theorems for their whole life)
* It's very easy to get very deep in graph theory and VERY lost. Easy to state problems with no solutions
* You just know it's all CONNECTED and it's going to drive you nuts forever@futurebird graph theory is extremely useful but only after you have linear algebra
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* Anyone can understand some of the big questions in graph theory
* People think graph theory is "great for kids" for some reason (yeah if you want them to be obsessed with unproved theorems for their whole life)
* It's very easy to get very deep in graph theory and VERY lost. Easy to state problems with no solutions
* You just know it's all CONNECTED and it's going to drive you nuts forever@futurebird I saw a video recently talking about how there is only one infinite random graph and had my mind blown, I can see it driving people mad
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F myrmepropagandist shared this topic
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@futurebird I saw a video recently talking about how there is only one infinite random graph and had my mind blown, I can see it driving people mad
@orman @futurebird hey i saw that video too
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@futurebird graph theory is extremely useful but only after you have linear algebra
@futurebird graph theory is a tool for turning any problem into a linear algebra problem, or for getting visual intuition for unintuitive linear algebra problems
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@futurebird I saw a video recently talking about how there is only one infinite random graph and had my mind blown, I can see it driving people mad
@orman @futurebird *knowing I may regret this, and yet* Imma need that link
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@orman @futurebird *knowing I may regret this, and yet* Imma need that link
I will add it to #fediverseTV
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I will add it to #fediverseTV
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The "math most likely to make you mad" is continuum theory. But the math that will most reliably lead to a being fixated on it?
Graph Theory.
@futurebird I learned a tiny bit of queueing theory and that’s the one I can’t get out of my head. I see it everywhere, of course. Traffic. The grocery store. The airport. Restaurants. I know enough to say “I bet there’s some queuing theory principle that explains this” but not enough to know more than that.
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Ants are the graph theory of biology.
@futurebird for a quarter of a century I thought cladistics was the graph theory of biology!
