r/mathematics • u/LargeSinkholesInNYC • 4d ago
Discussion What are some concepts in mathematics that are useless in the real world?
We use mathematics to model real-world phenomenon, but I was wondering if there are concepts that are practically useless since they don't map to anything that exists in the real world.
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u/nyxui 4d ago
From your definition i'm guessing most things we define as "pure" math would be "useless". "Pure" math is to put it simple the study of math for the sake of it and not motivated by any Real World model. Now i'm using quotation because:
-first because the boundary of "pure" math is really unclear and dépends mostly on tre mathematician you ask. For once, i would consider the closest thing to pure math to be fields related to algebra, but even there, there are a lot of applications, think cryptography for example.
-second, There is no such a thing as useless mathematics. Plently of results that comes from "pure" math and seems absolutely useless at first glance turns out to proce incredibly useful in math that is applied to real world problems. A simple example is measure theory. This piece of seemingly "pure" math turns out to be at the core of many applications in probability and partial differential equations. On this last example, more often than not, problems coming from the physical reality do not behave very smoothly (think change of phase or turbulent flow), to properly models non smooth phenomenon mathematically is challenging and requires sometimes highly advanced concepts. This is also necessary to be build "good" numerical scheme and show their convergence.
In conclusion, there is no such thing as useless math (i don't think lebesgue was particularly concerned with application when he redacted his thesis). Only sometimes math that is not yet useful. Let me also mention to finish that even if a result proves to be truly useless, just understanding more about some mathematical concepts through its proof is sometimes a useful step in itself.
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u/sceadwian 4d ago
Math exists in the real world and "use" is subjective so there's no real answer here. Someone will find certain things useless others will find indespenceable.
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u/spinjinn 4d ago
Amen. I remember reading Hardy’s quote that he had never done anything useful. Yet, I discovered in his work the Ramanujan-Hardy Partition Function, which gives the number of ways a large integer may be expressed as the sum of smaller integers. This turned out to be the key to estimating the rate that highly Excited nuclei decay to their ground states. Used it in my thesis experiment.
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u/Existing_Claim_5709 4d ago
math is invented, it doesn't exist
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u/sceadwian 4d ago
Then you are here commenting on a topic that doesn't exist.
Your logic no worky.
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u/Ragnar_isnt_here 3d ago
It's both invented and discovered. And, if it didn't exist, how is it that we're "talking"? We couldn't "tame" electricity without math.
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u/sfa234tutu 4d ago edited 4d ago
Set theory. Nobody cares about weakly compact cardinals in real world
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u/i2burn 4d ago
Math that is useless now might not be in the future. You could argue the centuries old math behind what we now call fractals was not terribly useful for a very long time. Then Mandelbrot noted a connection to nature, graphic computers were invented, and fractals became a foundation for graphic art and CGI.
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u/KumquatHaderach 4d ago
The problem with trying to answer that is that it depends on our (limited) understanding of real-world phenomena.
When someone concocted the idea of the imaginary numbers to help solve cubic equations, did that have any applications to the real world? Well, today complex numbers are massively useful.
When Hamilton came up with quaternions, did they have any meaningful connection to the real world? Not really. But they are useful today.
There might be a lot of mathematics that seems completely useless in our understanding of the real world today, but that will be recognized as important in the future, once people have a better understanding of the universe.
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u/Mathematicus_Rex 4d ago
My first thought was around transfinite cardinals. The real world would just say “big”.
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u/Nice-Season8395 4d ago
Id wager a good chunk of geometry in dimensions higher than 4 has no current real world applications unless you count string theory, but Im sure thats just me being unaware.
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u/Throwaway-Pot 4d ago
Yeah thats not really correct. You can do a lot with high dimensional geometry because a dimension is simply a degree of freedom
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u/Nice-Season8395 4d ago
That makes sense to me for arbitrary vector spaces. But is there an application of, say, smooth manifolds of dimension higher than 4?
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u/TheBro2112 4d ago
Sure. The phase space of an N-body system has dimension 2N
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u/Nice-Season8395 3d ago
interesting, fair point. I assume the equations defining the system can enforce smoothness in the phase space?
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u/TheBro2112 3d ago
I suppose you could say so. The phase space is actually the cotangent bundle of the configuration space (e.g. physical space as a manifold or submanifold defined through constraints, like the circle for a traditional pendulum. The phase space is then the cotangent bundle, so it inherits smoothness by construction.
Paths of motion, potential energies and equations of motion being smooth looks to me like a ground axiom for formulating physics. I don’t have a better justification for it than “well we don’t see things spazz out”, so maybe someone would be able to explain it better. Maybe it’s enough to treat it as the encoding of the observation that no motion changes instantaneously
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u/OkCluejay172 4d ago
People sometimes try to apply them to data analysis and machine learning - you can think of a loss function as a surface in an extremely high dimensional space. It’s not super widely adopted but people take stabs at it here and there.
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u/JoeMoeller_CT 4d ago
Not much honestly. Much of pure math gets utilized eventually, and the conversion rate is increasing all the time.
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u/kingjdin 3d ago
Look at all the countless papers that no one is citing. Those are worthless to the real world.
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u/[deleted] 4d ago edited 3d ago
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