r/PhilosophyofMath • u/Potential_Version_34 • 11d ago
How far could a civilisation progress without mathematical proofs?
Imagine a parallel civilisation that never built a formal mathematical model of the world and could only progress with ‘experience’ and no mathematic proofs or calculations.
What is the greatest technological level they could attain without the use of calculation?
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u/QtPlatypus 10d ago
It could progress quite far. Consider that formal proofs as we think about them as a modern thing are a quite recent invention. Whitehead and Russell only published PM in the 1910's.
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u/OriousCaesar 10d ago edited 10d ago
Do you not think Euclid's proof should be counted in this scenario? Saying only proofs from 1910+ should be counted seems to be constraining the definition of a proof too much, imo
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u/QtPlatypus 10d ago
The thing is that geometry was for quite a long part of it's history the odd one out for math fields. Being the only field that was axotomized. The rest of mathematics where algorithms that just worked.
Consider the fact that calculus existed before the measure theory and analytics that allow us to justify that calculus works.
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u/felipezm 8d ago
That's a huge oversimplification of math history
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u/QtPlatypus 8d ago
Well yes. It is two paragraphs summarizing the entirety of human existence. It can't be anything but an oversimplification.
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u/felipezm 8d ago
It's an oversimplification which leads one to wrong conclusions. Of course what consists a formal proof has somewhat changed since the 20th century, but claiming everything between ancient greek math and 20th century math was just "algorithms that worked" is preposterous. That encompasses all the work of Descartes, Fermat, Euler, Gauss and too many others to name.
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u/DeathToAmerica2026 10d ago
The first time math got really ahead of technology and practical experiment was Einstein, so probably there.
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u/marsattacks 10d ago
Maxwell would like to have a word..
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u/DeathToAmerica2026 9d ago
Was Maxwell not trying to describe with a better theory then observations made by Faraday, etc? Did he predict much with no observational antecedents?
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u/Efficient-State-7300 10d ago
I think there are SciFi stories of aliens that can perform advanced math instinctively or without conscious process.
We can consider dolphins and other animals processing sonar purely via hardware. Humans too, one example is filtering our hearing, or resolving objects from visual input. This would require advanced math to do computationally.
So my answer is, it's a fun thought experiment, and I don't know what your answer is for humans. But for a generic anything species, perhaps there is no limit.
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u/Potential_Version_34 10d ago
That’s a very interesting take, that we evolve ourselves out of the problem.
Great rebuttal
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u/Mono_Clear 10d ago
Math is just a formalized recognition of nature's patterns it's not impossible that you could discover a lot of things through trail and error but it would take longer. Your technology would basically be evolving the way life does.
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u/Potential_Version_34 10d ago
I guess the question is “when does trial and error give such diminished results such that progress is almost negligible”
Heading into the Iron Age we did well, but I wonder if we trial and error ourselves into solar panels, vaccines or other technologies that are too precise for the human mind to notice
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u/Mono_Clear 10d ago
Trial and error isn't necessarily random in theoretically over a long enough period of time you could trial an area yourself into developing techniques that you don't fully understand but that still work.
But without the language of math you couldn't automate things as effectively you'd have to be using mechanical automation and extreme precision builds like a phone or a solar panel require such tight tolerances that without having some kind of a way to gauge mathematical precision it's much more likely that you'd simply create a lot of failures and occasionally stumble across a good version.
But the more precision is required the more improbable trial and error becomes.
A spaceship can explode because it has one bad gasket how many spaceships are you going to sacrifice before you figure that out
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u/Mono_Clear 10d ago
Also certain branches of science simply could not exist. Theoretical physics is based on mathematical conceptualization you can't do trial and error to figure out black holes or the age of the universe. The whole point of theoretical physics is that it's based on the fact that the math makes sense
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u/Intrepid_Land_6143 10d ago
Look at all the amazing buildings that have been constructed without advanced mathematical knowledge.
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u/Diet_kush 10d ago
The book Children of Ruin has an interesting take on this. It’s a society of hyper-advanced octopuses, and since their nervous system can act independently, all of the “technical details” of their actions are more intuition than knowledge.
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u/OriousCaesar 10d ago
Proofs while nice, are ultimately just confirmations of patterns we've already noticed (with some exception of course. I've made counting proofs where I don't know the answer before I finish for example.).
So, I feel like we could get as far as we normally would up until our faulty conclusions become too constraining to make further progress. Like, imagine Euler made a bad conclusion and later people added onto that faulty conclusion. Until one day we find something that doesn't work. And this happens over and over again. How could progress be made at that point?
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u/Smart-Button-3221 10d ago
No matter how advanced the civilization may evolve naturally, I can't imagine you can make a computer without some kind of precise language.
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u/Appropriate-Ad-3219 10d ago
It would be probably difficult to create theories. We know that a theory holds by seeing the logical consequences of theories then see if these consequences hold in practice.
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u/Useful_Calendar_6274 10d ago
I don't think they would ever figure out computers so no information age for them
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u/nanonan 10d ago
I think they would, what do you think would require proofs?
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u/Useful_Calendar_6274 9d ago
that's how math progresses. Maybe they get a super genius that can see things and never bothers them to write down proofs and they realize his method just works. It's possible they get all of our math but it would take like a million years vs what it took us
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u/TommieTheMadScienist 9d ago
Math also advances when Magicians like Wolfram create entirely new branches like cellular automata.
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u/Willing-Sample-8847 10d ago
You need calculations of varying difficulty just to for civilization to progress economically. For instance, how do you build a house without estimating how long it's going to take, how much wood (or other materials) you're going to need, and how much food you have to have stored away in order to survive while building your house? Or how do you figure out how much many sheep can graze on your pasture without calculating how large your pasture is (area) and how much grass each sheep consumes each week (area over time).
Much of early mathematics developed because of farming, and later, commerce. Really, it is very difficult for a civilization to even survive if no calculations are ever made. (Never mind calculating bartering value of various items)
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u/BasicError9043 10d ago
Just take a look at the tribes of the Amazon or the one crazy tribe on that Island. If you can't create a rigid standard than its just mysticism and sorcery.
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u/nanonan 10d ago
Calculation does not require proofs. Mathematics does not require proofs to function, just a coherent logical framework. Proofs help to create such a framework but they are not essential to it.
Think of a cpu. It has powerful calculation capabilities. It's basically just a bunch of wires and logic gates in a certain configuration. Certainly nothing resembling proof is present.
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u/Tribe-Less 8d ago
You assume technological development is a sign of advancement as opposed to being a sign of a species or community being so out of sync with their local environment they need external technology as a crutch for its failure to adapt to the environment.
Which is more advanced, aspecies who has developed stamina and speed through generations of adaptations or a species that need wheelchairs, cars, etc. to get around because they lack the natural speed and stamina to get around using their own body?
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u/Dirichlet-to-Neumann 7d ago
Can't do GPS without global relativity and can't do global relativity without the concept of mathematical proofs
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u/etzpcm 10d ago
Proofs and calculations are two very different things. Most things we've achieved don't need proofs, but without calculation we wouldn't have got very far.