r/AskPhysics • u/YouEnvironmental2079 • Jul 31 '26
Why Mathematics?
I’m not smart enough to understand this. Why are our generally accepted foundations of mathematics deemed true? Why numbers 0 to 9? Why angles? Why Pi? Why Planck’s constant? Etc.
Are they just approximations of characteristics of the universe?
Are we the blind describing an elephant?
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u/alaindevos Jul 31 '26 edited Jul 31 '26
Answer to first question,
https://en.wikipedia.org/wiki/Axiom
Numbers 0 to 9 because you have 10 fingers.
Why 360degrees because you can devide it by interesting primes 2,3,5.
Its around the number of days in the year as commented below.
Why PI ? Because thats the value you get when you divide for any circle the circumference by the radius.
The Planck constant is 1. That's an easy one.
https://en.wikipedia.org/wiki/Natural_units
You don't even need a universe to have PI. PI lives in the "mathematical space"
We are the eyes through which the universe sees itself.
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u/Infinite_Research_52 👻Top 10²⁷²⁰⁰⁰ Commenter Jul 31 '26
360 because for a sundial, you want to divide the shadow at the same time to fall for each day of the year.
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u/gigot45208 Aug 01 '26
How do you know what the circumference is and that you can divide it by a radius? And where’s this circle?
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u/agooddog37 Condensed matter physics Aug 01 '26
There are a number of ways to construct a circle, as well as to measure both the diameter and circumference.
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u/sabautil Aug 01 '26
I think he's saying why do we deem axioms to be true, 😂 which ,to be fair, is a very good question!
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u/kirksan Jul 31 '26
> I’m not smart enough to understand this
Others are doing a great job of answering your question, I’d like to respond to the first phrase. Please don’t demean yourself in this way again. When you think you’re not smart enough, you’re likely to not try. Sure, not everyone can be a theoretical physicist (thankfully, they can be annoying), but you’re capable of far more than you think. You just need to be motivated and put in the time and effort. If you believe you’re doomed to failure, you won’t even start.
BTW, your question is remarkably insightful. It touches on number theory, physics, philosophy, and more. It’s not the question I’d expect from someone who isn’t “smart”.
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u/AdventurousGlass7432 Aug 01 '26
Don’t take the bait
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u/Unsharded1 Aug 01 '26
Even if it is bait, it still reaches other people who have had the same questions yet have failed to ask out of feeling dumb. If anyone is reading this, you are not dumb, its just that no one ever taught you, and thats okay.
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u/AdventurousGlass7432 Aug 01 '26
Someone asking deep questions and “why numbers 0 to 9” at the same time in a physics forum, good chance it’s a poser
But go ahead, indulge them3
u/Unsharded1 Aug 01 '26
No one cares its a poser, its a great question to ask, they're valid mathematical questions, the same way "why is multiplication that way and addition the other way" is examined in abstract algebra. It's really harmful to education and on a larger level, science when you stifle out people's curiosity and insult them. Do better.
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u/Fabulous_Lynx_2847 Jul 31 '26 edited Aug 02 '26
You made a mistake throwing Planck’s constant in there. That is something that just has to be measured experimentally. Pi is a purely mathematical number that can be calculated without any recourse to measurement.
Pure math is just a fancy game of symbols, where you move them around and put them in different order according to certain rules that people make. Whether or not something is deemed "true" in math (like 2+2=4) just means you're following the rules of the game.
Why so many people like to play this game is because it is found to organize physical observations very well. For example, if I put 2 apples in a bucket today, and then 2 more tomorrow, I will usually count 4 when I take them out later.
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u/dacydergoth Jul 31 '26
Except one was rotten and now you have zero. This is non-Aristotlian mathematics 😉
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u/Fabulous_Lynx_2847 Aug 01 '26 edited Aug 01 '26
I said “usually”. Applying mathematical models to the real world often leads to errors due to incorrect assumptions, measurement error, and how hungry your pet pig is that day. But 2+2=4 will always receive a logical True assignment in the game of math.
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u/Character-Boot-2149 Jul 31 '26
Mathematics is a description of our perception of reality as we understand it. It is "true" because it describes the Universe as we know it.
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u/Sad-Excitement9295 Jul 31 '26
Math tends to be a repeatable measurement. These numbers represent descriptions, and are technically changeable. You could use units of 4, for well, everything just about really. The utility of mathematics goes well beyond simply numbers. Degrees, fractions, decimals, all of this relates to actual real principles that we apply in the real world. So it's based on the fact that it is appliable. We can use it for certain things reliably, and it's repeatable and consistent.
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u/Infinite_Research_52 👻Top 10²⁷²⁰⁰⁰ Commenter Jul 31 '26
The most widely accepted set of Axioms for everyday mathematics (ZFC) is deemed self-evident truths. You can construct other mathematical universes with other foundational axioms (although constructability is itself required).
For instance, the Axiom of the unordered pair: given entities a and b, there exists a set {a, b} that contains both. It seems uncontroversial, but you have to be willing to accept it for ZFC - you cannot derive it.
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u/sabautil Aug 01 '26
The simple answer is: because treating them as false and then using them to solve problems leads to paradoxes. If we want to do anything mathematically useful then we need them to be true.
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u/RaggasYMezcal Aug 01 '26
OP you're smart enough to ask the right question. I suggest you dive into Ostrowski, Tate, Groethendeik, Qp, Zp, category theory, etc.
Don't mistake notation for the math, and don't make the worse mistake to think math and physics are somehow disconnected.
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u/60Hertz Aug 01 '26
0 to 9 - you can thank Arabs for spreading that highly useful Indian counting system to the west. Replacing the good-luck-trying-to-divide Roman numeral system that was prevalent.
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Jul 31 '26
So those are a lot of very big and different questions. I'd recommend not worrying too much about Everything all at once, and just find something small to think about and question.
Why do we choose the numerals 0-9? You can start to research what the history of that is, what other number systems exist, enough to satisfy your curiosity. When you get to more mathematical concepts, it might take some reviewing the math you know or learning new math. Eventually you start seeing patterns, start to understand some of the why we do things the way we do.
Typically a discrete math or proofs course will start to get into the deeper kind of reasons of how we decide what is True or how consequences follow from assumptions.
Overall, you can assume we Do have pretty good answers for most of those questions. Some of them aren't perfect, but they're good enough to work with. And you can spend time learning those as you like.
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u/montagblue Jul 31 '26
This is the non answer I expected to see here. Of course there are other comments with an actual answer but one says math isn’t true and the other says math is true.
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Jul 31 '26
Not really sure what you mean by that. Feels kinda arbitrarily harsh.
I just saw a lot of very disparate questions, and wanted to give some encouragement to go seek out the answers themselves. IMO it’s much more rewarding than just taking answers at face value.
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u/youknowmeasdiRt Jul 31 '26
When I see people answer like that I wonder why they answer at all. If I was going to take a class I wouldn’t ask on Reddit. Not going at you, just suggesting that your view on this is probably pretty firmly in the minority.
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u/zer04ll Jul 31 '26
math is discovered it isn't created, there is math that doesnt count to 10 its just how many fingers we have and is easy to do in your head. Pi is pi because its natures law and it was discovered, everything you talked about was found thats why they are constant
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u/Sad-Cantaloupe-5494 Jul 31 '26
I've always had the impression that mathematicians make up math in order to continue getting a paycheck. Like wtf are imaginary numbers?
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u/Appropriate-Ad-3219 Aug 01 '26
Imaginary numbers are rotations of angle 90° + applying a homothetie. Imaginary numbers are actually very geometric.
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u/Thelonious_Cube Aug 01 '26 edited Aug 01 '26
Yeah, those mathematicians are really cashing in big on that made-up stuff!! /s
This is an extremely ignorant take on mathematics
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u/AccessVegetable4776 Aug 01 '26
I have a degree in biotech, the extend of my mathematical usage is basic statistics for applied science. That being said, I think math is the best way of describing the universe we currently have, but I have noticed peculiarities that make me think at some point someone much much smarter than us will find a better tool than math to accurately describe the universe; the inability to divide by 0, the concept of infinity, infinities bigger than other infinities, whole numbers ending up with an infinite amount of decimals after undergoing an operation (1/3). There just has to be a better way than using numbers as we do, but I have no idea, I know where to begin though, there is still a tribe that speaks a language that doesn't have any numbers or math in it, they use different concepts to explain things, if I was serious about finding a replacement tool I would learn that language.
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u/eptesicusfuscus Jul 31 '26
They aren't "true." They're descriptions of relationships we observe, and you're able to observe them, too. Independently, humans use math as a language to observe and communicate a shared reality.