<blockquote>
  <p>That the network is secure by means of math instead of some central
  authority (e.g. a bank overseeing everything)? If so, what math? The
  math that makes PoW possible?</p>
</blockquote>

<p>The math that makes proof of work possible is a one-way function, specifically the <code>SHA256</code> algorithm. This combined with public key cryptography secures the ownership of digital assets in a distributed network in a way that makes Bitcoin truly an innovation. @Raghav Sood is right, it isn't the mathematics that's innovative it's the application of the mathematics.</p>

<h2>Proof of Work</h2>

<p>Proof of work secures the <a href="https://en.bitcoin.it/wiki/Block_chain" rel="nofollow noreferrer">blockchain</a> by making it difficult to compute a solution that satisfies the network requirements for a valid block of transactions, but that is easy for other nodes to verify. This is the property of a <a href="https://en.wikipedia.org/wiki/One-way_function" rel="nofollow noreferrer">one-way function</a>, see <a href="https://bitcoin.stackexchange.com/questions/9078/what-is-proof-of-work">what is proof of work</a>.</p>

<h2>Cryptography</h2>

<p>In order to spend bitcoin, you have to prove that it was sent to you by signing with your private key. Only the private key can sign a bitcoin transaction that was sent to your public address. This is standard <a href="https://en.wikipedia.org/wiki/Public-key_cryptography" rel="nofollow noreferrer">public key cryptography</a>, though bitcoin specifically uses the <a href="https://en.bitcoin.it/wiki/Secp256k1" rel="nofollow noreferrer"><code>secp256k1</code> elliptic curve</a>.</p>

CC BY-SA 4.0
2018-08-11T22:55:54.830Z
2018-08-13T15:00:17.097Z
2018-08-13T15:00:17.097Z
JBaczuk
<p>Bitcoin consists of several basic elements, the first of which is a hash-function. Hash-function - is a mathematical transformation. But I can be mistaken. Pls, correct me if I’m wrong.</p>

CC BY-SA 4.0
2018-09-03T14:58:54.637Z
2018-09-03T14:58:54.637Z
richcoin
<p>This question may be opinion based in some ways, but I'm going to attempt to answer it as it is an important concept, and somewhat unlike traditional systems.</p>

<p>Bitcoin is governed by math, in some places. At the end of the day, it's software, and even the math rules can be updated to use different rules, or removed altogether by means of a soft or hard fork (depending on how drastic the change is).</p>

<p>As for the math, there are primarily three sections where it is in play.</p>

<p>The first is mining - the hash function is used to calculate a value, which is compared against the mining target.</p>

<p>The second is signatures - elliptic curve signatures are used to enforce utxo ownership (for standard outputs anyways).</p>

<p>The third is the block reward - The Bitcoin block reward halves every 210,000 blocks, lea</p>

<p>That said, none of these are particularly math-y. As with any computer program, math is used to enforce certain functionality.</p>

<p>It may be more appropriate to say that Bitcoin is governed by code - The code is ultimately what decides things such as block reward halving, signature technicalities, and mining process. As the abundance of altcoins shows, there are many permutations and combinations on all of these parameters that still result in valid and functional networks. Even Bitcoin has gone through a series of network upgrades that have altered some of these rules, such as moving from an infinite supply to a fixed supply.</p>

<p>As chytrik mentioned in the comments, the infinite supply fix was actually a bug fix (the infinite supply was a side effect of C++ behaviour, and would not have occurred for equivalent code in many other languages). </p>

<p>Bitcoin can indeed be looked at as a model of social governance governing the code, and the code governing the network.</p>

CC BY-SA 4.0
2018-08-12T00:57:36.630Z
Probably worth clarifying: the infinite supply was a bug, not the original intended behaviour. I think that in the context of this topic, it is worth making a distinction between "a fork for a bug fix" and "a fork that represents a change in social consensus". The crux of the question does sorta come down to *"governance by code vs by social consensus"*, after all.
chytrik
CC BY-SA 4.0
2018-08-12T01:00:12.197Z
@chytrik Good point, I've clarified in an edit, thanks
Raghav Sood
CC BY-SA 4.0
2018-08-21T09:57:58.457Z
+1 for the nearly philosophic closing: *"Bitcoin can indeed be looked at as a model of social governance governing the code, and the code governing the network."* ;-)
DJCrashdummy
CC BY-SA 4.0
2018-08-21T09:58:49.800Z
...and even more important to point out and correct that ***Bitcoin is governed by code***!
DJCrashdummy
CC BY-SA 4.0
2018-08-11T22:47:20.413Z
2018-08-12T01:00:02.427Z
2018-08-12T01:00:02.427Z
Raghav Sood
<p>I keep hearing talks from Bitcoin evangelists that claim Bitcoin isn't governed by any central authority, rather it's governed by mathematics.</p>

<p>What exactly do they mean when they say "governed by mathematics"?  </p>

<p>That the network is secure by means of math instead of some central authority (e.g. a bank overseeing everything)? If so, what math?  The math that makes PoW possible?</p>

<bitcoin-core><consensus><governance><math>
How is Bitcoin governed by mathematics?
lolololol ol
# How is Bitcoin governed by mathematics?

(Asked by: username_0 on 2018-08-11)

I keep hearing talks from Bitcoin evangelists that claim Bitcoin isn't governed by any central authority, rather it's governed by mathematics.

What exactly do they mean when they say "governed by mathematics"?

That the network is secure by means of math instead of some central authority (e.g. a bank overseeing everything)? If so, what math? The math that makes PoW possible?

**Tags:** bitcoin-core, consensus, governance, math


---

## 3 answers

### Answer by username_3 on 2018-08-11. Score: 11 | Accepted answer

This question may be opinion based in some ways, but I'm going to attempt to answer it as it is an important concept, and somewhat unlike traditional systems.

Bitcoin is governed by math, in some places. At the end of the day, it's software, and even the math rules can be updated to use different rules, or removed altogether by means of a soft or hard fork (depending on how drastic the change is).

As for the math, there are primarily three sections where it is in play.

The first is mining - the hash function is used to calculate a value, which is compared against the mining target.

The second is signatures - elliptic curve signatures are used to enforce utxo ownership (for standard outputs anyways).

The third is the block reward - The Bitcoin block reward halves every 210,000 blocks, lea

That said, none of these are particularly math-y. As with any computer program, math is used to enforce certain functionality.

It may be more appropriate to say that Bitcoin is governed by code - The code is ultimately what decides things such as block reward halving, signature technicalities, and mining process. As the abundance of altcoins shows, there are many permutations and combinations on all of these parameters that still result in valid and functional networks. Even Bitcoin has gone through a series of network upgrades that have altered some of these rules, such as moving from an infinite supply to a fixed supply.

As username_4 mentioned in the comments, the infinite supply fix was actually a bug fix (the infinite supply was a side effect of C++ behaviour, and would not have occurred for equivalent code in many other languages).

Bitcoin can indeed be looked at as a model of social governance governing the code, and the code governing the network.

> **Comments:**
> **username_4**: Probably worth clarifying: the infinite supply was a bug, not the original intended behaviour. I think that in the context of this topic, it is worth making a distinction between "a fork for a bug fix" and "a fork that represents a change in social consensus". The crux of the question does sorta come down to *"governance by code vs by social consensus"*, after all.  
> **username_3**: @username_4 Good point, I've clarified in an edit, thanks  
> **username_5**: +1 for the nearly philosophic closing: *"Bitcoin can indeed be looked at as a model of social governance governing the code, and the code governing the network."* ;-)  
> **username_5**: ...and even more important to point out and correct that ***Bitcoin is governed by code***!  

---

### Answer by username_1 on 2018-08-11. Score: 5

> That the network is secure by means of math instead of some central
> authority (e.g. a bank overseeing everything)? If so, what math? The
> math that makes PoW possible?

The math that makes proof of work possible is a one-way function, specifically the `SHA256` algorithm. This combined with public key cryptography secures the ownership of digital assets in a distributed network in a way that makes Bitcoin truly an innovation. @username_3 is right, it isn't the mathematics that's innovative it's the application of the mathematics.

## Proof of Work

Proof of work secures the [blockchain](https://en.bitcoin.it/wiki/Block_chain) by making it difficult to compute a solution that satisfies the network requirements for a valid block of transactions, but that is easy for other nodes to verify. This is the property of a [one-way function](https://en.wikipedia.org/wiki/One-way_function), see [what is proof of work](https://bitcoin.stackexchange.com/questions/9078/what-is-proof-of-work).

## Cryptography

In order to spend bitcoin, you have to prove that it was sent to you by signing with your private key. Only the private key can sign a bitcoin transaction that was sent to your public address. This is standard [public key cryptography](https://en.wikipedia.org/wiki/Public-key_cryptography), though bitcoin specifically uses the [`secp256k1` elliptic curve](https://en.bitcoin.it/wiki/Secp256k1).


---

### Answer by username_2 on 2018-09-03. Score: 0

Bitcoin consists of several basic elements, the first of which is a hash-function. Hash-function - is a mathematical transformation. But I can be mistaken. Pls, correct me if I’m wrong.


---

