Craig Wright with mathematical equation background

A mathematical proof that Craig S. Wright is Satoshi Nakamoto

This post originally appeared on the ZeMing M. Gao’s website, and we republished with permission from the author. Read the full piece here.


Assume N independent attestation factors, each factor having an attestation value measured to be 1/10 random probability (that is, given the credibility of the attestation itself, and if the subject matter satisfies the attestation, there would be only 1/10 of a chance for the subject matter to be false), then the subject matter that satisfies all N attestation factors has a probability P of being untrue as follows:

P= 10^-N.

P=10^-10 when N=10, which is one in 10 billion.

In real life, it is hard to have attestations that are truly completely (100%) independent, therefore the probability (of being false) P would be greater than the above estimate. But even if you increase the above probability by 1000 times, it is still only 10^-7, which is one in 10 million.

And remember the highest 5-Sigma standard of proving a fundamental physics discovery is 3×10^-7 (one in several million), at which level no reasonable mind could doubt.

In the case of proving that Craig Wright is Satoshi Nakamoto, there are at least 10 such independent attestation factors, and many of these attestation factors have an attestation value higher than that equivalent to a 1/10 random probability (that is, given the credibility of the attestation itself, and when the attestation is applied alone, it results in less than 1/10 of a chance that Craig Wright is not Satoshi Nakamoto).

For examples of such attestation factors, see the next section “Mounting evidence and attestations.”

Alternatively, one may use the Bayesian methodology to estimate the probability of a hypothesis being true.

Start with specifying a prior probability of being true.

Let’s say:

Prior probability = 10^-10

(That is, one in 10 billion, a very small probability to be true. Roughly any random person living on earth has such a probability of being Satoshi without any relevant evidence attesting for the person.)

This prior probability, in turn, is then updated to a posterior probability in the light of new, relevant data (evidence).

The posterior probability is continuously updated with additional independent evidence.

With the case of Craig Wright, you would soon reach near certainty of him being Satoshi Nakamoto, given the multiple pieces of evidence of high attestation values (see below).

(A graduate student could do an actual Satoshi Nakamoto Bayesian modeling for a thesis; but I already know the result.)

What does math have to do with this?

The main point of this article is not to enlist all the evidence and attestations (which are mounting high, see below) supporting Craig Wright’s Satoshi identity, but to make a mathematical argument.

A proper mathematical model is important to collectively evaluate the weight of evidence that has multiple attestation factors. It is so even if one assumes variable or partial credibility of each attestation (see below).

Fundamentally, this has to do with human psychology and how human minds work.

Human mind is usually good at measuring a single or linear factor, but becomes increasingly poor with a progression of multiple multiplications, which are typically exponential phenomena.

That’s why we must rely on math.

In the realm of investment, for example, people who trust math understand the compounding effect, while people who just trust their gut feeling tend to miss the profound compounding effect, not because they are stupid, but because our minds, or the “brain muscles”, are not made to naturally measure or cope with exponential phenomena.

Likewise, in the realm of evidence and testimonies, people’s minds are relatively good at evaluating the weight of each piece of evidence, but tend to fail to see the combined effect on the weight of the evidence, as human minds tend to look at each piece of evidence separately, not understanding that independent pieces of evidence corroborating together actually result in exponentially heavier weight in evidentiary value.

Mounting evidence and attestations

Australian polymath Craig S. Wright is Satoshi Nakamoto, the inventor of Bitcoin. Despite the negative or distracting impression that most people get from the popular narrative and propaganda, the truth is gradually breaking out from a net of misinformation.

As someone who for certain reasons has always had strong aversion to personality cult, I started by accepting the then prevailing (and still prevailing) narrative that Craig Wright was a fraud, but reached an opposite conclusion after an independent study.

One has to study the entire history to draw a reasonable conclusion. This could take articles or even books to explain (and books will be written and movies will be made), but one may start with the following (and also further follow through the links provided in the references):

While doing your research, ask yourself some very hard questions:

  1. How many people in the world who are both known to be related to at least the early stage of Bitcoin and also know how to program in Forth (the requisite language used for Bitcoin script designing)? (Answer: exactly one)
  2. How many people in the world who are both known to be related to at least the early stage of Bitcoin and also worked extensively on digital cash systems for years before Bitcoin’s release? (Answer: exactly one)
  3. How many people in the world who are both known to be related to at least the early stage of Bitcoin and are also an expert on all the following key disciplines which are clearly a requisite for inventing Bitcoin (if you have read the actual white paper you would agree): economics, monetary systems, law, computer sciences, cryptography, and gaming theory? (Answer: exactly one)
  4. How many people in the world showed understandings of Bitcoin scripts and gave explanations of their theoretical considerations and practical applications to a level that only their designer would? (Answer: exactly one)
  5. How many people in the world knew the answers to such questions about Bitcoin that even the question itself seemed strange let alone an answer: why double hash? why 21 million coins? etc. (Answer: exactly one)
  6. Who gave an original (the first ever) explanation for why Bitcoin is not encrypted (and therefore is not crypto), and why Bitcoin protects privacy but does not create anonymity, and why Bitcoin is designed to not only comply with the law, but in fact further enhance the rule of law, rather than be antigovernment (something that would become crystal clear with hindsight once one has learned about it and goes back to read carefully the whitepaper again)? (Answer: Craig Wright and no one else)
  7. Who gave the original explanation for why Bitcoin’s security is not primarily based on a computational design, but rather on economic principles (again, something that would become crystal clear with hindsight once one has heard about it and goes back to read carefully the whitepaper again)? (Answer: Craig Wright and no one else)
  8. How many people in the world knew that Bitcoin was Turing complete from the very beginning, before they have seen it proven or heard it from someone else? (Answer: exactly one)
  9. How many people in the world have multiple witnesses who were the earliest prominent participants of Bitcoin and had intensive personal interaction with Satoshi Nakamoto (these include Gavin Andresen, Ian Grigg, etc), and were later convinced based on intimate personal knowledge that the person Satoshi they had interacted with matches exactly the person in question? (Answer: exactly one)
  10. How many people in this world have multiple witnesses testify under oath that they knew the person had been working on something that was clearly and identifiably the subject matter of Bitcoin, before the Bitcoin whitepaper was released? (Answer: exactly one)
  11. How many people in this world can produce evidence, any evidence, that they had some work products, including the registration of the domain name, before the Bitcoin whitepaper was released (the evidence is there, although not presented in the recent Kleiman v. Wright trial due to its lack of sufficient relevance in the case, but will come out eventually)? (Answer: exactly one)
  12. How many people in this world are known to have reported Bitcoin as capital gain in his/her year 2009 tax return, and were further identified and attacked by the tax authority as the one who owned and controlled Bitcoin in those earliest years? (Answer: exactly one)
  13. Who has the registered copyright to the Bitcoin whitepaper and Bitcoin genesis database? (Answer: Craig Wright and no one else, and no one else has challenged the copyright by producing any evidence or even just claiming to be the true author instead)?
  14. How many people in this world have invented and filed hundreds of patent applications for technologies related to or derived from the original Bitcoin? (Answer: exactly one)
  15. Who leads the building of the only platform in the world that is truthful to the original Bitcoin whitepaper, claims to be Satoshi Nakamoto, and has a world-class teams agreeing with his claims and devoted to building the Satoshi vision, even though they know quite clear the whole digital currency world is against them, and they’re going to lose opportunities of making quick money by not following those “number go up” Ponzi schemes? (Answer: Craig Wright and no one else)

The list can go on.

Then, plug your answers to the above questions into the mathematical framework outlined in this article (see the first two sections), reach an objective and honest conclusion.


With regard to the above, I hear the following objection:

“I hear one million people claiming they saw Jesus, but that doesn’t mean I’ll accept that as truth with certainty.”

This objection may sound odd, but is highly representative in its underlying misunderstanding.

First, that is a different realm. Spiritual truth is established by a spiritual witness which speaks to one’s heart, not one’s mind. But with respect to Satoshi identity, we are not talking about spiritual truth here. It is mostly a material truth, which can only be based on objectivity and math.

Second, in the above objection, the premise is that the observer does not accept (rightfully or not) the objectivity of any personal testimony in the first place. The difference is in the premise, not in the math. The repeated multiplications of one million 1’s is still 1; or that of one million 0’s is still 0.

The math model in its simplest form assumes complete credibility of each attestation. But people assume variable credibility, which is why human reality is more complex than math. With partial credibility, one would need to adjust the probability of the respective individual attestation factor. If the credibility of a certain attestation is zero, you’d throw out that attestation factor completely.

However, on the other hand, one cannot simply assume that, just because a certain attestation is by another human being, it therefore has zero credibility. The more realistic model would estimate a partial credibility for each attestation. In the math outlined above, the simple assumption that each attestation factor has an evidentiary value of only 1/10 (or 10%, instead of 100%) has already taken partial credibility of each attestation into consideration. If you disagree with the value(s), you may put in your own value(s), but you can’t deny the math logic.

Third, and more important, in the case of proving Craig Wright is Satoshi, each individual attestation is not an expression of a personal opinion that they believe Craig Wright is Satoshi (if that were the case, even 1 million people’s opinion that he is, or he isn’t, wouldn’t really matter ultimately), but to give personal testimony of certain events or facts that the person has actually witnessed firsthand.

There is a fundamental difference between the two. When it comes to an opinion, not only could people be wrong, but are in fact often wrong, especially when people are subject to certain propaganda. When it involves a propaganda, not only could people be wrong in the first place, but also their attestation further lacks the requisite independence (required in the math model), because they are a correlated result of an orchestrated scheme.

But when it comes to a fact for each event that was witnessed (just the fact or event itself, without reaching a conclusion, which could be a person opinion), a witness has to consciously lie knowing the truth in order to give a false testimony. Of course, people do lie about facts that they have supposedly experienced firsthand, but the likelihood for that to happen is far less than people being simply wrong or misled into forming an incorrect opinion.

This is especially so when it is a trial court witness under oath. There is a good reason that all common law based legal systems have very strict evidentiary rules with regard to witnesses, differentiating a first-hand witness and hearsay or an opinion.

We like to claim with pride that we only accept “firm” evidence, by which we usually mean evidence that is not subject to any third party’s subjective human mind. But problem is that, other than the natural laws, very few important truths in this world can be established that way.

A lot of truth has to be based on personal testimonies. That’s how human society functions. One can’t blindly trust, but one can’t do without any trust either. For example, which part of the history is not relying on a personal testimony of somebody else (other than yourself)?

We are entering into a time where not only the history, but also even the contemporary happenings are becoming impossible to prove objectively, to an extent that every person will have to choose what he or she believes.

And coincidentally, that is also one of the major reasons that motivated Craig Wright to invent Bitcoin and Blockchain. His invention will be helpful if the true Bitcoin prevails. But even then, it won’t solve the problem completely.

Given the totality of the evidence, I’d say:

1) Those who haven’t examined the evidence should stop saying Craig Wright is not the inventor of Bitcoin, just so that you don’t find yourself embarrassed one day; and if you can’t say yes, just honestly say you don’t know, and are willing to learn about it.

2) Those who’ve examined the evidence but are still able to believe Craig Wright is not the inventor of Bitcoin, you’ve got an extremely hardened heart, capable of denying any truth or fact you don’t want to believe. It’s a detriment, not a blessing.

3) People who already know that Craig Wright is the inventor of Bitcoin yet for some reason have to deny it publicly, I’m sorry life has come so hard on you. Losing freedom due to earthly bribes is a sad thing.

Check out all of the CoinGeek special reports on the Kleiman v Wright YouTube playlist.

Watch: Dr. Craig Wright’s keynote speech “Time is a Personal Experience” at the CoinGeek New York Conference

YouTube video

New to blockchain? Check out CoinGeek’s Blockchain for Beginners section, the ultimate resource guide to learn more about blockchain technology.