Here's The Problem That Made The New Alleged Bitcoin Inventor A Mathematical Rock Star

Shinichi Mochizuki

This weekend computer scientist Ted Nelson claimed that mathematician Shinichi Mochizuki was the man behind Bitcoin. 

See, while the digital currency has moved markets and attracted major investors, nobody actually knows who came up with it.

The paper describing the system was published under a pseudonym, Satoshi Nakamoto, and people are clamoring to find out who the genius behind the Bitcoin system actually is. 

And while there is a mountain of compelling evidence demonstrating that Mochizuki probably isn’t Nakamoto, this is still an excellent opportunity to revisit why people are obsessed with the Japanese mathematician — namely, his rock-star status achieved after publishing a bold proof of one of the thorniest problems in Diophantine analysis, the abc conjecture. 

In short, the abc conjecture explores the relationships between prime numbers.

It’s been described as the most important unsolved problem in Diophantine Analysis.

Diophantine analysis is a branch of mathematics that works with some of the most simple number systems (like ax + by = 1 or xn + yn = zn) and in doing so explores some of the deepest relationships in maths.

Some of the earliest work with mathematics — we’re talking ancient Greek number-crunching here — was with prime numbers, especially the relationships and frequency between them. 

The abc conjecture — a younger problem in the field, originally proposed in 1985 — is as follows.

Take three positive integers that have no common factor and where a + b = c. For instance, 5, 8, and 13.

Now take the distinct prime factors of these integers—in this case 2, 5, and 13—and multiply them to get a new number, d.

In most cases, like this one, d is larger than c. The conjecture states that in rare instances where d is smaller than c, it is usually very close to c. Most importantly, the conjecture also shows that there are a finite number of instances of a, b, and c where d is smaller than c. 

Mochizuki claims to have cracked this conjecture in a 500-page proof.

Even if you didn’t catch all of that, solving this would be the necessary missing link for a dozen different, more advanced problems in Diophantine Analysis, including the legendary mathematical problem Fermat’s Last Theorem.

So it’s not unreasonable to expect that Mochizuki — an exceedingly intelligent mathematician who Nelson thinks had time to complete such an undertaking — has the brains to be the guy behind Bitcoin. 

But even if the evidence doesn’t come together, Mochizuki should still he hailed as the guy who potentially cracked one of the most difficult problems in his field, still a huge achievement. 

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