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Comment by auggierose | Hacker News Reader

Really exciting connection, and I am glad I read the article. What I hate though is the box at the end of the article:

   So why is this work so important?

   As we have said, prime numbers are the basic building blocks of mathematics. 
   And primes are vital to cryptography and therefore to the ever-burgeoning world 
   of online commerce and security.

Nope, cryptography is not why this work is important. What a lot of bull.

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Its a reason the average person can see value in. Since it's the average person's tax money often funding this stuff, it makes sense that academics try to explain uses that benefit the people paying for it.

While I agree that its worth it just for its knowledge pushing value alone, academics and researchers do need to take the public with them, especially these days when finances are squeezed and more people are struggling to make ends meet.

I know WHY the box says what it says. But it is nevertheless bull. If you want to improve online security, the LAST thing you should put money into is research into the Zeta function.

So, if this is what you are telling the tax payer, then you are just telling lies to the tax payer.

If there exists a fast factoring algorithm that breaks RSA, then investing in research to discover that would allow us to design and switch to better cryptosystems. If there does not exist one, discovering that fact would allow us to prove security guarantees about RSA; either way, we improve security.

If we avoid such research out of fear that we might discover something that breaks RSA, we are relying on security by obscurity.

Nobody is 'avoiding' that research. People already know a fast quantum algorithm exists for the factorization problem, which is the core of RSA. hence, people are already working on cryptosystems more computationally complex than RSA. Hell, even more computationally intensive than what quantum computers are thought to be able to do. The class of algorithms called lattice based cryptography are known to be impossible for quantum computers to break, even though these are fully classical methods of cryptography.

So where exactly should we have stopped doing math, in order to remain optimally secure for all time?

I had the same thought: One of the deepest mysteries of mathematics is important because.... of online e-commerce?

Nice to know we've got our cultural priorities straight!

There can be no higher "cultural priority" than closing the intellectual feedback loop between research and the people who pay for it. It drives our progress as a society.

Exactly. And that's why you shouldn't lie but tell the truth.

Do people really consider prime numbers the basic building blocks of mathematics? Isn't that supposed to be sets?

I think people like to say the prime numbers are the basic building blocks of arithmetic (or numbers), and we say this because of the Fundamental Theorem of Arithmetic (which says that every natural number has a unique factorization of primes).

I would have thought it would be Peano's axioms for natural numbers or whatever axiomatic system is being used; depends on what area of mathematics one is studying.

Does the riemann hypothesis even have ground breaking applications to crypto?

Not necessarily. The methods used to confirm the Hypothesis could be used in other related fields. The techniques used to solve the Hypothesis could potentially be applied to break RSA. I've read there are similarities between the Riemann Hypothesis and RSA's workings.

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