Computer proof ‘blows up’ centuries-old fluid equations
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Computer proof ‘blows up’ centuries-old fluid equations
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Re: Computer proof ‘blows up’ centuries-old fluid equations
#2I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians.
This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time) reachable truth!
Re: Computer proof ‘blows up’ centuries-old fluid equations
#3I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…
Huh? Mathemathical proof is not a social construct. This makes no sense.
Re: Computer proof ‘blows up’ centuries-old fluid equations
#4I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…
Huh? Mathemathical proof is not a social construct. This makes no sense.
I suppose they mean what's commonly accepted as true and can be referred to as truths. No one can read all the proofs, so they have to trust others who have. There was that one example where a mathematician "proved" something terribly complicated using his own methods and terminology developed over several years. The truth value of that kind of proof is very much a social construct.
Re: Computer proof ‘blows up’ centuries-old fluid equations
#5I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…
Huh? Mathemathical proof is not a social construct. This makes no sense.
The mathematical truths are the fruit of the work. The social consensus is an implementation "detail". Yet it's the implementation we have. Does this make better sense now?
Re: Computer proof ‘blows up’ centuries-old fluid equations
#6I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…
There are such reachable truths, but every mathematical system has a non empty set of axioms - or assumptions- which are 'given'.
Re: Computer proof ‘blows up’ centuries-old fluid equations
#7I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…
A proof is a rhetorical device to convince others of the truth of a proposition.
Re: Computer proof ‘blows up’ centuries-old fluid equations
#8I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…
Huh? Mathemathical proof is not a social construct. This makes no sense.
And yet nonetheless you feel the need to object to this formulation publicly and have it considered by others
Re: Computer proof ‘blows up’ centuries-old fluid equations
#9I remember my math professor at university telling me that truth in mathematics was a social construct, and that nothing was true until a social consensus had been reached between mathematicians. This struck me at the time as a very powerful statement, yet unexpected, since very much not what most people expect from mathematics. After all, it's supposed to be a field where there is such a thing as a (most of the time…
Huh? Mathemathical proof is not a social construct. This makes no sense.
It's certainly a social construct, but it is not merely a social construct.
Re: Computer proof ‘blows up’ centuries-old fluid equations
#10> Hou and Luo’s work was suggestive, but not a true proof. That’s because it’s impossible for a computer to calculate infinite values. It can get very close to seeing a singularity, but it can’t actually reach it — meaning that the solution might be very accurate, but it’s still an approximation.
I feel certain that if you run a process that approaches infinity using ordinary floating-point numbers, you will actually reach infinity. This is a case ("can a calculation yield an infinite result?") where computers have less of a problem than people do.
You'd have to deal with the question of whether the infinite value accurately reflected an infinite limit of the process or whether it was spurious. But there's no difficulty in calculating infinite values.