Can someone explain what the author meant with the following passage?
"... Navier-Stokes equations, which govern the flow of fluids, including air currents. In this case, let us hope that it does not have a real-world application."
The Mind of a Mathematician
21–30 of 68 posts
Re: The Mind of a Mathematician
#22I very much like that people like Tao are famous. It’s relatively good for the intellectual spirit and hopefully it inspires others. However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it. Let’s talk about the awesome work and why it’s awesome. Let’s play through some of it: I’m relatively sure most people know nothing more about Tao than “he’s a genius”. What’s…
i've said this same thing (on r/math), because it feels like blind hero worship and fetishization, but i got pushback that "it's only human". oh well. most people don't care about the math but only about hero worship and math is just another opportunity.
Re: The Mind of a Mathematician
#23I very much like that people like Tao are famous. It’s relatively good for the intellectual spirit and hopefully it inspires others. However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it. Let’s talk about the awesome work and why it’s awesome. Let’s play through some of it: I’m relatively sure most people know nothing more about Tao than “he’s a genius”. What’s…
For my own mental (and moral) health, I always remind myself to focus on what's published, not the publisher. Too often when I see a cool math result I think, "darn, I wish I published that." Then I realize what that attitude does to me.
Re: The Mind of a Mathematician
#24Can someone explain what the author meant with the following passage? "... Navier-Stokes equations, which govern the flow of fluids, including air currents. In this case, let us hope that it does not have a real-world application."
One of Terry Tao's recent results shows that an equation that he calls the "averaged Navier-Stokes equation" can have solutions that "blow up" in finite time, starting from a perfectly nice initial condition [0]. Presumably the writer is referring to this, as such solutions would not be very nice to have if they are actually physically realizable, for example by an airfoil.
[0] https://terrytao.wordpress.com/2014/02/04/finite-time-blowup...
Re: The Mind of a Mathematician
#25Can someone explain what the author meant with the following passage? "... Navier-Stokes equations, which govern the flow of fluids, including air currents. In this case, let us hope that it does not have a real-world application."
I believe the author might be trying to say, for example, "let's hope water won't blow up." To make this implication, I believe the author meant to refer to "Tao's most fanciful work" rather than the equations themselves.
Re: The Mind of a Mathematician
#26What strikes me the most is the amount of support he received and the people he was able to meet when he was a child. I don't want to dismiss his talent, but this level of support is NOT available to 99%+ of population. His parents have done a wonderful job. To recall my days as an undergraduate at a well-known UK university studying mathematics - large classes (300+) where everyone is disposable, nothing to do but s…
+1, Kudos to the view. I also believe the support matters. There are many overqualified students who cannot skip grades because of the system, Most probably students graduates at the average age of 22-23 and then PHD and research may well take 6-7 years if not skipped, meanwhile the presence of good mentor is also a luck.
Re: The Mind of a Mathematician
#27I would argue that Terrence Tao is overrated. He has solved tons of problems in mathematics, but none groundbreaking.
If you want to argue it, please do so in depth. But don’t post shallow dismissals here.
Re: The Mind of a Mathematician
#28> Yitang Zhang, a mathematician at the University of New Hampshire, proved that there are an infinite number of primes that are separated by, at most, 70 million.
> To date, they have managed to prove that there are an infinite number of primes separated by, at most, 246
I'd like to ask a very noob question. What kind of an approach would give us such an exact upper bound, when primes as a concept (in a layman's intuition) seem abstract and unconcerned with such specific figures?
I hope the question made sense.
Re: The Mind of a Mathematician
#29I very much like that people like Tao are famous. It’s relatively good for the intellectual spirit and hopefully it inspires others. However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it. Let’s talk about the awesome work and why it’s awesome. Let’s play through some of it: I’m relatively sure most people know nothing more about Tao than “he’s a genius”. What’s…
I agree and think that the drippy accolades are actually counter productive. Why? Because it can become discouraging (as opposed to encouraging) to most (what I would consider) 'normal' smart people. It's the equivalent of walking into perhaps a high school dance and seeing a bunch of tall and good looking men (if you are a man) or beautiful, thin and poised women (if you are a woman). It becomes overwhelming in so many ways and intimidating. Now sure that feeling will spur some people on but just the same it will also turn some people off. And good people. [1]
Think of all the people that might think 'wow this is what you get at Princeton'. Of course logically you know that is not the case and that this is a feature on one very special person. But emotionally (more powerful) that is not what the feeling is.
[1] In reverse if you want proof of this point look at all the people that have entered politics and in particular the Presidential race since Trump was elected. People who in years earlier would have been scared off thinking they were not 'smart' enough. These are people who never realized that a President (regardless of what you think about Trump) does not have to know everything as he relies on others who have expertise (in theory).
Re: The Mind of a Mathematician
#30> Yitang Zhang, a mathematician at the University of New Hampshire, proved that there are an infinite number of primes that are separated by, at most, 70 million. > To date, they have managed to prove that there are an infinite number of primes separated by, at most, 246 I'd like to ask a very noob question. What kind of an approach would give us such an exact upper bound, when primes as a concept (in a layman's intu…
Not an expert, and not answer to this exact question, but the video https://www.youtube.com/watch?v=PtsrAw1LR3E
and these slides https://pdfs.semanticscholar.org/41c5/e01cf7e3975efdc5a27f74...
could answer some of your questions.
One way to think about this, without any number theory requirements: if we keep throwing a coin with probability of heads p which is around 1/2 at the beginning, but then keeps decreasing on the rate of log n / n, we would expect (using undergraduate probability theory) that two heads indeed come up very close infinitely many times.
As primes up to n have the frequency of log n / n, this would be enough if the primes behaved like coin flip results. However, that is not the case, as primes are leftovers of some sieve, rather than totally independent and random.
The goal of some of the current methods is to establish a good ``probabilistic'' model of the primes, so that this intuition can be transformed to reality.