zornthewise

You got the hindu date wrong. The Hindu cosmology actually has scales comparable with what modern cosmology believes.

Sure, the best chess/go players on this planet are not humans anymore and those games are full of novel situations with no known solutions.

For the stacks project, absolutely yes.

While there can be advantages to reading a lot and reading fast, I would also suggest that there is value to reading less (but still consistently) and letting your brain mull things over. Some thoughts really do require time.

Mathematician too. I would say we still don't really know what a set is. ZFC "explains" sets in terms of... axioms and models of them which are also just sets? Should I worry about this recursion? Who knows, we just pretend things work.

I am not pursuing a PhD in pure math so I certainly have both interest and ability in doing academic stuff but I found it incredibly hard to get acceptable grades in high school.

He has spent a large amount of time coordinating and strategizing health care interventions in multiple countries over the last couple of decades. Seems like he would be in a very good position to explain this stuff to the public.

I am one such mathematician.

No comment about the broader picture but there have been very smart people who have quit academia and gone into industry for whatever reason. Maybe the most famous is Jim Simons (he had an exceptional mathematical career before going into finance) but I know a few more examples.

The discussion is really about the Chinese (and American) governments. The US government is really... Not great. See wars in the middle east, spying on its people, military industrial complex, bad environmental record, bad civil rights record and all of these are ongoing problems. I dont think the US government is any better than the Chinese government. They have been responsible for so much instability in the world in the middle east, Africa, south asia and south America even if we just want to focus on how they treat people.

You can get them in mobile for like a dollar each and they are just as good if my memory is anything to go by!

This is one of the best interviews I have ever seen. The interviewer is really good and some of the stories are amazing.

No, for any practical applications, we might as well work assume it is true, the same way we assume quantum physics or relativity are true when building stuff.

Can you define precisely what you mean by random in this context?

A very approximate proxy might be pets.

You are correct, group theory did start with the permutations of roots of polynomials. In the other hand, the modern perspective is to consider these groups as coming from geometry (the etale fundamental group point of view) and is really a very successful theory.

I think it is generally useful to try and give a geometric interpretation to whatever we are interested in and groups certainly benefit from such an approach.

Moreover, the groups relevant to physics are very geometric things (they are literally spaces in the sense that the real number line is a space ) and the geometry plays a large role in these groups.

In fact I am struggling to think of an application of groups to mathematics where geometry does not come into play.

Even the abstract classification of finite simple groups uses ideas from geometry on a very crucial way (representation theory).

Maybe this is not the right forum but my lichess app has a big where if I am watching a chess game on it, the pieces sometimes disappear or change position. It's been going on for a while but seems to game gotten worse recently. It seems to be triggered by going to the watch games tab, then switching apps and coming back.

You have to keep in mind that gaming is a very new medium. The more artistic variety of games has only been around for a few years. To demand something on the level of Shakespeare is very disingenuous.

A better way of seeing why games can be art is through a comparison to movies. Games can be made to essentially be movies but with the crucial difference of immersing the viewer entirely into the world through the choices it presents.

I do not see how adding more possibilities to an existing art form (movies) can ever demote something from art to non art (whatever you think these things mean).

I think a game like last of us is a great exploration of the potential of this form of game play.

Well, P/NP really has almost no bearing on this problem. That is a theoretical problem and even if P=NP, the algorithm could have a ginormous constant or degree. Conversely even if P=/=NP, the problem might be very easy to solve at human timescales with advanced enough algorithms/processing speed.

I don't think most people intentionally do this. It just makes someone look smart if they proclaim things confidently and so they do it. I try to be as honest as possible when communicating and I have caught myself sometimes stating things with more confidence than I had. I think it might just be part of how humans communicate...

It's a specific term in chess like castling or checkmate.

The black knight plays for black.

I found in on mathoverflow in one of the comments posted by a prominent mathematician not featured in the interviews.

There are sixteen interviews each of them about 18 pages long. The interviewers are really good and the answers are long and detailed and reveal a lot about how universities have changed over the last century among other things.

They might be able to save up money and get more efficient hardware that eventually beats the science/electricity cost of distributed computing.

The simple idea is that while linear maps(matrices) are generally a combination of rotations, scaling and other stuff in higher dimensions, sometimes they will act on a vector simply by scaling it.

Since scaling is a really easy operation to understand, the space generated by these vectors will be really easy to understand. Note that different vectors can be scaled by different amounts.

Now it often turns out that the space generated like this is actually the whole of the space under consideration and this really simplifies the linear map we started with. Hope that helps.

My reading of Feynman is a little different: I think the point is that philosophy of science has only analysed history so far and has never by itself brought about a change in the way science is done.

This is not to say that the philosophy is useless or that it will never influence science in the future - Feynman is just stating how things have been.

Put another way, I simply don't see philosophy of science as it is helping someone do better science. I would be very interested if this were false.

This is just something I thought of and I am not sure if this makes sense but mathematicians explore objects much in the same way particle physicists do. So the physicists bounces particles off each other and see what happens to understand how these particles work.

Similarly, mathematicians study objects by looking how they act on other objects. So if it turns out that two differently defined objects have the same actions on other objects, we call them isomorphic and don't really distinguish between them.

So for instance, we say that the set of rigid motions that preserve the triangle and it's orientation is the same as the set of permutations of the roots of say: x^3-3x+1 even if the two sets are absolutely not defined in the same way.

Hope that makes some sense.

From that point of view, the interesting thing would then be why this particular abstraction layer works well which is what linear algebra answers.

This is in some sense the process all math students go through. The formulas for computing determinant and multiplying matrices look really complicated and it feels like a mystery as to why it works at all but then linear algebra explains all of that slowly.

I have no idea about physics but Noether(with Artin) certainly changed the mathematical landscape. She was probably the first person to really do modern algebra(building on Dedekind) and is the first person whose works really seem modern.