jgill

There may be a whole spectrum of attitudes and reasons for extreme sports. Certainly, there is the exhilaration of substantial risk in some of them. I...

It makes me a bit uneasy when I read this sort of thing about extreme sports. It's similar to the Simone Biles' thread where everyone except a gymnast...

Will the Taliban allow refugees to flee the country once it is in power?

A circle and a square are topologically equivalent. In a sense they are the same collection of points, deformed continuously from one to the other. So...

From a retired mathematician who still dabbles with it, when I work on convergence theory in a dynamical system in the complex plane I always demonstr...

You make it sound attractive, but democracies are messy and making and moving on decisions can be ordeals. Look at the problems with the infrastructur...

Eudoxus (370 BC) laid the foundations for integral calculus by approximating areas and volumes by breaking them up into an infinite number of division...

In mathematics an example of a two dimensional manifold is a sphere. Each point on the sphere is approximated by a flat plane (very small). As we stan...

Being full of hot air makes that possible. Be sure to tether yourself to the living room floor. :cool:

If I had my druthers I would have high school math teachers end with a decent introductory course in analytic geometry, rather than do what they might...

Would you expand on this or provide links?

From CNN, Elle Reeve: When I get up from a chair too quickly I experience a moment of wooziness. I suppose I am mentally ill. Or maybe I have a mental...

Reasonable abstract models would be welcome. Comparing Simone's "twisty" problem with the Blitz in England during WWII? (I suspect this was satire). A...

From Wikipedia: Where does physics end and math begin? Lots of unknowns here.

An entire thread of clueless babble. Lots of armchair athletes here. :roll:

It's not "mental health" the way you may think. I was a gymnast many, many years ago and recall how little glitches can occur in complicated routines....

Me too. Good post.

Philosophy costs nothing. And is "worth" nothing. Sad but true. Ditto for lots of mathematics. :sad:

(converging sequences of partial sums: S(n)= a(1)+a(2)+a(3)+...+a(n) -> S, or a(n)->0 fast enough) It's nit-picking, but there are several "summabilit...

I can find only two papers, neither related to this topic. If he taught at a community college it might have been difficult to do research and publish...

A moderator should speak up and explain.

Campus or departmental politics regarding subject matter and its relative "importance" can depend upon current interests of the faculty - and grant mo...

Yes, of course. But even the notion of addition was expanded in 1801 when Gauss introduced the modern concept of modular arithmetic. As formalized, th...

Depends on what you refer to as "rules of math". For instance, the Law of the Excluded Middle is useful in traditional or standard math, but not allow...

Interesting to see what PhD theses in philosophy look like. The ongoing search for originality.

But one left on the ground while math, like Buzz Lightyear, has gone "To infinity and beyond ! "

If one doesn't wander into transfinite math, Choice is not necessarily required. A finite dimensional vector space doesn't require it for a basis. And...

Take heart, MU. You may think yourself alone and ridiculed, but you have only to find the Yellow brick Road and follow it to Emerald City where your i...

In mathematics there are "wandering sets" where points wander off under iteration. The same can be said of threads in which someone goes off on a tang...

Out of curiosity, did you know my old high school friend Zach Hall? He created a department of neurobiology at UCSF in the 1970s.

Here's a counterpart of this idea in mathematics. (1) is called left composition or outer composition, and (2) is called right composition or inner co...

Good! Glad to hear. :cool:

I agree. It's nonsense. Regress means going backward. I am more than familiar with these notions, as I investigate dynamical processes going forward a...

Fishfry and Tones have far better grasps than me of the logic and set theoretic aspects of this subject. I just like the observation that naive set th...

The late George Simmons taught at Colorado College, not far from where I live. He is a marvelous author, and his Introduction to Topology and Modern A...

Now, where were we? :chin:

At first I thought these ideas nonsense, but upon further reading, noting that nothing done here likely disturbs the course of mathematics as it is no...

In doing math research, one frequently uses previous results (theorems or axioms) to verify steps in logical arguments. And sometimes actual numerical...

By computation do you mean reasoning?

That's the world that MU lives in. :roll:

Grow older. At my current age it seems five minutes passes in a minute.

How can one argue about this? It is so silly. :lol:

For most mathematicians proof is separate from computation. But one can go down the rabbit hole of computerized proofs if one is so inclined. For me, ...

I know what you mean. Stay put and let the world come to you. I admire your convoluted reasoning. Oh wait. Those coming to you will drive or walk, so ...

Mathematics earns meaning through use.

Au contraire, over many years I have found that computation enriches and supports concepts. :roll:

I'm missing your point also. What's your gripe about the innocuous Riemann sphere? :chin:

That could be true if the first marriage is to a high school flame. Sometimes, no matter where one goes in life that emotional fire still quietly smol...

That certainly lets the USSR and the CCP off the hook. Marxists thank you! :smile:

Certainly a balanced account of history is desirable. But is that possible these days in the USA?