Would this thread be considered good physics or bad physics? I can't tell because its a foreign language for me. :chin:

Taxpayer here. Make math, not war — fishfry

Math maker here. Where the hell is my tax refund!! :confused:

Since I last checked 137 math papers have been uploaded to ArXiv. The rate of research in math is staggering, as are the number of specialized topics. It looks like algebra and its offshoots account for about 26% of the total. Only 2% in complex variable theory, my general area, outdone by logic/set theory/p-s topology/formal math - one category - which comes in at 2.13%. How much of that is foundations is difficult to ascertain. Even in CV theory its hard for me to understand many of the titles.

I hope taxpayers are not footing the bill for most of this activity - much of it just intellectual exercises useful for academic promotion, prestige, etc. I've been on grants before and even at the time felt it was not a productive use of public monies. :brow:

Is this analytical geometry? — Daniel

No. Limits don't usually arise in the elementary aspects of the discipline. But boundedness certainly exists for figures like circles and ellipses. However, a parabola is unbounded in the plane. Does a circle in the plane occupy space in the plane? How about a circular disc in the plane?

Analysis at arXiv runs about 25% of the papers in math in May. Foundations 2.13%. Surprisingly, topology runs only 3%. Algebra and its offshoots looks like it dominates.

The American Philosophical Society doesn't seem to separate PhD areas, so its hard to estimate how many are in math.

It's natural that on a philosophy forum discussions of mathematics will mostly lie within the intersection of philosophy and math. I've mentioned in the past that most mathematicians are not heavily involved with foundations, a speculation on my part stemming from my career. It's really hard to pin down exact figures but from the AMS site it would seem that very few degrees from math departments are in foundations, set theory, logic, etc. The 2017-18 stats show that, of 1,960 PhDs, 7% were in a grouping of discrete math, combinatorics, logic, and CS. So that perhaps 3% might have been in foundations, a guess.

Philosophy departments sometimes grant degrees in the philosophy of mathematics, and I don't have any figures there, beyond the figure of 477 total PhDs in philosophy in 2018. Also, CS departments might get deeply into foundations of math. Another glimpse into stats is papers submitted to ArXiv.org, and looking at May it would appear about 2.13% of papers in math were in logic or foundations, out of 1,505 papers submitted. My area(s) - Complex Variables and Dynamic Systems - account for about 8%.

I looked this info up out of curiosity. You may or may not find it of interest. :cool:

This must be related — fishfry

It's notation for an infinite composition like . . . g3(g2(g1(z))). Ultimately the result comes from the structure of functional equations.

which, if I counted correctly, can be expressed in exactly 15 symbols. — fishfry

That probably beats my expansion (for z=1):

$ArcTan(z)=\underset{k=1}{\overset{\infty }{\mathop L}}\,\frac{2z}{1+\sqrt{1+\tfrac{1}{{{4}^{k}}}{{z}^{2}}}}$

You two are going at it, hot an heavy. I'll steal away.

f I understand you correctly, sure, one can feel that one is being religious. I am not disputing that he is accurately describing the way he feels or even views what he does. — TonesInDeepFreeze

I think you are being too literal. I am working on a conjecture right now, as I have on others on and off for fifty years, with a sort of pleasing fervor that could be described more as a religious mood than a purely problem-solving commitment. Its true than mathematicians can be very competitive, even mean spirited at times, and I have been in an unpleasant situation that reeked of it, but exploring math - rather than learning it - is a delight and has its rewards.

so mathematicians will forever be searching for the finite sequence of proofs that are certainly knowable. It's enticing to look for total certainty in your field of study but it can cause problems — Gregory

You are expecting too much of us. We are mere mortals, and few of us commit ourselves to this challenging task.

We can list the essential attributes of religion, and see which of those are attributes of mathematics — TonesInDeepFreeze

No no no. It's what you feel, not what you know. You are thinking like a logician. :gasp:

Some people like to be cheeky like that — TonesInDeepFreeze

Au contraire, he was right!

I don't know what a "set" is, you haven't defined it. — Metaphysician Undercover

In my naivete I once thought of a set as a collection of things called elements. Then I learned the error of my ways. Now I try to avoid thinking of them at all. It's a refreshing experience, like standing at the beach with the soft winds off the ocean caressing your body. :cool:

Mathematics is usually practiced as a Platonic type of religious practice — Gregory

I had a colleague, a fellow math prof, who was a devout Catholic. I once asked him what he thought it was that we do as mathematicians. He said, "We are like priests who practice their faith, it's what we do."

I tried to start a discussion once about what it would mean if all math was wrong and the *opposite* of every equation and theorem was true. — Gregory

That sounds exciting! Sorry I missed it. :lol:

Hmmm. Live and learn. :chin:

Do you think mathematics of the infinite can be done without finite numbers? — Gregory

I don't mess with infinities. Others here do.

. . . but if everything that is real is just infinite sets . . . — Gregory

Whoa! That is quite an assumption. :scream:

Common practice is pretty rigorous once you accept the axioms.

When I gave a mathematical representation of a count. — TonesInDeepFreeze

For your next trick, do one of an earl. :cool:

I'm arguing against accepted mathematical principles — Metaphysician Undercover

How do you feel your campaign is doing?
Has it been worth the struggle?
Have there been casualties?

Are you holding up? :chin:

If you threw something away from you, it would hit you in the back. — noname

In a way this describes this thread. :roll:

What I contend the mathematician is unlikely to do is add the postulate that the probabilities "collapsed" in some sense on the way to the final answer, but rather would just plug in the provided parameters and constraints (i.e. the fundamental constants and whatever values for initial conditions we provide) into the equations and solve for the question. — boethius

That's what I might do. The metaphysics could be fun, though. :cool:

Is it a word game to believe a block of stone has stone outside, and inside, of it as well? Can a thing be hollow and still be a thing? — Don Wade

What of the air inside the garage, inhabiting its space and therefore part of the garage? You open the garage door and the air dissipates as it flows outside the garage. Oh wait, that is part of the garage outside the garage now. As it dissipates further the neighborhood is a former part of your garage. What effect will this have on property values?

These are not just word games — Don Wade

All philosophy arguments are word games. :grin:

This is simply not true. Numbers are defined by quantity, not order. — Metaphysician Undercover

You're failing to distinguish between cardinals and ordinals. — fishfry

MU knows so little of mathematics and yet is so confident. It's almost an admirable trait . . . but not quite.

The point I'm trying to make "when the car is in the garage" the space occupied by the car (while in the garage) - that space is still part of the garage (even though it has a car also in that same space). To me, that means, at that time, both the car and the garage are (in fact) occupying the same space - Not all of the space - just the space where the car is parked — Don Wade

The garage defines the space within it, that space is not part of the garage. The garage door is part of the garage, the cement floor is part of the garage, etc. ff is correct: you are playing a word game.

As has been noted, there are various ways of opening the doors of perception that, once experienced, render philosophy inconsequential. My initial exposure occurred nearly a half century ago, and my first thought was Now I understand the ancient origins of religion. Experience triumphs over reason.

I did some Venn diagrams on a drawing program but haven't worked out how to post it here. — Mark Nyquist

If you become a subscriber ($/month) you can upload images. Otherwise to link them it seems you need a source that is secure.

Encyclopedia Britannica is simplifying and reifying the model more than is necessary. — Enrique

And they should know better! :gasp:

(The good and bad threads should be combined under the rubric, Physics Jabber.)

Is "pure" mathematics, meaning, mathematics that does not apply to the world (via physics, for example), something invented or discovered? — Manuel

Most practicing mathematicians at one time or another spend a short period contemplating this question. Then they move on and do mathematics. My thoughts are that some is invented and some is discovered. For example, I recently "invented" an attractor transform for certain functions. Then I set about trying to discover its features. (of course, it may have been invented before - that happens not infrequently in math)

Some philosophers like to ponder the question you posed. Most math people don't care. :cool:

As usually propositions do not change with layers,
we do not notice this change of layers in our surroundings.

But the layers could be there all the time ... — Trestone

You have developed a personal philosophy based on LL. Congratulations.

The sequence a,b,c,d,e is a sequence of five letters. e is letter five. — jgill

That's an arbitrary designation, dependent on a stipulation that there is a left to right order to the sequence. "a" could just as easily be letter five, or we could assume an ordering which makes any of the letters number five — Metaphysician Undercover

No. I have implied the order of the sequence. It's not arbitrary. A more mathematical format would be
(a,b,c,d,e). This omission may have confused you. :roll:

A physical observer is an objective instrumental observer not a person — magritte

Bingo!

As the article says, "the absolute square of the wave function is interpreted as an actual matter density" — Enrique

Really?

"The square of the wave function, Ψ^2, however, does have physical significance: the probability of finding the particle described by a specific wave function Ψ at a given point and time is proportional to the value of Ψ^2." (Britannica)

mathematics is called the "Queen of the Sciences" — jgill

The 'queen of sciences' used to be theology. — Wayfarer

I was unaware of that, thanks. It was Gauss who coined the phrase I quoted and he is a mathematical deity! :cool:

He also claimed number theory to be the Queen of Mathematics. :roll:

From the Stanford entry: "One way to distinguish between science and religion is the claim that science concerns the natural world, whereas religion concerns both the natural and the supernatural."

That pretty much does it for me. But then I'm not a scientist (although mathematics is called the "Queen of the Sciences", it's not one itself.)

On one day we get for a number n the prime decomposition P1.
One week later we get on the same computer with the same program for n
another prime decomposition P2 (and similar disturbing results with other computers). — Trestone

Why would another prime decomposition, P2, arise if not for a computer implementing this layer logic? Thus, avoid disturbing results by ignoring layer logic.

Sorry. I see things from weary old eyes. :roll:

The sequence a,b,c,d,e is a sequence of five letters. e is letter five.

Imagine not having the pressure of trying to figure everything out, instead, just going with the flow of ideas, allowing them to come and go as do all things — synthesis

Like a leaf in a stream, floating quietly in sluggish waters, but skimming past whirlpools to be on its way, frivolous and ethereal. :cool:

With a closed mind, you will always be wasting your time — synthesis

Good troll thread, eh doctor? :cool:

Possibly because simple ideas like "and" and "or" are defined as type, whereas set theory is not so bizarre. Maybe not.