"If in others sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics." - Roger Bacon

So this thread is all about the studies of mathematics. It is the study of its history and the individuals who contributed to it.

Let us begin..

2 + 2 =

Sakuntala Devi from India. A real mathematical genius.
Just for the display of her talent once she was given a randomly written 102 digit number and was asked to find its 31st root she managed to find it out in 55 seconds where as the most advanced of the super computers at her time took 1 complete minute to solve the same problem. Crazy stuff. She wasn't a savant either, just a bad ass.

Truly amazing!

"Compound interest is the most powerful force in the universe." - Albert Einstein

a² + b² = c²

Oh Oh Oh OH! 4

Hippasus, a disciple of Pythagoras, showed that the diagonal of a unit square was incommensurable with its (unit-length) edge: in other words he proved there was no existing (rational) number that accurately depicts the proportion of the diagonal of the unit square to its edge. This caused a significant re-evaluation of Greek philosophy of mathematics. According to legend, fellow Pythagoreans were so traumatised by this discovery that they murdered Hippasus to stop him from spreading his heretical idea.

Yep I can imagine. Unfortunately many mathematicians would be sentenced to death. A lot of these discoveries were too difficult for people to comprehend and they upset the natural balance or what the perception of the natural balance was at the time so it was easier to imprison or kill people.

Is mathematics a construct of the human mind or is it evidence of intrinsic properties of physical reality?

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? -- Albert Einstein

"as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." Albert Einstein

Then later once it became accepted in the sect members who revealed this amazing secret where hunted down and killed, usually by drowning.

Yes math has to be a construct of the human mind!

I mean at this moment billions of miles away on another planet a different life form probably has a different way of doing math

Something utterly unimaginable that we don't understand.

Sometimes I wonder if their math gives formulas on how to create warp drive engines or information on how to create space flight?

Okay enough imagination flowing through my head. Time for dinner!

y=mx+b

To begin with I'm truly baffled why Einstein would say that mathematics a product of human thought which is independent of experience. The history of Mathematical thought simply doesn't agree with this view at all.

As to the question, "Is mathematics a construct of the human mind or is it evidence of intrinsic properties of physical reality?"

Modern mathematics is currently a combination both!

Smiless posted:


That's partially true, and partially false.

This is because our current modern mathematics is partially invented and partially reflects the intrinsic properties of the universe.

So the aliens would agree with that parts we got RIGHT, and may very well disagree with the parts we are WRONG.

I can even point to which parts we got right and which parts we got wrong. In fact, I REALLY need to write a book on that very topic.

pi*R squared

If A equals success, then the formula is: A = X + Y + Z. X is work. Y is play. Z is keep your mouth shut. ~ Albert Einstein

Mathematics itself IS a human construct.

The relationships that math is built upon are intrinsic.


What Einstein meant was that math exists in a pure form which is NOT necessarily relevant to reality.

This can be illustrated and has been.




The physical world gives rise to minds, but only a small subset of what exists in the physical world has a mind. Minds can discover relationships and create mathematics, but only a small part of the imagined mental world deals with math. Just the same only a small part of the imagined platonic mathematical world relates to the physical world; there are many more mathematical models that do not exist in nature, then do . . .



Math allows exact answers, the real world tends to be about approximations.

tag

Well, the whole idea of a Platonic Mathematical World is a belief that has no more validity than any other mythology.

The very assumption that such a perfect world of abstract mathematics actually exists is the fallacy.

In truth, pure abstract mathematics is necessarily logically incomplete and ultimately inconsistent. In fact, Kurt Gödel was the mathematician who proved this to be the case.

Actually there is another model that can be constructed without using Plato's Mathematical delusions.



In fact, I'm kind of surprise at you Jeremy for embracing Plato's entirely fabricated and imagined "mind of God"

Why do we need to invent that?

The world gives rise to mind. Mind contemplates the world.

Where does this supposedly pure divine mathematics of Plato's exist if not within our own minds?

I totally disagree with Plato's ancient archaic view.

So I don't buy it.

Unless you can give me some reason to believe that mathematics actually exists outside of both the physical universe AND the minds of men.

But if you can do that then won't you have just proven that the mind of God exists?

I see no reason to believe in any make-believe Platonic world of Pure Mathematics. I personally believe that ALL mathematics arises from the physical universe. Even the math that doesn't readily appear to map back onto it.

In fact, I would also hold that any mathematics that cannot be mapped back onto the universe is necessarily FALSE mathematics. It's simply wrong.

We can dream up pink elephants too. Does that make them true?

If we have a mathematical ideas (or relationship) that cannot be made to work in the real world, can we truly say that they are anymore valid than a pink elephant?

You're first thought might be to point to mathematics of dimenions higher than three.

However, I would argue several things on that point.

1. We haven't truly established the dimensions of the universe for sure yet.

2. Often times higher dimensional mathematics can actually be understood using multiple sets of lower dimensions.

I'm not going to get into actual mathematical examples, but the need for imaginary numbers to properly describe the behavior of electromagnetism should be somewhat illuminating on this point (no pun intended).

In short, I totally reject Plato's "Pure Mathematical World".

That's truly no different from a religious concept that isn't even required actually.

We only need two things. The physical world, and our mind.

Making up a third ficticious entity is pure baloney, IMHO.

As seems to be typical you have taken it far past anything I intended.

The diagram does represent the concepts accurately, and to understand the meaning does not mean to accept the notion of a platonic reality that actually exists.

Concepts can be only mental, there does not have to be a separate reality.

This is a great example of baggage that gets added later taking a great idea and trashing it . . . .

The Diagram does not represent that at all . . . if you take just the diagram and not all the woowoo plato blather of an actual world where things are perfect in form and absolute then it makes perfect sense, from the physical world spawns minds which think up things which may not exist in the physical world.
Sure that's just it, its not about where the math comes from . . that's a stupid question, its what it represents.

Math CAN and often does represent things that DO NOT exist in this reality, is it possible there exists a reality where those models represent the reality there . . . sure and thus the diagram is accurate, just don't tag absolutist baggage to it . . .


_______________________________
PS Abra.

Anytime you find yourself surprised at me . . . think about it, and try to ask yourself if what you think I am saying is really what I am saying, or have said. So far every time its not been the same.

So what we have correct would be considered absolute correct for a alien no matter how different their math would be is what you are saying James?

I guess that would make sense since math is often referred in many instances absolute correct for us anyway.


They would just do the math different to come to the same conclusion or maybe have math we have not discovered yet.

I am sure there is more math to be discovered. This couldn't be the end right?

That is if there are any aliens out there, which would be ironic if there wasn't anything else living in all these universes, but everything is possible I suppose.