What is Math?

[Tfbandie]

So what do you guys think of as math?

This was a question posed to me in my 'teaching of math' course, and I was wondering what the general feel was out there. I know it's not really debate, but I think it'll be interesting, and it'll help me better understand my students when I start teaching.

[Em7add11]

A field of study that most teachers don't demonstrate its practical use well enough, often times.

[Xavier]

I think of Math as the understanding of numbers and their application to the "Real World" via modeling, etc...

[HRG_new]

So what do you guys think of as math?

This was a question posed to me in my 'teaching of math' course, and I was wondering what the general feel was out there. I know it's not really debate, but I think it'll be interesting, and it'll help me better understand my students when I start teaching.

I regard math as a curious mixture of total rigor and absolute creativity, of strict reason and aesthetics. Some theorems or disciplines can only be called beautiful, and the mathematician sculpts them out of pure thought like Michelangelo sculpted his David out of marble.

I'm not talking about long division, of course :)

Regards,
HRG.

[Tfbandie]

I regard math as a curious mixture of total rigor and absolute creativity, of strict reason and aesthetics. Some theorems or disciplines can only be called beautiful, and the mathematician sculpts them out of pure thought like Michelangelo sculpted his David out of marble.

I'm not talking about long division, of course :)

Regards,
HRG.

This is very similar to my view. True math to me is in the abstract, it is in the ability to firmly prove things absolutely from a given set of axioms (another tremendous asset of math; the need to recognize all your assumptions to have true rigor). I've seen some spectacular proofs (written a few on well written tests too) and ones I've hated [I can't stand the 'diagonal proof' of real number (o,1) being uncountable]. But it's all good.

But I also see the real life stuff which comes long after the theoretical work, which to me, points to math as an exploration of an ultimate truth. I've seen many examples of mathematicians playign around with theory, only to have the theory serve a vital role hundreds of years later.

But I'm just a math nerd who often spends free time proving or exploring little math ideas, like maximizing volume of box for given SA, or writing algorithm to compute a sum of sequential integers.

And thanks to you other guys as well, because I need to know that the whole world (and particulary my furture studnets) might not be as naturally curious and excited about math., and see it differently in many other senses as well

[TheOneAndOnly]

rue math to me is in the abstract, it is in the ability to firmly prove things absolutely from a given set of axioms (another tremendous asset of math; the need to recognize all your assumptions to have true rigor).

Maths does not require proof. The Babylonians were brilliant mathematicans and had algorithms for solving quadratic equations, but there's no sign they proved any of their algorithms. And even if they did, their proofs would look little like the way we prove statements today.
School children do maths without proving what they're doing is correct. How many school kids can prove that the sum of the angles on any triangle always add up to 180? These kids are certainly doing maths, but they probably don't prove any of the theorems they use.

[Tfbandie]

the children learning basic skills do not always do proofs, but the proofs have been performed and they allow us to use the skills with confidence. And trying to prove a triangle has 180 degrees (or the equivalent, Euclid's V) led to a major revolution in math towards rigor and proofs (as well as opened the door for things such as theory of relativity)

[TheOneAndOnly]

the children learning basic skills do not always do proofs, but the proofs have been performed

hmmm.. then the mere existence of a proof somewhere in the world, or the hope that someone else has proved a theorem, is enough to do maths? Seems quite strange. Most young school kids are oblivious to what a proof is. They happily do maths without needing to prove theorems, propositions and lemmas. Maths is much more than simply proving one result from another. That's when maths gets boring when you simply churn out theorem after theorem.

And trying to prove a triangle has 180 degrees (or the equivalent, Euclid's V) led to a major revolution in math towards rigor and proofs (as well as opened the door for things such as theory of relativity)

I never said proofs were unimportant or redundant, only that they are not requisites to do maths.

[Tfbandie]

see all goes back to the question of what is math? For students very certainly proofs are necesary (though can be extremely insightful) but if taking math as a subject. It all depends on what context, which is why i asked (p.s. thanks for posting )

[TheOneAndOnly]

see all goes back to the question of what is math? For students very certainly proofs are necesary (though can be extremely insightful) but if taking math as a subject. It all depends on what context, which is why i asked (p.s. thanks for posting )

I think any definition of maths has a hard time incorporating the history, the breadth and depth of the subject. Mahts meant a very different thing to the ancient Greeks to what it now means to us. The Egyptians were interested in astronomy and their maths, presumably reflected this. The Greeks were interested, to the point of obsession, in geometry, and in the Pythagorean tradition, in number. Modern maths since the end of the 19th century, can be characterized by being obsessed with set theory.
I wonder whether the ancient Greeks would consider what we do today maths, or some twisted perversion of their art?
SO I think any definition will fall short in covering the whole subject, without being so broad and vague as to be trivial.

[Tfbandie]

I'm fascinated with all that the ancient cultures were able to accomplish as you noted. The greeks with their love of rulerstraight-edge and compass proofs especially. I think on thing all eras of mathematicians would agree would be math as pushing bounds of logic and the mind, I see that present in all the advanced mathematics cultures throughout history

[kofh2u]

Maths does not require proof. The Babylonians were brilliant mathematicans and had algorithms for solving quadratic equations, but there's no sign they proved any of their algorithms. And even if they did, their proofs would look little like the way we prove statements today.
School children do maths without proving what they're doing is correct. How many school kids can prove that the sum of the angles on any triangle always add up to 180? These kids are certainly doing maths, but they probably don't prove any of the theorems they use.

Mathematics is founded upon Twelve Field Postulates.

A postulate is an axiom that can not be proven.

You must tske them on faith if you wish to proceed and descover the power that lies beyond the triad of negative numbers, positive numberd, and zero.

Postulates are "givens" agreed to in the same way philosophers must agree to an unknown but assumable "First Cause."

Therefore, mathematics is a hoise of cards build upon our belief in these twelve postuales. From these 12 field postulate we prove, based on our acquiescence, all the theorms that follow.

However, this mathematics also reflects upon us. How we think. How we make sense of the world which we construct and measure and explain by mathematics. Msth reflects on our own thinking itself.
We also think that there are seven "kinds" of numbers.

We see these numbers as either positive, negative, or zero in each of the seven number systems, N, W, I, Ir, R, Q, C.

Ahmes, thenfirst ever recorded mathematian, an Egyptian, believed numbers were a secret way of reading people's thoughts.. He wrote that numbers, the mathematical use of numbers, was "the secret method by which to know men's minds."

Rene' Descartes went into a shock of a shaman-like trance for 7 days. Emerging, he wrote his now lost book
"The Rules for Reading Men's Minds."

Gen. 1:27 So God, (the theistic Almighty Universal Force), created man (whose facility of mind enabled him to image The Universal Reality, abstractly and mathematically), so created (the external theistic Universal Force), God, him (man, in God's own immanent reflection); male and female created he them.

[Raptor]

So what do you guys think of as math?

The primary cause of agony and despair.

[Tfbandie]

[Raptor]

:bman: