Mathematics: Invention or Natural Phenomenon?

wayneh

Joined Sep 9, 2010
17,498
No idea, but worth the search. It directly takes on the title (of this thread) subject, which I find fascinating. I'm pretty sure the RadioLab show did a segment on the topic as well.
 

tcmtech

Joined Nov 4, 2013
2,867
May I suggest you request the assistance of @@Hypatia's Protege to help you with your.... errr.... diction impediment ? :p
I went to public school and graduated 22 years ago. You should be thrilled that I can even type and that I show the decency of running things through spell check. :oops:

As far as math skills go my high school math teacher was a dumb drunk who really didn't like me. I bumped into him about 10 years ago and it was like watching a war vet have a bad flashback when he realized who I was. :D

I would say I was surprised but by then I had already had similar experiences with other former teachers having had reacting like that and to be honest I sort of take reactions like that from people who I didn't see eye to eye with in school as a sort of complement!. :D
 

#12

Joined Nov 30, 2010
18,224
I bumped into him about 10 years ago and it was like watching a war vet have a bad flashback when he realized who I was. :D
And there is probably the largest difference between you and me. You terrorized the lame teaching staff. I was much too lazy to do that. Still, I don't object to your method.
 

tcmtech

Joined Nov 4, 2013
2,867
I never felt I was terrorizing.:D

I however had no problem pointing out when our textbooks were wrong and when someone was clearly not capable of performing their job properly which to that effect the way I always saw it was if you want to slack off in your job then by all means you had better let me do it too and not ride my butt for not doing my work to the fullest of my capability. It's only fair.

BTW we honestly had some really crappy math books which didn't help things. :mad:
 

#12

Joined Nov 30, 2010
18,224
And I had a chemistry teacher that said, "electrons don't have mass". :D
Maybe that is close enough for chemistry, but the important part (to me) is that I had the good sense not to antagonize him.
 

cmartinez

Joined Jan 17, 2007
8,253
And I had a chemistry teacher that said, "electrons don't have mass". :D
Maybe that is close enough for chemistry, but the important part (to me) is that I had the good sense not to antagonize him.
It's called "challenging the experts" dude... :D
 

darrough

Joined Jan 18, 2015
86
Historically mathematicians believed they were discovering an absolute truth. It was a "discovery" because it was a description of reality, like a natural law. Euclid's geometry was the gold standard in this regard.

In the early 1800's certain mathematicians, such Lobachevsky, Bolyai, Riemann and Poincaré discovered that they could take alternative versions of the parallel postulate that were contradictory to the parallel postulate and create valid mathematical systems. Now, natural laws are consistent throughout time and space. They are absolute truths. The parallel postulate then could not be a natural law or an absolute truth, since contradictory versions of it still give mathematical systems.

Over the course of a century mathematicians came to see that mathematics is separate from reality. It is the logical conclusions (called theorems) derived from a set of axioms that the mathematician "invented". The art of mathematics is in inventing axioms so that the resulting theorems are plentiful. The final nail in the coffin was delivered by Godel, who showed that there cannot be a mathematical system where every statement that is true is also provable. Physicists are still looking for a grand unified theory, but mathematicians have by and large accepted that there is no grand unified mathematical system.

I know that this is the message that students of mathematics will get at college, or at least it was in the 80's. It was repeatedly explained that this or that axiom was the correct choice because it made the system richer. At first this sounds odd and illogical, like when biology professors personify nature. But with time, one becomes quite comfortable with it.

However, thanks to studiot and cmartinez, I recently learned that the "discovery" school has risen from the dead. Physicist Max Tegmark has created the Mathematical Universe Hypothesis, which claims that "All structures that exist mathematically also exist physically".

If you want to know more, Wikipedia has a good article.

http://en.wikipedia.org/wiki/Philosophy_of_mathematics
 
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