Our quantum problem

In 1909, Ernest Rutherford, Hans Geiger and Ernest Marsden took a piece of radium and used it to fire charged particles at a sheet of gold foil.

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Mathematics — Created or Discovered?

Well in some sense, perhaps it's both?  Okay, not really.  But...

First, let's all agree to drop the incredibly egotistical, human centric view of reality — the idea that without the human mind, mathematics would not be present in the universe (quantities and ratios would not exist, periodical orbits and sinusoidal waves: gone, spherical stars and planets would beeee... no idea here).

We've carried this unbelievably inflated view of our importance down through the millennia and have yet to shake it.  (Take the need for an "observer" in the Copenhagen interpretation of quantum mechanics to collapse the "unreal" wave function into reality, for example.  And science scoffs at religions having believed in the geocentric model of the universe?  Reality does not exist without an observer?  That being us?  Let us try get over ourselves, shall we?)

So let me be clear.  Math is discovered.  About this, there can be no rational debate.

However...

I do understand where the "mathematics is created" idea has it roots.  And I offer an analogy which may bring peace between the two camps.

Consider the European exploration of our own world.  Copenhagen nonsense aside, the rest of the globe existed prior to Europeans "discovering" other continents and seas.  This is mathematics — waiting to be discovered.

But to discover and explore these lands requires the creation of an endless array of new tools, techniques, skills, and so forth.  These, in turn, allowed explorers to expand their knowledge of and experience in the newly discovered regions.

And now we have a cycle of discovery of new realms and creation of new tools to explore them and learn more about them, leading to yet more discoveries.

We can take this analogy further with modern space exploration.  Are we not all willing to accept that we can barely imagine what is yet to be discovered "out there", beyond our pale, blue dot in the backwaters of just this one galaxy among billions?  We must be, as we continue to create and advance our set of tools to do so.

Is it not reasonable, therefore, to make the same observations about mathematics?  An infinite subject by its very nature?

Ontological mathematics being the basis of all reality, it is the pinnacle of arrogance for some hairless apes to take credit for the existence of math.  But I suggest that it is reasonable to be quite proud that we have been able to discover mathematics, comprehend some of it, and create tools and techniques to help us further our understanding.

Non-physical Phenomena

“The day science begins to study non-physical phenomena, it will make more progress in one decade than in all the previous centuries of its existence.”

— Nikola Tesla

Given my thoughts on the underlying foundations of reality being ontological mathematics, I was particularly struck by this quote from Tesla.

Ontological mathematics being inherently non-physical, I'd submit for your consideration that this is what would be found should science (mainly quantum physics) ever break free from its habit of doing particularly poor philosophy, and instead let their equations take them into a non-empirical realm of unobservables that rationally must exists

Outlet Needed

And so it begins... finally... I think... Oh, screw it.  We'll see how it goes!

Euler's Identity becomes Unity
when expressed with Tau

In the late 80's,  a young engineering student's love for mathematics came to an abrupt end, essentially destroyed during a course in linear algebra and differential equations by a professor disinterested in the actual teaching of the subject— droning on and on in an almost unintelligibly thick, monotone German accent with no care whatsoever whether those he taught could comprehend him, let alone the subject at hand.

Mathematics became no more than a tools in the engineer's arsenal.  It was a language of symbols that simply allowed one to construct best estimate models of the world around us.  Applying formulae correctly and making the correct calculations were all that was of importance.  Mathematics was... mundane.