First, what mathematical calculations?
I learned it the hard way when by the first time I proposed an graduate course on Quality at the IMECC at Unicamp, which is basically state of the art as it is possible in my country, Brazil. Professors there typically graduate from MIT of UCLA or some equivalent in Europe.
You have “pure math”, and “applied math”, which, before defining it, it must be said that pure mathematicians do it for the enjoyment of it. Something similar to what poets do. And many of them consider applied mathematics some sort of profane or defiling act, if not foul, as it became very clear to me in my first interaction with IMECC.
On top of that pure math has a tradition of discovering things that seem at the moment of discovery useless and after 50 to 200 years become a must of some kind of applied science or technology.
So, it is a very loaded subject to deal with.
Doing applied math means that you are trying to solve real-world problems by applying mathematics.
Pure math means developing mathematics without an application in mind. Although probably there are no applications yet, they might come up with.
There is a tendency from unwary people to consider pure mathematics useless, what, with the whole picture in mind is not the case.
There is a lot of quarel about the relationship of computers and mathematics, pure or applied.
You do not have to understand at all how a computer works or major in computer science. Simply because it is humanly impossible to deal with the amount of information embedded in a computer as a machine.
You simply have to know how to transform your mathematical idea into some kind of alghoritm and how do program it tol feed it to a computer.
Nowadays, Alghoritm Research became Advanced Mathematics… and what was once Advanced Mathematics became Elementary Mathematics…
One big issue I see is that there is a tendency to hide real world problems with unpronounceble names, such as, for instance, if you are interested in how light is reflecting off some object and how the objects affects it, you eventually will come up with “Blinn-Phong shading to sub-surface scattering and also the many variants of Ambient Occlusions” if you are interested in smooth, realistic shadows in graphics. To explain that crap will take eventually hours not to mention actually reading and understanding it.
Another example, in Financial technology, or fintech, if you are given a finite amount of data and not being able to completely predict the future, in order to find ways to predict the market you may use “generalized autoregressive conditional heteroskedasticity models or GARCH models”.
At the end of the day, after working in IBM for 22, mostly in developing, manufacturing and supporting mainframes, it seems to me that:
- We think mathematically about the world, or reality if you take in consideration also the world we have within us, because the natural world, specially the one outside of us, presents to our mind, or brains, that is an accurate and truthful way to figure it out. We do it specially under one capability of our brain or mind which is generally named logically or with rationality. From that you can fairly assume that all of mathematics is the reflex of the reflex in our mind of the natural world or the world inside of us.
- But the world is neither rational or irrational. It defies understanding with the equipment we are able to have to try it. As an example, take Newton Physics, Relativity and Quantum Mechanics. Each one perfectly explained mathematically, but destroying what was accepted by the other. This will go on and on, simply because the mathematics involved reflected in our minds about the reflex or reality does not reflect it as it really is. We were built or developed in such a fashion that this will never happen.
- Bottom line is that the real world or the reality we are stuck with does not proceed mathematically. The mathematical structures we conceive are not capable of expressing paradoxes or come up with some reasonable way to tackle time, distance and above all, size.
- What the world we live in is, inside or outside, is a mystery yet to be solved if it ever will.
- This doesn’t mean that the fact that Math is a reflex makes it useless. If you leave out all the glamour and complication to the average mind it has, you end up with a powerful tool and decision maker our human nature can provide in most cases. But you have to use it with wisdom, which is a human nature only capability.
- The landing procedures explained at the introduction of this topic is the perfect example. If you ad to it real world math, where most often it is applied to what economists call “expected costs”, when you try to figure out what is the cost of some risk and what chance that if will happen is the issue, you have a very good figure of what mathematics and the computers are all about.