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Mathematician Keith Devlin writes about how the capabilities to work with maths have changed since the late 1960s. He summarizes what he considers to be the essential skills and knowledge that people can focus on as more and more is turned over to software.
The shift began with the introduction of the digital arithmetic calculator in the 1960s, which rendered obsolete the need for humans to master the ancient art of mental arithmetical calculation. Over the succeeding decades, the scope of algorithms developed to perform mathematical procedures steadily expanded, culminating in the creation of desktop and cloud-based mathematical computation systems that can execute pretty well any mathematical procedure, solving—accurately and in a fraction of a second—any mathematical problem formulated with sufficient precision (a bar that allows in all the exam questions I and any other math student faced throughout our entire school and university careers).
So what, then, remains in mathematics that people need to master? The answer is, the set of skills required to make effective use of those powerful new (procedural) mathematical tools we can access from our smartphone. Whereas it used to be the case that humans had to master the computational skills required to carry out various mathematical procedures (adding and multiplying numbers, inverting matrices, solving polynomial equations, differentiating analytic functions, solving differential equations, etc.), what is required today is a sufficiently deep understanding of all those procedures, and the underlying concepts they are built on, in order to know when, and how, to use those digitally-implemented tools effectively, productively, and safely.
Source : What Scientific Term or Concept Ought to be More Widely Known?
(Score: 4, Insightful) by MichaelDavidCrawford on Monday February 05 2018, @07:16AM (3 children)
I first heard about it when I was in graduate school. But some special cases of Noether's Theorem are so easy to prove that I fail to understand why it's not taught to Freshman, if not high school students.
It's simply this:
Every symmetry implies a conservation law.
For example of you rotate an object around an axis it eventually returns to its original position. From just that and that alone one can derive the conservation of angular momentum.
Einstein said her theorem was "quite deep".
Yes I Have No Bananas. [gofundme.com]
(Score: 0) by Anonymous Coward on Monday February 05 2018, @09:43AM (1 child)
That is wrong. You know, with a physical pendulum (the one going vertically in a circle), it is also true that it returns to its original position after rotation around its movement axis. But its angular momentum around this axis is very decidedly not conserved (at low enough energy it even changes direction periodically!)
(Score: 2) by PiMuNu on Monday February 05 2018, @03:03PM
I believe the correct formulation is that isotropy (same in all directions) implies conservation of angular momentum. Obviously, gravity in this example is anisotropic, i.e. it pulls down. AC probably already knows this.
(Score: 3, Informative) by deadstick on Monday February 05 2018, @01:13PM
This set of MIT lectures on quantum physics goes into some detail on Noether's Theorem: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-videos/ [mit.edu]