What is mathematics?
Math is changing. Since the computer revolution, a new image of the subject is gaining acceptance: the study of space-time patterns. Dynamic math is outpacing the static concepts established by the ancients. Presently th main branches are usually listed as: arithmetic, geometry, algebra, and dynamics (aka analysis). Sometimes logic, topology, chaos theory, and others, are listed as well. We may refer to the branches by the code: RGADX (mnemonically, argadix) for arithmetic, geometry, algebra, dynamics, and chaos theory.
How did math evolve?
Math has evolved in giant steps since the development of language by our ancestors. Math may be older than speech. In fact, it is even possible that speech evolved from mathematics. More recently, the larger steps in the evolution of math have coincided with the major transformations of world cultural history, as noted by Thompson in his book, Pacific Shift:
When a new one comes to the fore, the earlier ones continue.
- R/G, ancient greece, 600 BCE
- G/A, early islam, 800 CE
- A/D, newton and leibniz, enlightenment, 1660
- D/X, atomic, computer, etc, 1945 or 1972
What is arithmetic?
Arithmetic is all about number, counting, order, etc. It is ancient but still evolving, albeit slowly, eg, finding more primes.
What is geometry?
Geometry is the study of spatial (static) patterns such as triangles, circles, cubes, pyramids, etc. This ancient branch of math is still evolving, eg, noneuclidean geom, 1750, fractal geometry, 1972.
What is algebra?
Algebra is an extension of arithmetic dealing with the solution of equations. Geometric algebra is an intermediate step in which geometrical consstructions are used to solve equations.
What is dynamics?
Dynamics deals with the analysis of motion in terms of distance, velocity, acceleration, and so on. In its recent development there is an emphasis on the so called qualitative theory, and the long term behavior: where will this moving system end up?
What is chaos theory?
Chaos theory is a further development of qualitative dynamics, in which the long term behavior is chaotic, that is, not fixed nor periodic.
Why do we learn RGA in school but not DX?
All are useful in daily life as well as in scientific professions. RG were established in the classical tradition as part of the quadrivium, A arrived in middle ages and became part of the traditional school program in the renaissance. D is relatively new, was for college seniors in my parents time, and has now descended to high school in europe, and early college in USA. X has just arrrived into popular consciousness in the past decade, and has yet to make a dent on most schools, but we are working on it.
How have computers changed things?
Computers have radically changed the way math is done and taught, and new knowledge found, esp in X.