Math

Three Arithmetic Essentials. Questionable.

One of the three R’s. ‘Rythmatic,’ aka math. Fundamental. Essential in national standards.

Let’s take a look at three of the mathematical essentials and the “godfathers" of the subject:

  • Euclid- Geometry

  • Pythagoras- Theorem

  • Algebra- (Muhammad ibn Musa al Khwarizmi)______________________________________________________________________

Euclid: “Father of Geometry” 300 BCE

Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in  the history of mathematics.

Geometry is required in nearly every state in the US. “Required for its real-world application.” A gateway for higher math. Included in all standardized testing making it “vital” for the ACT and SAT.

“The theorems obtained via deduction by Euclid remain

fundamental to the study of geometry, and for this reason the geometry studied in school is,” well, Fundamental.

National Assessment for Educational Progress, Page 28.

Page 28  in the NAEP, if read, is rhetorical gobbledygook. One page goes on and on about Euclid and the importance of ‘real world’ thinking, and not much else of substance. Yet the teaching of Euclid is mandatory. Essential (is the repetitive word).

One question. How often do we refer to Euclid in the real world? Ok, two questions- how often do we really use Euclidean Geometry on a day to day basis. One could argue its usage, but is it really essential?

Euclid. Fundamental, as in “serving as an original or generating source.”

And what do we know about Euclid?

13 Books called Elements.

Conic Sections.

Optics.

  • “Other than that, nothing else is known for certain.”

  • Euclid, all of uncertain historicity, which "picture him as a kindly and gentle old man” is completely unverifiable.

  • Origin stories, Most scholars consider them of dubious authenticity.

So, essentially the time spent learning real-world concepts in Euclidian Geometry- Concepts of essential proportions as original and mandatory, are unknown.

Not that the math itself is flawed. On the contrary. It is perfect, math and geometry are a most beautiful language. The teaching of it is not.

Pythagoras: The Pythagorean Theorem 570 BCE

By grade 8, “students should be able to use the Pythagorean theorem to solve problems in two- dimensional situations.”

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: a squared plus b squared equals c squared.

Yea, we are taught the theorem, but what about Pythagoras?

“Known as the Lover of Wisdom,”

Numerology enthusiast.

Believed in the “transmigration of Souls”. Musica universalis- math of the planets.

A Vegetarian.

Had students sworn to secrecy due to the political and economic perversion of mathematics (assumed).

Lived a communal, ascetic lifestyle. Conflicted with followers of democracy.  Had meeting house burned. Unknown death- fled or fire.

  • “Other than that, nothing else is known for certain.”

  • No authentic writings of Pythagoras survived; and almost nothing is known for certain about the life of Pythagoras.

  • Sources are ambiguous and satirical.

  • “There is not a single detail in the life of Pythagoras that stands uncontradicted.” Walter Burkert 1972.

Algebra: Muhammad ibn Musa al- Khwarizmi  C. 780-850

Algebra is a branch of mathematics that deals with abstract systems and the manipulation of expressions within those systems.

Elementary algebra is the main form of algebra taught in schools. It examines mathematical statements using variables for unspecified values and seeks to determine for which values the statements are true.

What’s that now?

Abstract. Manipulation of the system. Truth.

Algebra. Originally meaning:

“a reuniting of broken bones.”

  • Around 820 CE, he was appointed as the astronomer and head of the library of the House of Wisdom and a follower of Zoroastrians.

  • Few details of al-Khwārizmī's life are known with certainty

  • Series of errors concerning the personality of al-Khwārizmī, occasionally even the origins of his knowledge, had not been made.

For such essential learnings based on facts- seem to get diluted upon a “deeper dive” into the why we are learning math.