Formal math: based on church myths and superstitions

Many smart alecs ask: what difference would it make if “Euclid” did not exist? They believe the lie about Euclid was told for no reason, and that it persists for no reason in our school texts today which mention “Euclid” 63 times, apart from giving children an image of “Euclid” (all of which makes them believe “Euclid” was real).

It is simple commonsense, however, that a lie is always told for a reason. But the reason in this case is beyond the understanding of our smart alecs. They miss the connection of the “Euclid” myth to church theology.

Our current school texts teach children the false history that “Greeks” did mathematics in some superior way which they must imitate. The myth goes that “Euclid” gave “irrefragrable proofs”, by using the axiomatic method. For this purpose, he supposedly arranged the theorems in a particular order.

Cambridge foolishness about “Euclid”

Cambridge University, a church institution, subscribed to this myth. As pointed out in this exhibit, it initially adhered to the practice of blind imitation of “Euclid’s” Elements. Then the Cambridge Special Board for Mathematics in its Report on Geometrical Teaching dated 10 May 1887 declared the proofs in “Euclid” need not be blindly imitated but the order of theorems in the Elements must be followed. On 8 March 1888 this was adopted by the Cambridge Senate as part of the amended regulations for the Previous examination.

This move by Cambridge University to “reform” mathematics teaching was excessively foolish. Thus,   while the book Elements has axioms and proofs, the simple fact is that it has no axiomatic proofs, as today understood in formal mathematics. Specifically, the first and fourth (SAS) proposition of the Elements have empirical proofs, and a chain is only as strong as its weakest link. (See, the detailed grievance against the NCERT.) If empirical proofs are admitted in one place, the order of the theorems becomes irrelevant, because the “Pythagorean theorem”, for example, can be proved in one empirical step, as was done in India. But the dons of Cambridge University failed to understand this, and made exam regulations based on their botched understanding.

Axioms but no axiomatic proofs in the Elements

The belief in axiomatic proofs in the Elements comes only from the “Euclid” myth not from a reading of the actual book, which our smart alecs never read. Even the dons of Cambridge University had not read it carefully from 1125 (when the book first came to Europe) until 1887. This Cambridge foolishness in mathematics, driven by the Euclid myth, easily exceeds  the foolishness of Sir John Lightfoot, Vice Chancellor of Cambridge University, who, in the 17th c., refined Bishop Ussher’s absurd date of creation, to fix the time of creation at exactly 9 am according to the gospel.

Eventually, Bertrand Russell, among others, pointed out the foolishness of the belief in axiomatic proofs in the Elements, calling the proofs in the Elements a “tissue of nonsense”. But, because of his Cambridge indoctrination, he kept believing in the Euclid myth that, the mythical “Euclid” intended axiomatic proofs. Hence, Russell along with David Hilbert invented formal math on that equally foolish belief in the intentions of a non-existent person, and in the church superstition about the superiority of deductive proofs (more details on that superstition in the next blog post).

Actual Greeks tied math to religion

Actual “Greeks” (Pythagoreans, Plato, Proclus) were NOT interested in axiomatic proofs, and interested only in the religious aspects of geometry, in arousing the soul and making it recollect its past lives (mathesis). This required turning the mind inwards. I have described this in great detail in various places, including my book Euclid and Jesus.

Axiomatic proofs a church tradition

But the church adopted the method of proof based on axioms (i.e., assumptions about the unreal), as in Aquinas’ proof about the number of angels that fit on the head of pin, based on certain axiomatic beliefs about the amount of space occupied by unreal angels. The church found the axiomatic method convenient, as part of its theology of reason (advocated by Aquinas and the schoolmen as the best way to convert Muslims). Obviously, basing reasoning on facts, as in universal normal math (including Indian gaṇita), would go contrary to all church dogmas (about angels etc.). As a loyal handmaiden of the church, Cambridge University, promoted the superstition that the axiomatic (or faith-based) method is “superior” to the empirical method, and that authoritatively laid down axioms (like Aquinas’ axioms about angels) are “superior” to facts.

We started imitating this way of doing mathematics as part of colonial education (which imitated Cambridge).

“Euclid” myth teaches us to imitate the church

So, when millions of students are taught the “Euclid” myth, and told that this way of doing math (formal math) is “superior”, they are being taught a church myth about “Greeks”, to teach them to imitate a foolish church practice. Neither they, nor our smart alecs,  understand this tricky way of indoctrinating children to teach them to imitate a church practice though a myth about the only “friends of the church” — the early Greeks. So, the Euclid myth is just a simple innocent lie, is it?

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