The Digital Revolution revs on! In computing, visual and sound recording, printing, etc. Its flip side is a Generative Revolution -- which could encourage girls and women to employ, in learning mathematics, their linguistic abilities confirmed in a 1998 magnetic resonance imagery experiment.

By uniting Digital and Generative revolutions, a "HiTech" Revolution could begin for all Generative Gennys and Digital Dots, enriching our economy! (Hamlet says I'm traitorous to my gender.)

Are boys mathematically more proficient than girls? I blame biased teaching and testing and a neglected ancient alternative. Prove me wrong!

We have sssssexxxxxxxxxx education in the schools. But children, teenagers, and college students believe by default (or from geobias) that numbers and their operations are not generated but brought by an axiomatic stork.

So a Generative Revolution is overdue, beginning (along with the Digital Revolution) ) over 2500 years ago in ancient Pythagorean mathematics, supplemented in 1840 by the great Irish mathematician, Sir William Rowan Hamilton (1805-1865).

What stalls the Generative Revolution?

• Discrimination! Clearly, Religious fundamentalism (Jewish, Christian, Islamic, etc.) controls women. (The first daily prayer of a male Hassidic Jew is, "Thank you God for not making me a woman!" Hypatia, greatest woman mathematician of ancient times. was butchered in a cathedral by a Christian mob -- some of whom later helped burn The Library of Alexandria, greatest library of ancient times, destroying all manuscripts of Archimedes, Eudoxus, and other creators, as well as Hypatia's works.)
• "Mathematical fundamentalism" (especially, by invoking "geobias") seems just as mysogynist.
• Platonist (Elitist) Mathematical Philosophy, whose (male) Priests stand between "Mathematics" and "The Laity".
• Can you think of other influences?

Generative mathematics parallels reading, writing, spelling, and decimal numeration. ("Word-bone connected to the number-bone!")

Two foundations engender mathematical systems: axiomatics and generatics.

Axiomatics originated with Thales of Miletus (c. 624-547 B.C.) for synthetic geometry (as in Euclid's Elements of Geometry). Generatics originated with Thales' pupil, Pythagoras of Samos (c. 580-496 B.C.), mainly for arithmetic.

Thales was analogic; Pythagoras was digital. Axiomatics is "top-down"; generatics "bottom-up". Axiomatics uses nonconstructive proofs; generatics is constructive. Two 20th century mathematicians represent the divergence.

The German mathematician, David Hilbert (1862-1943), formulated the first satisfactory axioms for Euclidean geometry. The other mathematician was Bertrand Russell (1872-1972), remembered as nudist; lover (seducer of T. S. Eliot's wife); nuclear weapons protest leader, sloganizing, "Better Red than dead!" (radicalizing Vanessa Redgrave). Russell co-authored a classic in logic, including excellent mathematical definitions.

Rebutting Hilbert's boast, Russell said axiomatics "has all the advantages" over generatics "that theft has over honest labor" -- assuming what should be generated from a basis of elements.

• Axiomatics is Moses descending from Mt. Sinai with "Ten Commandments" to restrain the Israelites. Generatics is a citizen's do-it-yourself kit.
• Axiomatics fractures "The Three R's". Generatics unifies them.
• Axiomatics disconnects concepts; generatics reconnects them.

Once Generative Gennys and Digital Dots thrived because Pythagoras venerated women at antiquity's highest level. Prejudice destroyed the generative movement and women's rights, upon the death (possibly violent) of this great thinker.

Historian Will Durant says, "[Pythagoras] gave his women students considerable training in philosophy and literature, but he had them instructed as well in maternal and domestic arts, so that 'the Pythagorean women' were honored in antiquity as the highest feminine type." What did Generative Gennys and Digital Dots learn at this first university?

Unlike "analogic" Euclidean geometry, "Pythagorean geometry" is "digital", constructing geometric shapes (triangles, squares, pentagonals, etc.) from dots of numbers. (Eventually, this inspired crystallography and solid state physics which have endowed the transistor and artificial insulin, something axiomatic synthetic geometry cannot do.)

My mathtivity, entitled "Bottle Cap Geometry", teaches "Pythagorean geometry" to first grade Generative Gennys and Digital Dots and boy classmates via bottle caps, or pegs in pegboard, or tiles on walls or floors. This, in turn, induces the Eristophanic Sieve, sieving prime from composite numbers. And sieving,models diagnostic tests which physicians performt, as well as strategies for repairing cars, TVs, etc.. (These children may occupy the "information-highway", and wish to protect their secret files by prime-number encryption.)

Plato's Academy replaced "digital" with "analogic" geometry, interrupting the Digital Revolution. A consequence of this, besides the stymie of "digital math", is the delay of "The Industrial Revolution", the prolongation of general slavery, and the subordination of women.