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!") So, where axiomatically-taught math bifurcates "The Three R's", generatively-taught math unites The Three R's.

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.

		Generative Genny and Digital Dot say,
		"Dig the digital !  Generative gigs hot!
		Tell geobias to kiss mias.
		Calculanga!  I'm a HiTech tot!
		Will men only play when the game is fixed?
		Stop picking on women to get your kicks!" 

If women don't take their education away from fix-game men -- and particularly the education of girls -- then women are continuing to get the education they deserve.