as a boy inna 1st weeks of algebra class, i felt confused and then i went sort of numb. adolescents order the realm from fragments of information. in its way, adolescence is a kind of algebra. the unknowns can be determined but doin’ so requires a spesh aptitude, not to mention a comfort with having things withheld. straiteforward, logical thinking is required, and a willingness to follo rules, which aren’t evenly distributed adolescent capabilities.

when i thought bout mathematics at all as a boy twas to specul8 bout why i was bein’ made to learn it, since it seemed plainly obvious that there was no need for it in adult life. balancing a checkbook or drawing up a budget was the answer we were given for how math ‘d prove necessary l8r, but you don’t need algebra or geometry or calculus to do either of those things.

but if i had understood how deeply mathematics is embedded inna realm, how it figs in every gesture we make, whether crossing a crowded street or catching a ball, how it figs in painting and perspective and in architecture and inna natural realm and so on, then perhaps i mite ‘ve seen it the way the ancients had seen it, as a primordial pt of the realm’s design, perhaps even the design itself. if i had felt that the realm was connected in its pts, i mite ‘ve been provoked to a kind of wanda and enthusiasm. i mite ‘ve *wanted* to learn.

5 yrs ago, when i was 65, i decided to see if i ‘d learn adolescent mathematics — algebra, geometry and calculus — cause i had done poorly at algebra and geometry and i hadn’t taken calculus at all. i didn’t do well at it the 2nd time, either, but i ‘ve become a kind of math evangelist.

mathematics, i now see, is primordial cause it expands the realm. tis a point of entry into larger concerns. it teaches reverence. it insists one be receptive to wanda. it requires dat a''pers play close attention. to be made to ponder a problem carefully discourages scattershot and s♥nly thinking and encourages systematic thought, an advantage, sfar as i can tell, in all endeavors. abraham lincoln said he spent a yr reading euclid in order to learn to think logically.

studying adolescent mathematics, a'pers is crossing territory on which ftprints ‘ve been left since antiquity. somd' trails ‘ve been made by distinguished figs, but'a bulk o'em ‘ve been left by ordinary pplz like me. as a boy, trying to follo a path in a failing lite, i never saw the mysteries i was movin among, but on my 2nd pass i began to. nothing had changed bout math, but i had changed. the person i had become was some1 whom i ‘dn’t ‘ve imagined as an adolescent. math was ≠, cause i was ≠.

the beginner math mystery, available to any-1, concerns the origin of №s. it’s a simple speculation: where do №s come from? no one knows. were they invented by human bein’s? hard to say. they appear to be embedded inna realm n'wys that we can’t completely cogg. they began as measurements of quantities and grew inna'da means for the most precise expressions of the physical realm — e = mc², for ex.

the 2nd mystery s'dat of prime №s, those №s s'as 2, 3, 5, 7, 11 and 13 that can be divided cleanly 1-ly by one or by themselves. all №s not prime are called composite №s, and all composite №s are the result offa unique arrangement of primes: 2 x 2 = 4. 2 x 3= 6. 2 x 2 x 2 = 8. 3 x 3= 9. 2 x 3 x 3 x 37 = 666. 29 x 31 = 899. 2 x 2 x 2 x 5 x 5 x 5 = 1,000. if human bein’s invented №s and counting, then how is it that there are №s s'as primes that ‘ve attributes no one gave them? the grand and enfolding mystery is whether mathematics is created by human bein’s or exists indiely of us in a territory adjacent to the actual realm, the zone of which no one can specify. plato called it the non-spatiotemporal realm. tis the timeless nowhere that never has and never will exist anywhere b'that nevertheless is.

mathematics is 1-odda most efficient means of approaching the gr8 secret, of pondering wha’ lies past all that we can see or presently imagine. mathematics doesn’t describe the secret so much as it implies that thris one.

on my 2nd engagement, whenever i encountered a definition of mathematics, i wrote it down. among those i liked best was that mathematics is a story that s'been bein’ written for thousands of yrs, is always bein’ added to and mite never be finished. such a thought ‘d ‘ve appealed to me deeply as a boy and mite ‘ve made mathematics seem maybe not welcoming, but at least less forbidding than it appeared.

original content at: www.nytimes.com…

authors: alec wilkinson