True nature of math remains, in sum, a mystery

Originally published 28 December 1992

If you are afflict­ed with math anx­i­ety, you may not like what I’m about to say.

Our most cer­tain knowl­edge of the world is math­e­mat­i­cal. Non-math­e­mat­i­cal knowl­edge is held sus­pect by sci­en­tists. Depen­dence upon math­e­mat­ics as the arbiter of truth defines the mod­ern, West­ern way of know­ing. For bet­ter or worse, it is the source of our pow­er, our wealth, and our phys­i­cal well-being.

There it is. Take it or leave it. Math offers our best crack at fig­ur­ing out what the world is all about.

And the big mys­tery is — no one knows what math­e­mat­ics is, or why it works so unrea­son­ably well.

Not even mathematicians.

Or the sci­en­tists who use math­e­mat­ics as their lan­guage of discovery.

There are, I sup­pose, three pos­si­ble explanations:

1. Math­e­mat­ics is an arbi­trary inven­tion of the human mind, like the Eng­lish lan­guage or the game of chess, that has proven par­tic­u­lar­ly use­ful for express­ing pat­terns we observe in nature.
2. Nature is itself math­e­mat­i­cal. We learn math­e­mat­ics by observ­ing the way the world works.
3. Math­e­mat­ics exists as a kind of Pla­ton­ic ide­al, beyond and out­side of nature. All real­i­ty, includ­ing mind, par­tic­i­pates in some mys­te­ri­ous way in this pre­ex­ist­ing order.

All of which is a wordy way of saying:

1. We invent math.
2. We dis­cov­er math.
3. We are math.

John D. Bar­row, Pro­fes­sor of Astron­o­my at the Uni­ver­si­ty of Sus­sex in Britain, takes up the mys­te­ri­ous effec­tive­ness of math­e­mat­ics in his recent book, Pi in the Sky: Count­ing, Think­ing, and Being. He takes us through the entire his­to­ry of math­e­mat­ics, from count­ing on fin­gers to the high-blown abstrac­tions of the­o­ret­i­cal physi­cists who use math­e­mat­ics to inves­ti­gate the Big Bang moment of creation.

He’s after the answers: What is math? Why does it work? Why is sci­ence up to its ears in num­bers — nay, to the very tip-top of its head? Bar­row’s answer: Uhhh…well…I guess…maybe…dunno.

The mys­tery remains.

And that, says Bar­row, is the point.

His claim: “We have found that at the roots of the sci­en­tif­ic image of the world lies a math­e­mat­i­cal foun­da­tion that its itself ulti­mate­ly religious.”

I think he’s right.

And if I were a the­olo­gian, that is exact­ly where I would start con­struct­ing a con­cept of God that is rel­e­vant to our time — with mathematics.

At first blush, the idea sounds pre­pos­ter­ous, even blas­phe­mous. But wait. Isn’t math­e­mat­ics the most effec­tive medi­um of exchange between the human mind and the cos­mos? Through math we have come to know the Big Bang, the uni­verse of galax­ies, the unfold­ing infini­ties of space and time. We have plunged into the heart of mat­ter, and explored mys­ter­ies of life and mind. Noth­ing else has tak­en us to there. Math, only math.

And we haven’t the fog­gi­est idea why it works.

By and large, the­olo­gians still offer us the God of Michelan­gelo’s Sis­tine Chapel ceil­ing — a gray-beard­ed ver­sion of our­selves ensconced in some pal­try heav­en up in the sky. “Oh, don’t be sil­ly,” they’ll protest, “the gray-beard­ed man is just a metaphor for some­thing we can­not ful­ly express.” Exact­ly. So why stick with a medieval metaphor that opens a gulf between sci­ence and reli­gion, between know­ing and feel­ing? Why not adopt a metaphor that embraces the full rich­ness of the cos­mos, a metaphor that links our minds to all that exists?

Name­ly, mathematics.

The human mind has evolved in response to the world in which we live, in the same way as did our sens­es of sight, sound, and smell. If we are math­e­mat­i­cal crea­tures, it is because the world is in some deeply-mys­te­ri­ous sense math­e­mat­i­cal. Call it, if you will, the mind of God. The phrase is metaphor­i­cal, but so is every oth­er def­i­n­i­tion of God. The math­e­mat­i­cal metaphor links us pro­found­ly, deeply, to all of cre­ation in a way that is total­ly con­sis­tent with the spir­it and the sub­stance of mod­ern science.

That’s where I’d start, if I were a theologian.

But I’m not a the­olo­gian. I don’t even have a reli­gion. I just know a rip­ping good mys­tery when I see one.

Of the three pos­si­ble expla­na­tions for the mys­te­ri­ous effec­tive­ness of math­e­mat­ics, maybe all are true. Maybe we invent math. Maybe we dis­cov­er it. And maybe, just maybe, we are math incar­nate — to the core of our souls. Maybe, just maybe, math­e­mat­ics is our glimpse of the eter­nal, omnipresent, cre­ative foun­da­tion of the world. Why else does it work so aston­ish­ing­ly well?

Bar­row may have got it exact­ly right: “Our abil­i­ty to cre­ate and appre­hend math­e­mat­i­cal struc­tures in the world is…a con­se­quence of our one­ness with the world. We are the chil­dren as well as the moth­ers of invention.”