Does Math Objectively Exist, or Is It a Human Creation? A New PBS Video Explores a Timeless Question

In a famous scene from Boswell’s Life of Samuel John­son, the biog­ra­ph­er and his sub­ject come to dis­cuss the bizarre the­o­ries of Bish­op Berke­ley, who posit­ed that every­thing is immaterial—nothing has any real exis­tence; it’s all just ide­al con­cepts held togeth­er by the mind of God. If God should lose his mind or fall asleep or die, every­thing would fall to pieces or cease to exist. Boswell insists there’s no way to refute the idea. John­son, kick­ing a large stone with such force that his foot rebounds, cries, “I refute it thus.”

Johnson’s lit­tle demon­stra­tion doesn’t actu­al­ly refute Berkeley’s rad­i­cal ide­al­ism. It’s a conun­drum still with us, like Plato’s Euthy­phro stumper, which asks whether the rules gov­ern­ing human behav­ior exist inde­pen­dent­ly of the gods, who sim­ply enforce them, or whether the gods make the rules accord­ing to their whims. In oth­er words, is moral­i­ty objec­tive or sub­jec­tive?

A sim­i­lar prob­lem occurs when we con­sid­er the exis­tence of the rules that gov­ern phys­i­cal laws—the rules of math­e­mat­ics. Where does math come from? Does it exist inde­pen­dent­ly of human (or oth­er) minds, or is it a human cre­ation? Do we dis­cov­er math­e­mat­i­cal prob­lems or do we invent them?

The ques­tion has engen­dered two posi­tions: math­e­mat­i­cal real­ism, which states that math exists whether we do or not, and that there is math out there we don’t know yet, and maybe nev­er can. This posi­tion may require a degree of faith, since, “unlike all of the oth­er sci­ences, math lacks an empir­i­cal com­po­nent.” You can’t phys­i­cal­ly observe it hap­pen­ing. Anti-real­ists, on the oth­er hand, argue that math is a lan­guage, a fic­tion, a “rig­or­ous aes­thet­ic” that allows us to mod­el reg­u­lar­i­ties in the uni­verse that don’t objec­tive­ly exist. This seems like the kind of rel­a­tivism that tends to piss off sci­en­tists. But no one can refute either idea… yet. The video above, from PBS’s Idea Chan­nel, asks us to con­sid­er the var­i­ous dimen­sions of this fas­ci­nat­ing and irre­solv­able ques­tion.

Relat­ed Con­tent:

The Math in Good Will Hunt­ing is Easy: How Do You Like Them Apples?

Incred­i­ble Men­tal Math Gym­nas­tics on “Count­down”

Math Doo­dling

Josh Jones is a writer and musi­cian based in Wash­ing­ton, DC. Fol­low him at @jdmagness