Wisdom begins with death. And death begins with life.

For the young, death may seem a long way off. It is well-known that as the years gather, as we pass through the years of our lives, time passes more quickly. A summer in our youth, a summer break between one grade and another, seems to go on and on and on. But even five years, or a decade, can seem to speed by for an elder. These are common experiences, shared by many people.

In the world of mathematics, part of which is measurement, and measurements of time, any five years, for example, is equal to any other five years. Five winters, springs, summers, and falls, for those of us in parts of the world that have these seasons. Five rainy seasons, five times around the sun, five birthdays, five New Year’s days, five grades in school, one year for each finger on a hand. Five Decembers, five Junes, five Marches, fives Septembers. Five winter solstices and five summer solstices. Five spring equinoxes and five fall equinoxes. One year for each numeral: one, two, three, four, five. This is the world of counting, of sets of things, arithmetic, adding one, all part of the world of mathematics. Five years is five years. It is measurable and countable. You and I can agree. Five years.

But part of the world of wisdom, and mathematics, is in knowing what does NOT belong to the world of measurement and counting and math. That five years for a child is not the same experience as five years for an elder. Here, five does not equal five. In mathematics, five = five. Always. Part of wisdom is learning, and part of learning is knowing what you are not learning.

A person might like to think of mathematics as a tool. A camera is useful when taking photographs. But not as useful when putting paint on a canvas.

A person might like to think of mathematics as a way of seeing and experiencing the world. Seeing the world as in interconnected web of different forms of energy, some easy to notice and some more subtle, is useful when making large-scale decisions. But maybe not if you are trying to figure out how to get home in time for your daughter’s birthday dinner.

Erik Erikson, a mid-twentieth century psychologist who was one of the first people to think about adult stages of life, distinguished the opposition of basic trust and basic mistrust that, in his view, a person developed in the first year of life. If you wish to investigate his particular ideas, his book Identity and the Life Cycle is a place to start. But for mathematics, which includes various structures of opposites, and for wisdom, which includes notions of trust and mistrust, the idea that some people have a basic trust in the world and other people have a basic mistrust of the world, could be a meeting point for wisdom and mathematics, an aspect they both include, or a meaningful part of their overlapping features.

A person might like to think of mathematics a a kind of reasoning or thinking in which there is no uncertainty, in which every statement that is accepted, every conclusion that is proved, is built on other statements that are certain themselves. By building certainty on top of certainty, a structure is created in which uncertainty is eliminated.

It could be wise to wonder why such a desire for certainty exists: is it from a basic mistrust of the world, of life? Is it a descendant of an evolutionary need for knowledge about high-probability events needed for survival?

Carl Jung, a 20th century Swiss psychologist , described certain people as introverts and others as extroverts. His analysis is much more complex and interesting than the oversimplified meanings we commonly give those terms. In his book Psychological Types, Jung describes that introvert attitude as an “abstracting” attitude, an attitude that is intent on removing energy from the world around it, as though it had to prevent objects from gaining power over it.

The extroverted attitude, on the other hand, shows a very positive relation with the world outside: the importance of outside events and objects is granted without question, and the person showing an extroverted attitude has inner thoughts and feelings that are constantly yielding to the outward conditions. The introverted attitude, oppositely, give unquestioned importance to inner events.

Using this way of looking and understanding, we could choose to view the desire for certainty in mathematics as consistent with the orientation of an introverted attitude: that the creation of axiomatic systems, or structures of statements meeting a particular criteria for certainty, provide a safe arena for the introverted attitude. We may then distinguish two different types of mistrust: the mistrust of the introverted attitude, which mistrusts in some sense everything outside of its inwardness, and the mistrust of the extroverted attitude, which mistrusts only particular things outside of itself, based in general on external experience (along with a basic mistrust of all thoughts and feelings that appear to originate within).

It is possible to even reverse the meanings of inside and outside: for an extroverted attitude, the outside (what the introvert experiences as outside) is experienced as inside, and vice versa.

The complexity of the duality of introvert and extrovert, and their richness and ambiguity, can also emerge when we wonder if the positive experience of certainty communicated by mathematical structures might actually be an experience desired by extroverts since it gives a sense of control over inward thoughts, the location of fear for the extroverted attitude.

The desire for mathematical certainty may also arise from Erikson’s idea that every person has either an orientation of basic trust or mistrust. Or we might find a more fruitful explanation by questioning whether certain cultures are more orientated to trusting or to mistrusting, to introversion or extroversion.

The intersection of mathematics and wisdom is not empty. And to become an area of study deserving of all the time and energy that we require our children to put into it, we must make mathematics more wise than what we teach now.