WEBVTT

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Hi. What does it mean to fail? Well, in school,

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failure seems fairly easy to define. We take

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a test, and then we receive a grade. And if our

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score falls below a certain number, well, we

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fail. My career is in actuarial science, and

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the actuarial exams makes this distinction especially

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clear. Each exam is created on a pass or fail

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basis. At the end, you receive one of two results.

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You either pass or failed. Now, it is true that

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this distinction serves a practical purpose.

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Schools and professional organizations need ways

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to evaluate progress. But when we carry that

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definition into mathematics itself, it just seems

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like we are losing something critical. Because

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math is so much more than arriving at the correct

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answer. For starters, doing math involves asking

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questions, looking for patterns, trying examples,

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making conjectures, and then following ideas

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whose destinations we cannot yet see. Sometimes

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we try an approach and discover it does not work.

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Sometimes we make a mistake. Sometimes we reach

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an answer but still do not understand why it's

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true. And sometimes we spend hours on a problem

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without finding an answer at all. So, did we

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fail? Perhaps we need to separate failing in

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an exam from failing at mathematics. A person

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may know key concepts and yet fail in an exam

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because of calculation errors. And just as bad

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is if a person can pass an exam by memorizing

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the right formulas without developing much understanding.

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Test scores can give useful feedback, but it

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likely does not tell us everything. In fact,

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often when mathematicians work on questions,

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those questions do not have known answers yet.

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Most of their attempts do not work. They test

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an idea, they discover a problem, then they adjust

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their assumptions, and then they begin again.

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This is not an interruption of mathematics. This

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is mathematics. The unsuccessful attempt reveals

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something. It closes one path, exposes a hidden

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assumption, or maybe suggests a better question.

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even when it does not provide the answer and

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may deepen our understanding of the problem.

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I have experienced this process many times in

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my career. Yet it is easy for us to view a wrong

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answer differently. A wrong answer often communicates

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we were not good at math. So we begin to protect

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ourselves by maybe not raising our hands or avoiding

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difficult problems. It is too easy to wait for

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someone to show us the correct method so we would

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not risk trying to the wrong one. Eventually,

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success in math came to mean avoiding failure.

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But what if it means almost the opposite? What

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if growing in mathematics requires choosing problems

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difficult enough that our first attempts probably

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will fail. So this week, we're going to explore

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failure and perseverance, not simply as obstacles

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that we must endure, but as essential parts of

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discovery. We will look at mathematicians who

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struggled for years and questions that remained

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unsolved for centuries. But we will also ask

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what those stories might teach us about our own

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lives. Because an unsuccessful attempt is not

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the same as an unsuccessful person. I believe

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that failure is not getting a wrong answer. I

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believe the deeper failure is allowing our fear

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of being wrong to keep us from exploring math

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at all.