Failing fast and failing forward

Tierney Kennedy

A few years ago mathematician Terence Tao created a Polymath[1] group to work on the Twin Prime Conjecture – a project where mathematicians collaborate together to solve vexing problems. As part of the approach, everyone agreed to immediately publish any progress on a problem before checking it rigorously for mistakes.

Why would they do this?

The answer has intriguing applications for how we approach failure in our own classes…

Despite the apparent problems inherent in publishing mistakes, the Polymath group managed to make major breakthroughs in mathematics research within only a few months…

On May 13^th 2013, Yitang Zhang proved that the maximum gap between twin prime numbers (e.g. 11 and 13) was at most 70 million. By the 4^th June, the Polymath group formed, and by 27^th July the group had managed to reduce that gap to just 4680! In November, the gap was reduced to just 600 by James Maynard. Maynard then joined with the Polymath group, which ended by decreasing the bound to just 246 by Feb 2014.

“There’s an explicit license to be wrong in public,” Morrison said. “It goes against a lot of people’s instincts, but it makes the project much more efficient when we’re more relaxed about saying stupid things.”

After reading a number of comments on the Polymath group page, it is obvious that the people involved really do publish their thoughts before editing them[3]:

…So, what does this mean for us?

It’s important to work on hard problems that seem impossible

Breakthroughs always occur when we start with a seemingly “unsolvable” problem. A breakthrough is not needed when the solution is obvious or known. That means that the way forward is also not obvious, so experimentation is necessary almost by definition.

Experimentation and failing forward

When we experiment with ideas, methods and conjectures, we are working out both what might work and also what won’t work. Our ideas will “fail” more often than not because we are trying something entirely new. We need to start thinking of wrong answers not as “failures”, but instead as disproving conjectures, or busting maths myths. What did the failure tell us? What can we use from that? What might work now?

Tao on the difficulty inherent in the polymath process:
“Great mathematicians make stupid mistakes, and this is a process that people often hide, because it is embarrassing.”[2]

Failing fast

At times we don’t want to admit when our idea is failing, so we keep pursuing the same path doggedly, and slowly. In situations like these, we often avoid evaluating the idea, or just end up taking a really long time to learn the lesson. Instead, perhaps we could implement an active evaluation process along the way that feels less “judgey”:

• What have we learned so far?
• What is definitely working? How can we do more of that?
• What does not appear to be helping? Should we cut it now or set a time limit for it to work?
• What should we change now to have a better chance of success?

By failing forward, failing fast, and failing together, we move towards progress at a much surer pace, learning the lessons we need to along the way and ensuring far better outcomes for our kids.

[1] http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes

[2] https://www.quantamagazine.org/mathematicians-team-up-on-twin-primes-conjecture-20131119/

[3] https://terrytao.wordpress.com/2014/09/30/the-bounded-gaps-between-primes-polymath-project-a-retrospective/