One retired teacher from East Anglia recently told me that she never sensed that she was ever at a peak stage in her career, even though there must logically have been such a time. 

So perhaps it happened on her very last day of teaching, I suggested - that she just got better and better with age - but she rather doubted it. 

She felt instead as if she had passed seamlessly from being at the “young and raw” stage to the slightly “past it” point, without any intervening period at all. 

Recalling ‘peak me’

After years of being advised to learn from her elders, she had passed, in a flicker, to that phase where the default suggestion was for her to check out what younger colleagues were doing. 

She was a fine teacher, though. There must have been a golden age for her somewhere along the line. But when was that most likely? 

Ever since our conversation, I have been haunted by the thought that my own finest hour has probably passed me by without my ever noticing. 

There will have been one particular day in my life when my teaching - like a bottle of fine wine or, perhaps more aptly in my case, a TV sitcom - will have been at its very best, before going off a bit. 

On that one day - probably on some wet and forgettable period six on a Tuesday afternoon - I will have unwittingly offered that unsuspecting class the best I would ever offer. They were getting peak me.

That day, the attributes needed to be at optimum teaching would not necessarily have all been at their highest, but they would have been at their highest possible combination, given the various benefits and drawbacks of ageing. 

I will have offered that ideal mix of all the teaching ingredients we tend to gain or lose as we slowly move from stages of youth to varying degrees of agedness. Admittedly, the score for that lesson may not have been a staggeringly high one in my case, but it will have still been my best ever. 

Our finest hour

Until recently, I had no idea when that finest hour might have been for me, nor even when it would have been statistically most probable. If I had known, there could have been some kind of coming-of-age celebration: a fanfare as I arrived in that classroom that Tuesday afternoon. 

Well, the good news is that I have now just worked out the definite answer. The figure may obviously vary a bit from teacher to teacher, as we are all built differently. And we obviously know some teachers who are amazing in their twenties and in their eighties - and others at every age in between.

But I can now confidently predict - thanks to a mysteriously thrown-out teaching algorithm I found at a refuse tip - exactly when that mathematically most probable best age is. 

A few preliminaries: in the calculation, I have assumed a teacher typically begins their career in their early twenties. I have not included the many distorting external influences that can potentially enhance or detract from performance at stages in our life. The effects of falling in love, falling out of love, boxset addiction, parenting and so on have all been deliberately left out of the algorithm. 

I’ve also used previous scientific research on the optimum age for various related attributes. For instance, peak brain processing will usually be at the start of our career; reading other people’s emotions, at the end of it. We are physically strongest at 25, and most likely to have the creativity and commitment to win the Nobel Prize at 40. We are likely to be most focused at 43, and to be best at playing a game of chess at 31. 

My computer has now absorbed all the data and just worked out the answer. 

The answer is 45 and a half. I’m glad that’s settled now. 

Stephen Petty is head of humanities at Lord Williams’s School in Thame, Oxfordshire