The Mathematics of Success

The Mathematics of Success

Before we can ask whether success can be measured, we must first ask: which success? The success of output, building an empire, a wonderful dissertation, a happy life? This commentary does not treat success as a vague aspiration. It treats it as a specific problem, the problem of whether the conditions for a flourishing human life can be calculated, predicted, or only, and imperfectly, understood.

Here is a thought experiment. You know from collision theory that a chemical reaction occurs only when particles collide with sufficient energy and at the correct orientation, a successful collision. Raise the temperature or concentration, and you raise the collision frequency, radically improving the probability of success (Atkins & Jones, 2016).


Now replace the reagents with a person, and collisions with opportunities, encounters with ideas, mentors, institutions, and circumstances. The multiplier effect of a well-positioned life is not mystical; it is probabilistic. The question of success reduces to a question of collision frequency and activation energy: how many meaningful encounters does a person experience, and how prepared are they to react productively when they occur?


But in a beaker, the reagents are identical, and the successful reaction is fixed. In a human life, none of these things is true. Which is why, before we can speak seriously about measuring success, we must first specify what we mean by the word.

The inquiry question

The inquiry this commentary pursues is precise: can success, understood as the realisation of a meaningful and flourishing human life, be measured with mathematical certainty, or only predicted through a constellation of probabilistic indicators?


To navigate this, we must untangle four central questions that split our current educational landscape:

  • The Definitional Problem: Are the metrics we measure being mistaken for the entirety of human flourishing?
  • The Structural Problem: Why does institutional assessment prioritise raw, empirical measurement to the exclusion of complex human traits?
  • The Standardisation Problem: How does the regional and national need for administrative legibility distort local teaching?
  • The Solution Path: Is the answer found in designing more nuanced measurement tools, or in adjusting our relationship with measurement altogether?


Regarding the definition of flourishing, the standard metric is not absolute; it is perspectival. In Confucian thought, success has historically been understood as the cultivation of virtue and the proper discharge of relational obligations (Yao, 2000). In Ubuntu philosophy, personhood itself is relational, umuntu ngumuntu ngabantu, a person is a person through other persons (Metz, 2011). Success, in this frame, is inseparable from communal flourishing. Western liberal modernity, by contrast, has tended to define success in terms of individual attainment: income, status, and credentials. When we narrow our definition of success to what can be graded, ranked, and printed on a certificate, we impose a single cultural interpretation and mistake it for a universal truth.

A fraction of a fraction

Addressing the definitional problem: Is the issue that the things measured are assumed to be the whole of flourishing?

Let us begin with the instrument most societies currently use to measure success: the examination grade. The cognitive psychologist Robert Sternberg argues that standardised assessments capture analytical intelligence while systematically ignoring creative and practical intelligence (Sternberg, 1996). Howard Gardner’s theory of multiple intelligences extends this critique, proposing that human cognitive capacity spans at least eight independent domains, of which formal education engages, at best, two (Gardner, 1983).

What a timed, closed-book examination most reliably measures is a combination of working memory capacity, retrieval fluency under pressure, and attentional stability (Deary et al., 2010). These are genuine cognitive capacities. But they represent a narrow cross-section of intelligence, ignoring extended reasoning under uncertainty, the integration of contradictory sources, and the tolerance of ambiguity.


We arrive at a disquieting arithmetic. Intelligence is one component of a successful life. Analytical intelligence is one dimension of intelligence. And examination performance is one proxy for analytical intelligence, a proxy further distorted by socioeconomic access, test anxiety, and cultural bias (Steele, 1997). We are measuring a fraction of a fraction, and treating the result as though it were the whole. The distortion is structural.

The pathology of standardisation

Addressing the structural and standardisation dilemmas: Why do we prioritise raw measurement, and how does standardisation drive this?


If better indicators of flourishing exist, such as Angela Duckworth’s metrics on grit (Duckworth et al., 2007), the Harvard Grant Study’s focus on relational depth (Vaillant, 2012), Carol Dweck’s growth mindset (Dweck, 2006), or Mihaly Csikszentmihalyi’s concept of flow (Csikszentmihalyi, 1990), why do education systems persist in using the narrow ones?

The central issue is not institutional ignorance; it is the administrative demand for scale and standardisation. As philosopher C. Thi Nguyen highlights, human values are rich and context-dependent, but large-scale institutions require simplified, highly portable metrics to compare massive populations (Nguyen, 2020). This pressure for regional and national uniformity works its way back down to the local classroom, forcing educators to alter their focus to what can be easily quantified on a spreadsheet.

This optimisation triggers Goodhart’s Law: “when a measure becomes a target, it ceases to be a good measure” (Goodhart, 1975). The moment an institution commits to a particular standardised metric, the metric begins to be optimised directly, rather than treated as a signal of the underlying capacity.

When we measure a student’s potential through examinations, we do not merely record a pre-existing fact about them. We intervene. In quantum mechanics, the act of observing a particle necessarily disturbs it, a phenomenon formalised in Heisenberg’s uncertainty principle (Heisenberg, 1930). Similarly, human systems adapt to the act of being measured. The measurement does not just find the student; it partly makes them. And if the measurement is narrow, it forces the student to become narrower.

The way forward

Addressing the solution path, what is the solution? Redefining the purpose or adjusting our limitations?

The solution is not to completely abandon metrics, nor is it to endlessly search for a more complex, flawless formula. The way forward lies in realising the inherent limitations of empirical assessment and deliberately rebalancing our educational ecosystems through two distinct movements:

  1. Validating Existing Non-Empirical Shifts
    First, we must acknowledge that a profound shift is already happening on the ground. In many progressive classrooms and organisations, educators have moved away from pure exam reliance to place significant weight on the socially complex, non-empirical elements of learning. Group work, holistic portfolios, continuous assessment, and class presentations are active frameworks designed to cultivate interpersonal intelligence, collaboration, and iterative growth. However, because these methods do not easily fit into a national standardisation matrix, they are often sidelined during final assessments. The hope lies in formally protecting these spaces, treating local, qualitative evaluations with the same systemic respect as centralised exams.
  2. Embracing the Spontaneous
    Second, reclaiming education requires an ideological shift among educators themselves. As Fifi Formson (an ARLLS facilitator) aptly put it, “Being an educator requires attentiveness to both the structured and the unexpected. While some learning experiences can be carefully planned and measured, others emerge spontaneously in ways that defy control. Human beings are complex, and meaningful learning rarely follows a perfectly predictable path. Educators who remain alert to these unexpected moments often discover that they become the richest opportunities for learning.”

What this means for the student

When students recognise that learning is fundamentally more than the narrow metrics used to grade them, a profound psychological liberation occurs. This realisation is the most hopeful, transformative part of their development. The student who understands this does not become cynical about education; she becomes clear-eyed. She can work within a system of narrow measures while simultaneously developing the capacities that those measures do not reach. She can perform on the examination and cultivate the depth that the examination cannot see.


This requires something the examination will never test for: the philosophical clarity to distinguish between the map and the territory, between the credential and the capability it is supposed to represent.


If success cannot be perfectly calculated but can be meaningfully influenced, then the practical question for any ambitious young person is this: which capacities, deliberately developed, most reliably increase both the frequency and quality of transformative collisions?


The answer does not lie in a new set of metrics to be gamified, but in a fundamental reclamation of agency. To navigate a world obsessed with standardisation, the most critical capacity a young person can develop is critical legibility, the ability to speak the language of the system’s narrow metrics fluently enough to pass through its gates, without ever letting those metrics define their internal boundaries.


This brings us squarely back to the chemist’s beaker.

In a controlled laboratory, success is simple because the components are passive; they are acted upon by their environment. But human beings are not inert reagents. We are the architects of our own activation energy. When we step outside the artificial constraints of the examination hall and into the raw complexity of the real world, we realise that the most transformative collisions cannot be scheduled on a syllabus or captured on a spreadsheet. They are found in the spontaneous, the relational, and the unmeasurable.


We may never find a flawless mathematical formula for human flourishing, and perhaps we shouldn’t want to. The true geometry of success is not a straight line plotted on an administrative graph. It is a dynamic, unpredictable path, forged by those who have the brilliance to ace the exam, the wisdom to look beyond it, and the courage to step boldly into the unexpected.

If you liked this commentary, we suggest you continue with a short read on a similar topic here.

Works Cited

Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight. 7th ed., W. H. Freeman, 2016. 

Csikszentmihalyi, Mihaly. Flow: The Psychology of Optimal Experience. Harper & Row, 1990. 

Deary, Ian J., et al. “The Impact of Childhood Intelligence on Later Life.” Journal of Personality and Social Psychology, vol. 98, no. 1, 2010, pp. 152–163. 

Duckworth, Angela L., et al. “Grit: Perseverance and Passion for Long-Term Goals.” Journal of Personality and Social Psychology, vol. 92, no. 6, 2007, pp. 1087–1101. 

Dweck, Carol S. Mindset: The New Psychology of Success. Random House, 2006. 

Gardner, Howard. Frames of Mind: The Theory of Multiple Intelligences. Basic Books, 1983. 

Goodhart, Charles A. E. “Problems of Monetary Management: The U.K. Experience.” Papers in Monetary Economics, Reserve Bank of Australia, 1975. 

Heisenberg, Werner. The Physical Principles of the Quantum Theory. Translated by Carl Eckart and Frank C. Hoyt, University of Chicago Press, 1930. 

Metz, Thaddeus. “Ubuntu as a Moral Theory and Human Rights in South Africa.” African Human Rights Law Journal, vol. 11, no. 2, 2011, pp. 532–559. 

Steele, Claude M. “A Threat in the Air: How Stereotypes Shape Intellectual Identity and Performance.” American Psychologist, vol. 52, no. 6, 1997, pp. 613–629. 

Sternberg, Robert J. Successful Intelligence: How Practical and Creative Intelligence Determine Success in Life. Simon & Schuster, 1996. 

Vaillant, George E. Triumphs of Experience: The Men of the Harvard Grant Study. Belknap Press of Harvard University Press, 2012. 

Yao, Xinzhong. An Introduction to Confucianism. Cambridge University Press, 2000.