If Life Were A Mathematical Problem, What Score Would You Get? | Kate Zhu | TEDxSCIE Youth

Key Concepts

• Additive vs. Multiplicative Models: The core distinction between linear, incremental progress (additive) and compounding, exponential growth (multiplicative).
• Compounding Effect: The power of small, consistent improvements over time leading to significant results.
• Persistence & Long-Term Effort: The importance of continuing even during difficult times, as the greatest gains often follow periods of struggle.
• Probability & Persistence: The mathematical demonstration of how consistent effort increases the likelihood of success, even with a low initial probability.
• Intersection of Skill, Social Need & Interest: Finding the sweet spot for creative and diversifying growth.

From Hierarchical Achiever to Rule Breaker: A Mathematical Perspective on Life Transitions

This talk details the speaker’s personal journey from a high-achieving, conventionally successful individual to a mathematician and innovator, framing this transition through the lens of mathematical models. The speaker argues that understanding the difference between additive and multiplicative growth is crucial for navigating life and achieving meaningful progress.

Early Life & The Initial Pursuit of Success

The speaker began with a traditional focus on hierarchical success – achieving top grades, securing a position at a prestigious firm (JP Morgan, Goldman Sachs), and climbing the corporate ladder. This initial phase was characterized by a “single-threaded” ambition focused on external validation and financial gain. At age 25, however, this path was abandoned in favor of pursuing a long-held dream of becoming a mathematician, returning to Oxford University to study mathematics. Alongside this academic pursuit, the speaker developed “Kuzu” from Oxford, a platform garnering three million fans, delivered speeches internationally (Hong Kong, US, UK), and authored ten papers/manuscripts during their PhD. This shift represents a move from being a conventional achiever to an “outsider,” “rule breaker,” and “innovator.”

The Additive vs. Multiplicative Model Explained

The central argument revolves around the distinction between additive and multiplicative models of progress. The speaker poses the question: if you improve by 0.1% each day, how much will you grow in 10 years? The answer, using a multiplicative model (1 + 0.001)^3650, is approximately 38 times your current self. In contrast, an additive model (simply adding 0.1% each day for 3650 days) yields only 4.65 times growth.

The speaker emphasizes that mathematics provides a framework for understanding life’s trajectory. The multiplicative model represents compounding success, while the additive model represents linear progress. Examples provided include:

• Multiplicative: Entrepreneurship, compounding interest, snowboarding, short video sharing, infectious disease spread (illustrated by the COVID-19 pandemic).
• Additive: Receiving a fixed paycheck each month.

The Transition from Additive to Multiplicative Learning

The speaker posits that learning initially occurs through an additive model – imitation and direct instruction (parents teaching language, teachers explaining problems). However, a “tipping point” is reached where learning transitions to a multiplicative model, characterized by moments of enlightenment and epiphany. This shift occurs when individuals move beyond rote memorization and begin to synthesize information and generate new ideas. The speaker suggests that students often operate within an additive model by focusing on contributing to existing societal needs, but true creativity emerges when pursuing the intersection of social need, skill, and personal interest.

The Power of Persistence: Lessons from the Stock Market

A chart from JP Morgan illustrating S&P 500 investment returns over 10 years is used to demonstrate the importance of persistence. A 10% annualized return over 20 years results in a sixfold increase in investment. However, missing the 30 best trading days reduces the return to 117 (nearly flat), and missing the 40 best days results in a return of only 80 (negative growth).

The speaker draws a parallel to life, arguing that the “best trading days” represent the most painful and challenging moments. Avoiding these moments also means missing the subsequent rebound and potential for significant growth. The S&P 500’s largest single-day gain (9.4% on March 23rd) is cited as an example – selling out of panic before this day would have meant missing the recovery. This illustrates the power of long-term effort and not underestimating daily progress. As the speaker states, “not to underestimate the progress you made every day. As long as you do not give up, you are growing silently every day.”

Probability and the Pursuit of Difficult Goals

The speaker introduces a final mathematical model: if a task has a 2% success rate, and you attempt it daily for 90 days, your probability of success rises to 84%. This is calculated as 1 - (0.98^90). This model highlights that consistent effort dramatically increases the likelihood of success, even when facing seemingly insurmountable odds. Examples include breaking personal records, solving difficult mathematical proofs, gaining admission to a dream university, or launching a novel entrepreneurial venture. The speaker emphasizes that failure is inevitable, but persistence is key. “Once again, I think mathematics is showing you the progress of bar in life and quantifying the power of effort.”

Conclusion: Idealism, Action, and Leaving a Legacy

The speaker concludes by describing themselves as a “down-to-earth idealistic person,” believing that idealism and a fulfilling life are not mutually exclusive. They emphasize that current actions shape future outcomes and that the goals pursued today will define how the next generation remembers us. The final call to action is to “change the world and leave bravely and set presidents.”