Sunday, 15 March 2026

The Courage to Say “We Don’t Know”

 In academia, authority is often associated with certainty. Students look at professors as repositories of knowledge, people who have studied longer, read more deeply, and mastered complex ideas. Yet one of the most powerful moments in teaching occurs not when a lecturer presents a flawless answer, but when they have the courage to admit a profound truth: there are still many things we do not know.


The day a scholar can stand confidently before their students and openly acknowledge the limits of current knowledge is, in many ways, the day they truly become a professor. It requires intellectual honesty and humility to say, “This question is still open,” or “Science has not yet found the answer.” 

Or even more simply,

“I don’t know the answer to this at the moment.”


For a teacher, admitting this does not diminish authority, it strengthens it. It shows students that scholarship is not about pretending to know everything, but about seeking truth with integrity.

Such moments transform the classroom from a place of passive learning into a space of discovery.


Ironically, the deeper we move toward the frontiers of knowledge, the more we become aware of its boundaries. Beginners often believe that science or mathematics contains answers to everything. But as researchers and educators explore more advanced ideas, they encounter a surprising reality: every solved problem reveals new unanswered questions.


In mathematics, physics, and many other disciplines, the history of discovery shows this pattern repeatedly. Each breakthrough, whether a theorem, an experiment, or a theory, illuminates a small region of understanding while simultaneously revealing the vast darkness beyond it. The closer we approach the edges of human knowledge, the clearer it becomes how much remains unexplored.


This realization is not a weakness of science or scholarship; it is one of its greatest strengths. A field that still contains mysteries is alive. The unknown invites curiosity, creativity, and the courage to think differently.


For students, hearing a professor admit uncertainty can be surprisingly inspiring. It shows that knowledge is not a finished monument handed down from the past, but a living journey in which they themselves may participate. The unanswered questions of today are the research projects of tomorrow.


True scholarship therefore lies not only in mastering what is known, but also in recognizing, and embracing, the vast landscape of what is not yet understood.


“The Mystery of π + e” An unsolved question at the heart of mathematics.

 


Mathematics has always been filled with mystery, elegance, and wonder. Perhaps this is why it is often seen as the hidden order behind the universe.

One of the most fascinating concepts in mathematics is that of transcendental numbers, numbers that are not the root of any polynomial equation with integer coefficients.

Two of the most famous numbers in mathematics, π (pi) and e, are both transcendental.

But the story becomes even more astonishing:

there are infinitely many transcendental numbers.

In fact, most real numbers are transcendental.

Yet a deep mystery remains.

Mathematicians still do not know whether the number


 π + e


is itself transcendental.

Despite decades of research, no one has been able to prove or disprove it.

And it is precisely this boundary between the known and the unknown that makes mathematics so beautiful, a universe where even the most familiar numbers still hide profound secrets.

Did you know that in mathematics… numbers (or rather spheres) “kiss”?


  Yes, Mathematics has its own version of a kiss!

And ironically, just like real kisses can lead to complicated stories, this mathematical “kiss” gave rise to one of the most fascinating geometric problems in mathematics.

It is called the Kissing Number Problem.

In geometry, the kissing number is:

The maximum number of identical spheres that can touch another sphere of the same size simultaneously without overlapping.

Imagine placing tennis balls around another tennis ball. How many can touch the central one at the same time? That number is called the kissing number.

In 1694, two giants of mathematics Newton and Gregory debated this problem. Newton claimed the answer in 3-dimensional space was 12. While Gregory suspected 13 might be possible.

The problem remained unresolved for over 250 years, until it was finally proven in 1953 that 13 spheres cannot simultaneously touch another sphere. Newton was right! 

Interestingly, the solutions in 8 and 24 dimensions were only proven recently and are connected to incredibly beautiful mathematical structures known as the E8 lattice and the Leech lattice.

The table below shows some knowing kissing numbers. 

The kissing number problem is not just a curiosity. It connects to major areas of science and technology such as:

• Error-correcting codes

• Information theory

• Crystallography

• Signal transmission

• High-dimensional geometry.

Mathematics often reveals that even the simplest questions, like how many spheres can touch another sphere, can lead to centuries of debate, deep theory, and beautiful discoveries.

Sometimes even a kiss can change mathematics!

         


#Mathematics #Geometry #STE #MathematicalBeaut #ScienceHistory

The Courage to Say “We Don’t Know”

  In academia, authority is often associated with certainty. Students look at professors as repositories of knowledge, people who have studi...