In Judaism, there is a cherished concept known as lishma—learning for its own sake. This idea is central to Torah study, where the act of learning is seen as inherently valuable, even when the knowledge gained has no immediate practical application. Classic examples include the study of korbanot (sacrifices) and yibum (when a man marries his deceased brother’s widow). These mitzvot are no longer practiced, yet we continue to learn about them. Why? What is the purpose of studying something we will never put into action?
This question extends beyond Torah study into my high school math classroom. Students often wonder why they need to learn topics that seem disconnected from their everyday lives. Almost every time I introduce a new concept, my students inevitably ask me, “When will I need this in ‘the real world?’” They wonder why we study the sum of the angles in a dodecagon, graph rational functions, or explore trigonometric ratios. They naturally assume that they can live happy and fulfilled lives without worrying about identifying a curve’s asymptote.
To counter their sense that our math skills lack practical application, I show my students that we never know when we will find a connection between our math learning and the world around us. For example, in my algebra 2 class, we spend weeks learning logarithm rules. Over and over my students wonder aloud about when they will ever need or use these rules. I ask them for patience. Finally we reach the lesson on compound interest. Many of my students are interested in finance and investments and look forward to taking economics classes. They quickly realize that solving many compound interest equations requires the use of logarithm rules. They finally see that something that seemed so random at first has a practical, real-world application.
I also want them to learn math lishma, even when it does not neatly map onto a pragmatic use like compound interest. I stress to my students that, just as with Torah study, the value of learning math is not solely in its practical application. There is an intrinsic worth in the process of learning itself—the way it shapes our thinking, sharpens our reasoning and challenges us to engage deeply with ideas. I like to tell my students that doing math is like doing push-ups for your brain. Just as a basketball coach has her team doing push-ups to build physical strength, so too we build strength in math class.
In our lishma learning of math, we spend a significant amount of time simplifying radical expressions without later moving on to related word problems or applications of this principle beyond the math classroom. In cases like this, I point out that in both Torah and math, lishma represents a holistic approach to education. Rather than focusing purely on memorization or immediate use, we emphasize questioning, critical thinking and intellectual curiosity. Study for the sake of study — to understand the world and everything within it — has its own value.
Sometimes, too, we cannot see in which practical directions our lishma learning might lead. Just as studying logarithms can lead to a deeper understanding of exponents and, eventually, practical applications like compound interest, learning about tzara’at (a biblical skin disease) can spark discussions about the ethical implications of lashon hara (gossip). Sometimes an idea that seems to lack practical application can come back to us months or years later, showing us its significance in an entirely new context. And even when a concept doesn’t initially seem directly relevant, engaging with it strengthens our ability to think, reason and appreciate the underlying structures of the world around us.
Torah learning at a high level brings us closer to Hashem by deepening our understanding of His wisdom. Similarly, studying math can help us better appreciate the beauty and order of creation. Recognizing patterns, uncovering mathematical truths and pushing ourselves to think in new ways—these experiences enrich us, regardless of their immediate practicality. Experience with these skills strengthen one’s ability to think profoundly and make unique, meaningful connections to the world.
As educators and learners, we can embrace the concept of lishma in every academic discipline by fostering an appreciation for the depth and beauty of the subjects we study. Whether we’re delving into ancient texts or graphing conic sections, the act of learning itself is a meaningful pursuit—one that expands our knowledge and appreciation of the world and also cultivates a lifelong love of learning.
Ms. Aviva Bukiet teaches math at SAR High School. Previously, she taught at Heschel High School and before that in the New York City public schools. She received her BS from New York University and MA from Touro College, both in Math Education.
About Machon Siach: Machon Siach was established in 2015 with a legacy gift from Marcel Lindenbaum z”l, honoring the memory of his wife, Belda Kaufman Lindenbaum z”l”.
