The LUMS Math Circle held on May 30, 2025, was a compelling and intellectually rich session titled “Detecting Genetic Disease.” The event brought together mathematics and life sciences in a unique and accessible format, led by two distinguished faculty members, Dr. Waqas Ali Azhar from the Department of Mathematics and Dr. Khurram Bashir from the Department of Life Sciences.
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Exponents, Logarithms, and Mathematical Connection
Exponents, Logarithms, and Mathematical Connection
The session began with Dr. Waqas Ali Azhar introducing the audience to the fascinating world of exponents and logarithms, focusing on their rules, behavior, and real-world implications. He captivated the students with interactive mathematical games and puzzles. One memorable question posed was: “How thick would an A4 paper become after folding it 42 times?” A prompt that led to a discussion on the explosive nature of exponential growth.
He demonstrated how exponential patterns appear in various phenomena, such as:
Viral Marketing: If one person informs ten others, and the process continues over 10 layers, the outreach grows to 10¹⁰ people.
Population Growth: With each generation having four children, the population multiplies to 4⁶ after six generations.
Connectedness: A fascinating exploration of the “six degrees of separation” suggested how closely connected humanity is through exponential links.
Inverse Laws: Dr. Waqas tied in the inverse square law to explain how light and sound intensity diminish with distance.
Tennis Brackets Puzzle: A fun math puzzle asked how many rounds it would take to determine a winner in a 128-player knockout tournament, a great demonstration of logarithmic reasoning.
To enhance engagement, he introduced a binary birthday trick, where participants identified which card contained their birthday number. Using binary representation up to 31, Dr. Waqas accurately guessed the date, a clever and entertaining application of base-2 mathematics.
Here are some highlights from the event:
From DNA to Disease-Understanding Genetics Through Science
From DNA to Disease-Understanding Genetics Through Science
After the mathematical warm-up, Dr. Khurram Bashir shifted the focus to the biology of hereditary diseases, particularly Thalassemia. His presentation blended science with cultural and poetic expressions, beginning with an Urdu verse that reflected the essence of inherited traits and genetic legacy.
He educated the audience about:
The structure and fidelity of DNA replication—how our body replicates DNA with remarkable precision, producing just one error in 1 billion bases.
Genetic mutations and how even a single defect can lead to diseases.
A specific case study involving Nicholas Volker, whose life-threatening condition was traced to a single gene mutation using full genome sequencing.
The genetics of Thalassemia, its autosomal recessive inheritance, prevalence in Pakistan, and how it can lead to either carrier status or full-blown disease, depending on the inheritance pattern.
To make science more tangible, Dr. Khurram introduced Polymerase Chain Reaction (PCR), a cornerstone of genetic testing. He broke down the PCR process—denaturation, annealing, and amplification—and related it to the concept of exponential growth in a manner that resonated with the young audience.
He also used vivid comparisons such as:
DNA replication speed and error rate.
Pakistan’s wheat production versus the legendary "Wheat and Chessboard" problem, demonstrating exponential escalation.
Here are some highlights from the event:
Conclusion
The event beautifully illustrated how mathematics and biology intersect in modern science. From exponential growth and base systems to the intricacies of DNA replication and genetic testing, the session was both educational and inspiring.
Dr. Waqas and Dr. Khurram succeeded in breaking down complex ideas for a youthful audience, sparking curiosity in both abstract reasoning and real-world science. The LUMS Math Circle continues to fulfill its mission of bringing advanced concepts to school students in a fun, interactive, and impactful way.
Heartfelt thanks to the organizers and volunteers who made this event a success, and to the students who brought vibrant energy and thoughtful participation throughout the session.
Special Thanks to Mr. Muhammad Javaid Qayoom for writing this wonderful recap.
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