A Revıew of Mathematical Conjectures: Exploring Engaging Topics for University Mathematics Students
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Keywords:
Conjecture, Mathematics, Python, Coding, ProgrammingAbstract
Throughout history, humanity has been driven by an innate curiosity to explore beyond
established boundaries, particularly evident in scientific and mathematical pursuits. The realm of
mathematics has seen numerous conjectures spanning ancient times to the present day, encompassing
various mathematical domains. These conjectures, some evolving into theorems upon proof, others being
refuted and replaced, and a few remaining yet unresolved, form a significant facet of intellectual
exploration. They captivate not only professional mathematicians but also enthusiasts, contributing to the
evolution of mathematics. Mathematical conjectures are statements that have not yet been proven to be true
or false. Typically created from observed patterns, these conjectures often originate from seemingly simple
propositions. Presently, advancements in computer programming have substantially contributed to and
aided in proving wrong by finding some counterexamples or confirming the conjectures for very large
numbers. Python, in particular, facilitates the verification of conjectures for larger numbers, the
identification of patterns and formulas, confirming conjectures or helping in finding counterexamples
leading to rejection, as well as refining existing ones or generating new ones. The article aims to present
several famous math conjectures, predominantly in number theory, and emphasize the importance and use
of working with students for a more interesting class. Notable conjectures include Euclid's perfect number
conjecture, Fermat's number conjecture, Collatz's conjecture, Landau’s conjecture, Mersenne's prime
conjecture, and more.
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