Borwein integrals, introduced by David and Jonathan Borwein in 2001, are a classic example of how intuition can be misleading in mathematics. Defined using the sinc function (sin(x)/x), these integrals initially appear to consistently equal π/2. However, this pattern unexpectedly breaks down when the factor sinc(x/15) is introduced, surprising even experienced mathematicians. This phenomenon underscores the importance of rigorous proof over reliance on patterns.

[David Borwein and Jonathan M. Borwein, “Some Remarkable Properties of Sinc and Related Integrals,” Ramanujan Journal 5:1 (March 2001)]