Ramanujan Auditorium

The finite part of infinity

Joseph Samuel

Raman Research Institute and ICTS-TIFR

Ramanujan's notebooks contain the equation 1+2+3....= -1/12.
While this seems to go against common sense, there is deep
mathematics behind this assertion. I will try to explain in what sense
this must be understood. Such mathematical interpretations of
divergent series have had an impact in physics, leading for example to
a quantitative understanding of the Casimir effect, which has been
measured in the laboratory. I will try to bring out how higher
mathematics meets physics. Finally, I will describe a connection with
infinities in quantum field theory and its connection to the
cosmological constant problem.