Category Archives: opinion

On reasonably sure proofs

I happened to come across a 1993 opinion piece, Theorems for a price: Tomorrow's semi-rigorous mathematical culture by Doron Zeilberger. I think it's a rather fascinating document as it questions the future of mathematical proof. Its basic thesis is that some time in the future of mathematics, the expectation of proof will move to a […]


Art vs. science in mathematical discovery

Is mathematics science or art? Mathematics resembles science. In math, data and examples are collected and hypotheses made. There is a difference in the hypotheses of math versus science: in the former they can be proved, but that could be considered a small point. But I have met mathematicians who don't consider themselves scientists, and […]


Three changes to mathematics I'd like to see

Three things I would like to see happen with the practice of mathematics in the next ten years are: Computer proof assistants… …that are easy to use for the typical mathematician. Why? Mathematics is expanding tremendously and some areas are getting quite abstract. Some areas are so complex that I even wonder if anyone in […]



Are we running out of problems?

A senior mathematician who will remain nameless recently said in a talk, "there is nothing left to prove". In context, he was referring to the possibility that we are running out of math problems. People who heard laughed, and first-year calculus students might disagree. Was it said as a joke? Because of the infinite nature […]