In the latest issue (December 2013) of the *Notices of the American Society*, noted mathematician Doron Zeilberger has published an Opinion piece on the state of pure mathematics, and then contrasts this with experimental mathematics. His article, entitled “[Contemporary Pure] Math Is Far Less Than the Sum of Its [Too Numerous] Parts,” is available here.

Doron Zeilberger is perhaps best known for his work with Herbert Wilf in developing the Wilf-Zeilberger method for computer-based proving of combinatorial identities, a problem that mathematician-computer scientist Donald Knuth once rated as “50” (meaning of the greatest difficulty) in his book *The Art of Computer Programming*. In 1998, Wilf and Zeilberger received the Leroy P. Steele Prize of the American Mathematical Society for their work.

In his *AMS Notices* Opinion piece, Zeilberger notes that while the recent much-heralded discovery of the Higgs boson grew out of mathematical physics, this is a subject that many pure mathematicians regard with disdain because it makes assumptions and utilizes procedures that are not fully rigorously established. What’s more, the discovery relied on heavy-duty computations that are “far afield from esoterica most pure mathematicians hold dear.”

He also mentions the RSA algorithm for encryption and e-commerce, which is often held up as an example of pure mathematics in action, but notes that its safety relies on the unproven assertion that factorization is sufficiently hard, and, besides, the mathematical principles behind the scheme were essentially known to Euler. He adds that mathematics is “useful” only because physical scientists and engineers largely ignore the “religious” fanaticism of professional mathematicians.

Zeilberger then takes aim at the “highly dysfunctional” process of mathematical communication in the field, where even at the highest level, mathematicians often make “completely unrealistic expectations” of the backgrounds of their audience. He adds that the field has become so splintered that “very few people see the mathematical forest. Most can barely understand their own trees.”

Noting that the purpose of mathematical research should be the increase of mathematical knowledge, broadly defined, Zeilberger then says that “A new philosophy of and attitude toward mathematics is developing, called ‘experimental math’.” He argues that experimental mathematics should trickle down to all levels of education from professional meetings to graduate school and even to K-12 instruction. In particular, he argues that every undergraduate mathematics major should take a course in experimental mathematics.

He concludes by saying that while he loves rigorous proofs, those who research and teach mathematics should have a more open-minded attitude. “We need to abandon our fanatical insistence on ‘rigorous’ proofs.”

Zeilberger’s complete text is available here.