The theory of fractional analysis has been a focal point fascination for scientists in mathematical science, given its essential definitions, properties, and applications handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest calculus convexity due to wide range almost all branches applied sciences, especially numerical analysis, physics...

We investigated whether mathematicians typically agree about the qualities of mathematical proofs. Between-mathematician consensus in proof appraisals is an implicit assumption of many arguments made by philosophers of mathematics, but to our knowledge the issue has not previously been empirically investigated. We asked a group of mathematicians to assess a specific proof on four dimensions, us...

18 NOTICES OF THE AMS VOLUME 44, NUMBER 1 The mathematical sciences professions are in a phase transition from which they may well emerge smaller and/or redistributed and much more dispersed. We are not an endangered species, but our health depends on being able to transcend our historic tendencies toward insularity, on our outreach to all of our sister and client communities. This message, in ...

According to some mathematicians, the formalist philosophy of mathematics faces the dilemma that a practising mathematician could not possibly hold a formalist conviction, although some of the weaknesses of mathematical foundations almost enforce a formalist position. I am a formalist, and in this paper I explain how this dilemma fails to materialise.

‘New Macsyma 2.2 Math Software understands plain English’. ‘We believe Macsyma 2.2 can halve the time and energy required to solve problems with math software’ (Richard Petti, President, Macsyma Inc.) This article looks at some of these advertising claims and considers the potential for such features as an aid in the teaching of mathematics to mathematicians, engineers and scientists. In a shor...

It is very unusual for a mathematical or physical idea to disseminate into the society at large. An interesting example is chaos theory, popularized by Lorenz’s butterfly effect: “does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” A tiny cause can generate big consequences! Mathematicians (and non mathematicians) have known this fact for a long time! Can one adequately ...

H ilbert, in his 1900 address to the Paris International Congress of Mathematicians, listed the Riemann Hypothesis as one of his 23 problems for mathematicians of the twentieth century to work on. Now we find it is up to twenty-first century mathematicians! The Riemann Hypothesis (RH) has been around for more than 140 years, and yet now is arguably the most exciting time in its history to be wo...

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate six mathematical arguments, purportedly produced either by fellow or undergraduate students. In this paper, we attend the role context mathematicians’ responses, leading four themes expectations when evaluating proofs that they read. First, evaluations identical arguments sensitive researchers’ ma...