Visual thinking-visual imagination or perception of diagrams and symbol arrays, and mental
operations on them-is omnipresent in mathematics. Is this visual thinking merely a …

In this paper, we investigate movement patterns of a particle in the particle swarm
optimization (PSO) algorithm. We characterize movement patterns of the particle by two …

Visual thinking is widespread in mathematical practice, and has diverse cognitive and
epistemic purposes. This entry discusses potential roles of visual thinking in proving and in …

Can an idea be beautiful? Mathematicians often describe arguments as “beautiful” or “dull,”
and famous scientists have claimed that mathematical beauty is a guide toward the truth. Do …

by Ivor Grattan-Guinness One of the distortions in most kinds of history is an imbalance
between the study devoted to major figures and to lesser ones, concerning both …

This paper investigates the following question: when can one reliably infer the existence of
an intersection point from a diagram presenting crossing curves or lines? Two cases are …

It is commonplace in the educational literature on mathematical practice to argue for a
general conclusion from isolated quotations from famous mathematicians. In this paper, we …

In The Logic of Number, Neil Tennant defines and develops his Natural Logicist account of
the foundations of the natural, rational, and real numbers. Based on the logical system free …

Philosophers of mathematics are often divided between 'mainstream'and 'maverick'. Ludwig
Wittgenstein could hardly be classified as 'mainstream'. He had in common with other …

Proofs of the fundamental theorem of algebra can be divided up into three groups according
to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs …