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In Foundation, we learn that a small group of mathematicians have developed "psychohistory", the aforementioned rigorous science of society.
Mathematicians have developed a theoretical model which envisages the end of the universe in around 22bn years, with a phenomenon called the "big rip".
Indeed, a few mathematicians have developed probability theory with only the weaker axiom of finite additivity, but the absence of interesting models that fail to satisfy the axiom of countable additivity has led to its virtually universal acceptance.
Just as molecules can be broken down into atoms, mathematicians have developed a periodic table of symmetry that describes geometric objects in many dimensions.
In the medical field, mathematicians have developed algorithms and computer models to investigate cardiac arrhythmias in patients, to sequence the human genome, and to understand the spread of pathogens like the bird-flu virus.
Practitioners and scientists have developed adaptive management and structured decision making techniques, and mathematicians have developed methods to reduce the uncertainties encountered in resource management, yet there continues to be misapplication of the method and misunderstanding of its purpose.
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The French mathematician has developed an "invisibility cloak," which will protect buildings from the shock of earthquakes.
To solve more complex problems, mathematicians and engineers have developed powerful computer-aided numerical methods, which can be categorized into two main types: differential methods and integral methods.
Mathematicians and engineers have developed in a joint research project a solution approach for performing simultaneous structural and design variable optimization in the design of cost-effective complex energy conversion systems.
And contrary to Tsiaras' assertion that development lies beyond the possible comprehension of mathematicians, theoreticians (starting with Alan Turing) have developed computational models to explain how complex biological patterns and structures are organized.
The medial structures has become a popular research area in recent years — mathematicians have studied the properties of these representations, and computer scientists and engineers have developed a variety of algorithms for computing and using these models; cf. [28] and references therein for a detailed survey of this topic.
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mathematicians have dreamed
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