Today, large language models are very powerful, informational and analytical tools that significantly accelerate most of the existing methods and methodologies for processing informational processes. Scientific information is of particular importance in this capacity, which gradually involves the power of large language models. This interaction of science and qualitative new opportunities for working with information lead us to new, unique scientific discoveries, their great quantitative diversity. There is an acceleration of scientific research, a reduction in the time spent on its (...) implementation – the freed up time can be spent both on solving new scientific problems and on scientific creativity, which, although it may not necessarily lead to a specific solution to a particular scientific problem, but is able to demonstrate the beauty of science in various disciplinary areas. As a result, the interaction of large language models and scientific information is at the same time a research for solutions to scientific problems, scientific problems, and scientific creativity. Solving scientific problems requires the ability to efficiently process big data, which cannot be done without an effective method – one of the significant methods was the Transformer architecture, introduced in 2017 and comprehensively integrated into the GPT‑3 model, which, as of September 2020, was the largest and most advanced language model in the world. Therefore, GPT‑3 can be called the basis of most scientific developments carried out in the context of using large language models. The interaction of science and large language models has become a factor in the emergence of a large number of questions, among which are: «Is the result of data analysis new knowledge?», «What are the prospects for scientific creativity in the era of big computing?». Currently, these issues are extremely important, because they allow us to develop the foundations for effective human‑computer interaction. Therefore, this study analyzes the issues presented. (shrink)

Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of (...) the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification. (shrink)