Since the earliest days of scientific thinking, logic has been the part of philosophy devoted to reasoning. Mathematical logic emerged from a need to formalise facts in the form of logical sentences and to reason systematically with this information to derive logical conclusions. Symbols and formulas resembling those of mathematics go beyond the reach of traditional logic. The advent of computers led to real-world applications. Today, mathematical logic plays a central role in software engineering, programming, artificial intelligence, linguistics and theoretical computer science. Having outgrown its philosophical roots, mathematical logic also continuously interacts with other branches of mathematics. 'From mathematical logic to applications' (MALOA) was a training network project reflecting a common research goal to unravel interactions between different branches of mathematical logic. A group of outstanding European mathematicians joined MALOA to provide 42 early-stage researchers (ESRs) with training in a broad range of concepts and state-of-the-art techniques. MALOA participants represented eight of Europe's most active academic centres in model theory, complexity theory, proof theory and set theory. The training programme included the latest advances in mathematical logic with potential industrial applications. Young scientists left the network after successful completion of their training with a set of aptitudes that enables them to produce influential research. Project efforts resulted in a long-lasting consortium for cutting-edge research, leading to accelerated discoveries even during its four-year lifespan. The recruited PhD students and postdoctoral fellows in MALOA have already contributed with new concepts to the model and proof theories. Moreover, the training programme that addressed the fragmentation of mathematical logic also boosted the trainees' career opportunities. Besides providing support to PhD candidates through the completion of their theses, many MALOA ESRs attained permanent academic posts or employment in industry, thereby strengthening the European research base.
Logic, mathematical logic, algebra, analysis, geometry, software engineering, programming, artificial intelligence, linguistics, computer science