One of Greek root words she's referring to is aisthanesthai 
which means "to perceive (by the senses or by the mind), to feel,",
By top-down/bottom-up synthesis she means that there is a conscious process of perception, the top-down, in which you observe, as well as a bottom-up process, in which objects exert affects  on you. These two processes link cognitive aspects of experience (even in abstract) to emotional/sensory aspects.
When we discover one of these links between the cognitive and the sensory, there is a stab of pleasure, an 'aha!' moment of understanding, when we recognise some pattern in our experience.
the easiest way to understand what that means is to consider music. We can immediately recognise when a song is sad or happy, because those songs imitate the way we feel when we are sad or happy. If you're excited your pulse starts to race, similarly up tempo songs start to make us feel excited. so there is a sense in which, not only do we understand a song cognitively, we also understand it physically, in terms of the affect it produces.
in terms of your question, could you give a bit more context? I feel like I need to read the paragraph that came before this one in order to answer what relation 'aesthetic' has to the argument, but from what is there she seems to be making some argument related to, maybe why we seek knowledge and understanding? at the very least she's talking about the pleasure we feel when we solve or understand something. The paper you're quoting from is also called 'Art and Science' so maybe she's trying to show that science has aesthetic qualities just like art?
So as far as 'Aesthetic' and 'I breath in', 'I gasp' acknowledging this frisson of emotion I think she is just referring to the fact that it's root words mean both to perceive and to feel. In other words, mind and body. So 'aesthetic' is word for understanding with both mind and body. Its important to understand that this does not mean understanding in the mundane sense of what we already know, but the kind that happens very infrequently in moments that seem like intuitive leaps, moments of spontaneous understanding that produce intense emotional shivers of excitement (think Archimedes in the bathtub), and are in some sense the aesthetic side of science.