I agree with Aristotle being on the list. He categorised the scientific fields, wirting treatises on all of them (their names are still those given by him) and provided a scientific method based on examination and proof.
Also the sheer volume of his work (of which only nearly half is estimated to have been saved) and the influence on scientists up to the 17th century, where Descartes and others begun the so-called 'new natural philosophy' justifies a position on such a list.
I am very much against granting such a position to jesus, mohammadh or st.paul. Afterall in my view they gave nothing scientifically, and instead caused a massive counter-evolution in the field of science. When the steam engine had already been discovered in the Hellenistic age, the dark age of christian (and other religious) thought burried it for the next 1700 years.
The amount of negative influence religion has had on science is simply massive on all respects, and the influence is analogous to that of ensuring human suffering for many aeons.
I would also place Freud on the list though, not so much because of his own work, but because he really started a new science, which is still developing.
Also one could mention several physicians and anatomists, for their inflience on neural science and general medicine. For symbolic reasons alone one should include at any rate Hippocrates.
Euclid could also be part of the list.
Also it is certain that we will never really find out who the very first influential people were, those who acted in the darkest of times, when man was still living in small groups, and hunting.