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Born in Switzerland, Euler's father was Paul III Euler, a pastor, and Marguerite Brucker, a classical scholar. He was initially educated by his father in mathematics, then began taking private lessons at a Latin grammar school in Basel. In 1720, Euler entered the University of Basel and in 3 years, completed a Master's Degree in Philosophy with a dissertation based on a comparison of Renee Descartes and Isaac Newton's philosophies. By 1744, Euler had held several positions teaching Physics and Mathematics, and now, he was the director of Mathematics in the Academy of Sciences in Berlin. From here and the next 20-30 years, he would write 380 works and publish 275 of these, contributing greatly to the world of Mathematics and Physics. One of these now known as the Euler Identity, e^ix = cos x + i sin x, is integral to modern day signals theory

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1746, "Enodatio Quaestionis Utrum Materiae Facultas Cogitandi Tribui Possit Necne"

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1746, "Enodatio Quaestionis Utrum Materiae Facultas Cogitandi Tribui Possit Necne"

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This paper written in 1746 details his final thoughts on the matter of the soul, and answers one of Descartes most famous quotes, "I Think, Therefore I am". In a rare showing of Euler's of Philosophical side, through this paper he answers the question of whether or not a Body can possess the faculty of thought, and thus, our very existence. He sums up his thought process through the application of the law of inertia in the following:

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In 1723 at the age of 16, Euler earned his Masters Degree in Philosophy with a paper comparing the philosophies of Newton and Descartes. This paper is unfortunately unavailable, or if it is, unattainable as it seems that this dissertation was never published. 

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Brian Hepburn - Presentation of Euler - Galileo 

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According to Brian Hepburn in his 2017 discussion on Euler and his Philosophy, he explains that Euler's study of Mathematics and Physics and the involvement of different systems in the universe with eachother, is also the study of metaphysics of material bodies, rather than what a typical philosopher would be writing about; the nature of and properties of bodies. Hepburn believes that the study of these mechanics, is one of the keys to understanding the metaphysics side of Philosophy.

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Brian Hepburn's presentation is a good example of how to explain the thought processes and goals of a Mathematician in the 1700s such as Euler, and how it can relate back to their beliefs on how to better understand the world around them at the time. When taking into consideration Euler's particular background with his Masters in Philosophy and the publication of Enodatio in 1746, it is clear what kind of beliefs and thoughts guided his work throughout his life. He was clearly influenced heavily by Descartes, in that, he applies the law of inertia to prove that the soul is not in the body, but immaterial. He would likely agree with much of Descartes theories, but at the same time, he would have probably also agreed with much of Newton's philosophies as well, as, it is clear that his study of mechanics has much basis on Newton's work. Euler's approach towards Mathematics and Physics, has helped me understand a little bit about how much the desire to understand the world and maybe the approach of God, may have influenced much of the advancements at the time.

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Visualization of Euler's Formula in 3D, Wikipedia

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One of the things that I most took away from studying Euler's work and those around him, is the understanding of how others will work towards their own goals, and how learning of these philosophers helps put into perspective the origin of all that is our current world and society. For example, Euler's attempt to understand the metaphysics of the world, has led us to unimaginable advancements in signal theory and communications; amongst many other things. He simplified much of what we know about calculus today, and deepened our understanding of trigonometry to an unparalleled degree. 

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Euler was the tutor to a member of the Prussian royal family, and his 234 letters to her in the attempt to teach her of the sciences, were eventually compiled into a textbook for "every female academy in the kindgom".

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One of main things I have understood from going through these projects, is the idea of questioning what we know, and taking a more critical approach towards understanding why things are, why things might be, and how taking even systematic or empirical approaches towards understanding is a philosophy worthy of embodying. So long as we try to understand and attempt to reach the root of our understanding, we can say we have contributed to the world in some small extent.