This hand powered mechanism discovered in 1901 and dated back to 100 BC. Presently located in National Archaeological Museum in Athens. Considered to be the first known analog computer.
See the nature publication by Tony Freeth et. al., discussing the science and mathematics behind this ancient machine based on the X-ray Computed Tomography studies: 'A Model of the Cosmos in the ancient Greek Antikythera Mechanism'
Although ''big bang theory' is the prevailing explanation, the quest to know about universe lead to more questions than answers. Well known mysteries: dark energy, anti-matter, existence of parallel universe, direction of time. The more you read about each one the the more dumbfounded you get (at least I do).
Noteworthy books to get started: 'Astrophysics for People in a Hurry' and 'Cosmic Queries' by Neil deGrasse Tyson; and the classic 'A Brief History of Time' by Stephen Hawking.
The original question examined by Charles Darwin—what is the mechanism that causes new species to evolve—has yet to be fully explained. He was haunted by a simple but profound question of how the first flowering plants evolved. One of the biggest mysteries in biology is whether natural selection is the only process that generate new species or are their other material properties that comes into play?
For example, evolution of eyes, bacterial flagella, wings, and turtle shells. Some of the big ideas toward this are phenotypic plasticity, self-organization, and novelties in nature.
You can explore this beginning with books such as: 'The Blind Watchmaker' and 'The Greatest Show on Earth' by Richard Dawkins, 'Why Evolution Is True' by Jerry Coyne, 'Charles Darwin: Voyaging' by Janet Brown.
This is one of the greatest mystery of physics. We all age and become decrepit, but there is not return to youth. The fundamental laws in physics does not put any restriction on the direction of time. However, per second law of thermodynamics the disorder always increases with time. This puts the direction on the arrow of time.
Scientists are debating whether spacetime, like the elementary particles represented in the standard model and the fundamental forces of nature acting on them (gravity, electromagnetism, strong and weak nuclear forces), is a fundamental component of physical reality or is emergent and only has a derivative existence.
You can scratch you head on this by starting with 'The Order of Time' by Carlo Rovelli , 'Einstein’s Clocks, Poincaré’s Maps: Empires of Time' by Peter Galison, 'From Eternity to Here' by Seal Carroll, also check his TEDx here.
The most obvious starting point of this subject is to address the question in mind: ‘How can I know anything at all?’ To know anything at all is to go through a process of a series of experiences which grow from an opinion, to a belief about it, and finally to justified knowledge. One can have an opinion that a particular event happened, but can’t lay claim to certain knowledge unless this knowledge can be justified. As the event is tested, knowledge about it attains greater certainty. This is true in particular about empirical knowledge, where claims made about certain events can indeed be tested.
A priori knowledge by its nature is not acquired in the same manner as empirical knowledge. In this case, it is a matter of reasoning through an idea to establish its truthfulness. We observe that the sun is round; but by the very definition of ‘round’ we can come to the conclusion that round objects have no sides: thus, objects that have sides cannot be classified as round. A fundamental work on this topic is by John Locke in his 1689 work 'An Essay Concerning Human Understanding'.
The Gettier Problem is a landmark problem in philosophy related to the understanding of descriptive knowledge. See his paper titled 'Is Justified True Belief Knowledge?' that sparked a period of pronounced epistemological energy and innovation.
This is my personal quest about fascinating scientific (and philosophical too) questions: What is this thing called color? And how in the world can two people see one color so differently?
We inherently think we see the world objectively. If we get technical about it then there are eyes, receptors, cell, brain processing and so on. And this system is working all the time. But how we see an object has everything to do with how that object is illuminated. Our brains have adapted to see white as white whether it’s under harsh fluorescent light or soft daylight, blue light or yellow light.
So we don’t really “see” color, but reflected light, as interpreted in our brain. “It’s a useful perception of our world, but it’s not an accurate perception of our world,” as per neuroscientist Beau Lotto.
The 8th century Hindu philosopher Adi Shankaracharya wrote, in a similar fashion, that no one thinks 'I am not', arguing that one's existence cannot be doubted, as there must be someone there to doubt. The central idea of cogito, ergo sum is also the topic of Mandukya Upanishad.
This is the first principle in Rene Descartes 1637 work titled 'Discourse on the Method'. It is asserted that the very act of doubting one's own existence served—at minimum—as proof of the reality of one's own mind; there must be a thinking entity—in this case the self—for there to be a thought.
"Therefore I suppose that everything I see is false. I believe that none of what my deceitful memory represents ever existed. I have no sense whatever. Body, shape, extension, movement, and place are all chimeras. What then will be true? … Thus, after everything has been most carefully weighed, it must finally be established that this pronouncement “I am, I exist” is necessarily true every time I utter it or conceive it in my mind. (Descartes, Meditations)"
Alas, this still remains a central philosophical question.
These are seven well-known and unsolved problem in mathematics selected by the Clay Mathematics Institute. It challenged the mathematical community in 2000 to solve these seven problems and pledged a US $1M reward for the solvers of each. The problems encompass a diverse group of topics, including theoretical computer science and physics, as well as pure mathematical areas such as number theory, algebraic geometry, and topology.
Poincare Conjecture (proved in 2003 by the Russian mathematician Grigori Perelman)
P vs. NP
Hodge Conjecture
Riemann Hypothesis
Yang-Mills Existence and Mass Gap
Navier-Stokes Existence and Smoothness
Birch-Swinnerton-Dyer Conjecture
Detail problem description can be found on claymath website
