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In this extended entry, Pythagoras and all discoveries in Mathematics credited to Pythagoras are discussed: https://docs.google.com/a/mix.wvu.edu/document/d/1euQyZkzZmEf-2sYVNFnUAmwWcoGuvpq7RzzN9cj4_mY/edit?usp=sharing
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Hippasus is said to have discovered irrational numbers and that the Pythagorean religion is false. Due to his discovery and inability to keep quiet about his findings, it is said that he was either thrown overboard/drowned at sea or he was banished and a tomb was built for him (despite still being alive).
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Inspired by what he heard about Pythagoras, Plato founded his Academy in Athens where he stressed that mathematics was a way of understanding the world around you. He believed that mathematics represented in an unchanging ways that were more real than materialistic things around him. In this academy, he presented mathematics to his students as a form of philosophy.
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In one of Plato's recorded dialogues, Socrates and Meno are discussing whether Virtue is taught or acquired. He uses this dialogue to show that mathematics and knowledge are something that are not made by humans, but rather is something only those who chose to pursue remember. It tells of his believing that it is better to have students challenge themselves because the confusion that may result can help them grow since they are aware of their ignorance on the subject.
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In the Republic, Plato argues that geometry and arithmetic are two subject areas in mathematics that are essential to students' education. He argues that through learning mathematics we can be lead to the truth about the world. In this dialogue, it is argued that people of various classes should learn arithmetic for a number of different reasons because it alongside geometry draws the soul closer to truth and being.
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Though it originally shut down in 87 BCE, it was reestablished in the year 410 BCE before finally being closed down once and for all after it came under the control of Roman emperor Justinian of Byzantium.
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Cardano used square roots of negative numbers to show how impossible it was to use them to solve equations in his book Great Art. He described these numbers as being useless, despite their uses in Algebra. He then proceeded to reject such expressions, rather taking it that multiplication of two such quantities resulted in the production of a negative number. He did this so that a negative multiplied by a negative would produce a negative and thus no "sophisticated" roots had to be evaluated.
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Following Cardano's ideas, Federico Commandino shows criticism towards his fellow mathematicians who say that a plus multiplied by a plus is a negative number. Following him, many others even went as far as to avoid such negative numbers by restricting their solutions. This protest to negative numbers continued into the 1600s where many avoided and even dismissed equations using negatives.
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Through the combination of bibliographical events, historical accounts, and the use of astronomical cycles James Ussher proposes that the Earth was created in 4004 BC
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This extended entry discusses how different mathematicians began to address the significance of both positive and negative numbers while continuing to disagree about the results of equations involving such operations. https://docs.google.com/a/mix.wvu.edu/document/d/14Y0QU0qL4Q3H19HI5e8nPWBvXqGaAamnZOuefA0qh-s/edit?usp=sharing
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Through his own calculations based on his observed decline of the sea level, Benoit de Maillet proposes that the Earth was created nearly 2 billion years ago.
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Trying to convince the scientific community that the Earth had been around since before 4004 BC, Georges Buffon uses calculations estimating the rate of the Earth's cooling from a more molten state to come up with it's true age. He proposes that the Earth was created 75,000 years ago.
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Based on the concept of Uniformitarianism, Sir Charles Lyell proposes that Earth's features were things that could be explained through the natural forces that worked upon them. He proposes that everything upon the planet was a result of ordinary, continuous forces that worked in a unified manner. Based on these ideas, he believed that there was no need for supernatural influences in the creation of different physical structures viewed on the planet.
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This extended entry talks about Lord Kelvin and some of the ways he came up with his conclusion that the Earth is likely 100,000 years old - though it's true age could range from 20 million to 400 million years. https://docs.google.com/a/mix.wvu.edu/document/d/1OYcJ9vEWS3cPZAe3z6_gRBMYRtAujRLBUg40vRCYBDI/edit?usp=sharing
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German Physicist Wilhelm Roentgen discovers a ray that could travel through solid wood or flesh and yield photographs of living people's bones; he called them x-rays. This discovery earns him the first Noble laureate in physics in 1901.
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Months after Roentgen's discovery of x-rays, French physicist Henri Becquerel reports compounds of uranium emit rays that show up on photographic plates to the French Academy of the Sciences. Despite this discovery eventually leading into a larger understanding of atoms and a change in the why the scientific community thinks, it was initially ignored by the community as most scientists turned their focus towards Roentgen's x-rays.
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In this extended entry, Marie Curie's research on uranium, pitchblende, and chalcocite are discussed alongside her hypothesis that helped to shift the community away from thinking that atoms were the most elementary particle there is. https://docs.google.com/a/mix.wvu.edu/document/d/1H7mtXqQ6sYh-vm34KXxggZEH0Gd0wSgiewxeptW2Nh8/edit?usp=sharing
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In 1903, Marie and Pierre Curie, alongside Becquerel, receive the Nobel Prize for Physics. In 1911, Marie Currie receives the Noble Prize for Chemistry.
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Marie Curie confirms that Radium is an element.
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Despite there being much debate about irrational numbers through time, we have come to accept it today and have worked them into our system of numbers. Though, there is not much clarity surrounding Hippasus discovering irrational numbers, he is still mentioned and accredited by some mathematicians today. From 1945-2010, there have been numerous papers that have attributed the discovery of irrational numbers to him.
