"When mathematicians, historians and scientists say that they have explained something, are they using the word "explain" the same way?

What exactly does one mean by explain? The dictionary defines it in five different ways. I am going to state two definitions that are the most varied of the lot:
1. To give an account of something with enough clarity and detail to be understood by somebody else
2. To give the reason for something, often as justification for something that has happened

We thus have various interpretations of the same word. We find that while dealing with history, math and science, some definitions hold true while others are not as appropriate. For example in history the first definition might be most suitable although the second applies as well. Historians provide an account of events, and many times from their point of view. The records of the Indian freedom struggle for example would include those written by the English and those written by Indians. Each one will portray the same set of events in a different light. Science and Math explain events in different ways. To explore this idea I would like to look at the phenomenon of the creation of the universe.

The creation of the universe is a mysterious event. Does anyone really understand the truth behind it? But aren’t there those that dare to suggest possible explanations? The Big Bang theory for instance, has not been based on concrete evidence yet there are those that believe in it. So can we consider the Big Bang a part of the history of the universe? But history is an account of past events. How can man account for something that took place when the human race did not exist? This is the reason why Historians do not venture to explain this phenomenon and leave it open to interpretation by others. They do not posses any documentation related to the creation of the universe and hence cannot draw conclusions about its origin. This history is thus left in the hands of others and as we often see in historical events, different groups have different perspectives. Some believe this event can be explained using science, others think it was an unseen force that caused the birth of the planets and hence man kind. Hence conditioning, perspectives and emotion play an important role in history as ‘explained’ by a certain individual. Historians are free to have their own point of view about an issue, but only with records of direct observation of the event by a person or by people, can they begin to act upon the issue. A historian has no say in this matter because evidence for a historian includes documents and other observations and in a situation like this none of these forms of evidence apply. Although perception and bias can cause the event to be told in different ways, without records a historian cannot do much. Since historians have not put an explanation for this phenomenon on paper it is open to suggestions by those in other fields.

So if this phenomenon cannot be ‘explained’ by historians why is it that scientists have various theories that try to explain it? Does the word explain not imply the same thing? The Big Bang theory was proposed stating that the universe was at first an infinitesimally small point with an extremely high density. Due to the explosion of this mass the universe expanded and space and time were created. These hypotheses are quite bold. Scientists have used experimentation and various calculations to prove this hypothesis and they have received results that back it up significantly, yet we cannot be absolutely certain. It is still merely a theory. Why is it then that these theories hold a place of importance in science books and are ‘explained’ elaborately by science whereas such theories are not thought as highly of in a history book? This is because in science the usual procedure used to ‘explain’ a phenomenon involves formulating a hypothesis, experimenting based on this hypothesis and hence proving or disproving it. In certain cases proving a hypothesis can be fairly simple. For example, proving that water vaporises at 100ºC. Some hypotheses however even after extensive experiments might always remain mere theories, like the Big Bang Theory. Hence although we accept the reasoning and logic behind scientific explanations and consider they’re results as true, they are only so until proven false. In fact, science ventures to explain what cannot be explained by history. It explains natural phenomena. It tries to make lucid to us those events that are not easily observable. Hence it seems normal that the methods of ‘explanation’ in the field of science should be different from those of history. If not, explaining what history cannot, would become impossible.

History and science thus explain events, those that are observable and recorded, and those that aren’t. What does Math explain? Math is used to explain the behavior of numbers and many a times Math is used to explain science.

Math deals with conjectures and derivation. It involves logic and reasoning. In math, you begin with axioms i.e. statements that are considered true. A conjecture is then made and using axioms, an attempt is made to prove this conjecture, usually through derivation. These conjectures are based on an observation of how numbers behave, and sometimes might be completely off track, yet each conjecture is tested. Once tested and proved a conjecture becomes a theorem. So what do mathematicians explain? Do they explain the characteristics of numbers that go beyond observation? In the Big Bang theory, math is used to support the hypothesis made by scientists. In science experimentation is used to give a reason for an event that will constantly hold true. In math the phenomenon or pattern of behavior is modeled using an equation that will always predict approximately the expected results. Today’s model of the universe in the opinion of scientists is one that is expanding. This expansion is the very reason why they believe the universe was once a small point. Math can help explain this by tracing back this expansion to estimate the age of the universe. Calculations using math are used to estimate the approximate time of the Big Bang because although science can attempt to ‘explain’ why the explosion took place or how it took place, only math can help create a model that can ‘explain’ or in this case estimate how long ago this explosion took place. These numbers, figures and results are not observable and change with the addition of every little variable. Math explains the abstract, or what cannot be seen. It deals with concepts rather than events.

History, Math and Science hence explain different things and in different ways. But if we look at this example itself, History can state what has occurred but only up to a certain limit. It involves mere narration and hence can only narrate what has been observed although in different forms. Science can go beyond that yet not every conclusion made in science is completely certain. Over the years we have seen the very essence of various theories being uprooted. Math can help explain patterns in various areas but every prediction will remain an approximation and might not represent the truth, for we do not know enough to state that our models have no flaws or minimal flaws. Hence science and math do not make history. The fact that in the times of Galileo the common people believed the Earth was flat did not make it flat. They can predict and explain but until the event has occurred nothing is certain. Everything is true until proved false. Science can explain the events that were part of the creation of the universe and math can add numbers and figures to support these events. We see these findings in the form of a theory but until history or historians explain it, it will remain merely a theory.