Physics with or without philosophy, and the relationship between them

According to dictionaries such as the Oxford English Dictionary and the Wiktionary, the word philosopher comes originally from Anglo-Norman filosofre, philosophre variant of Old French and modern French philosophe, from Latin philosophus, from ancient Greek philosophos (φιλόσοφος) lover of wisdom, formed as philo- + sophos, meaning wise. It is thought that Pythagoras coined this term to describe himself.

In Antiquity, thinkers such as Pythagoras and Aristotle were first defined as philosophers before being called mathematicians or scientists.

Things changed gradually with the advance of knowledge and technology, and disciplines got more or less separated, but the expression “Natural Philosophy” was still widely used a couple of centuries ago to designate physics and the physical sciences.

Physics as an exact science or a scientific field of study cannot “function” or provide exact measurable results without mathematics, and physics also needs or is enriched by philosophical reflections, ideas and considerations. Philosophy can interact with physics, and vice versa.

As an example, Kant built a philosophical system taking into account ideas from classical and Newtonian physics. At the beginning of the twentieth century, Henri Poincaré wrote instructive books about the philosophy of science, mathematics, and physics, such as “Science and Hypothesis” and “Science and Method”. Einstein (and Infeld) wrote a book entitled “The Evolution of Physics” about the history of the important concepts and ideas in physics, mostly from a philosophical point of view. Werner Heisenberg wrote a book entitled “Physics and Philosophy: The Revolution in Modern Science”, mainly dealing with quantum mechanics, its history, its implications, and its philosophical consequences.

More recently, there have been instances of books about the philosophy of science trying to discuss or explore “The trouble with physics” (title of a book by Lee Smolin), or trying to consider or examine why certain theories are possibly “Not even wrong” (title of a book by Peter Woit), because sometimes by their actions and theories physicists might be at risk of saying “Farewell to Reality” (title of a book by Jim Baggott), with authors sometimes cautioning against getting “Lost in Math: How Beauty Leads Physics Astray” ( title of a book by Sabine Hossenfelder).

As a branch of philosophy, epistemology
of science and of physics is useful to study the nature, source, scope and limitations of scientific knowledge. Ideas, notions and concepts related to philosophy, epistemology, science, and physics include induction, deduction, empiricism, positivism, rationalism, skeptical enquiry,…

Each scientist or physicist is usually guided or influenced by his or her own philosophy, philosophical background or readings.

Some useful books about the history of modern mathematics

There are some books that deal with the history of (modern) mathematics during the last 100 years, during the 20th century, or the last two centuries.

Two books by Jean Dieudonné:

A History of Algebraic and Differential Topology, 1900-1960

History of Functional Analysis

Here is a good book about the history of group theory and Lie groups:

Emergence of the Theory of Lie Groups, An Essay in the History of Mathematics 1869-1926, by Thomas Hawkins.

Other relevant or informative books include the following ones:

Elements of the History of Mathematics, by Nicolas Bourbaki.

The Mathematical Century: The 30 Greatest Problems of the Last 100 Years, by Piergiorgio Odifreddi.

Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics, by Mark Ronan.

History of Topology, Edited by I.M. James.

Mathematics and its History (3rd edition), by John Stillwell. The last chapters of Stillwell’s book deal with modern or recent mathematical topics such as Non-Euclidean geometry, group theory, hypercomplex numbers, algebraic number theory, Topology, simple groups, sets, logic and computation, and combinatorics.

Another useful book dealing with mathematics in the last two centuries :

Changing Images in Mathematics: From the French Revolution to the New Millennium (Routledge Studies in the History of Science, Technology and Medicine), by Umberto Bottazini, Amy Dahan Dalmedico.

Below is a book focusing on five mathematical theorems and results of the twentieth century :

5 Golden Rules: Great Theories of 20th-Century Mathematics and Why They Matter, by John L. Casti.

The following related links can also be helpful:

Books about history of recent mathematics

20th century mathematics

Estimating the date or the year when humans will land on Mars

Let us begin with some general facts and data.

Earth is the third planet from the sun, an Earth year is approximately equal to 365.26 days.

Mars is the fourth planet from the sun, a year on Mars is approximately equal to 687 (Earth) days.

Earth moves in an orbit around the sun at an average (semi-major axis) distance of 149,598,023 km, or 92,955,902 miles, or 1 AU (astronomical unit).

Mars moves in an orbit around the sun at an average distance 227,939,200 km , or 141,634,850 miles, or 1.523679 AU.

Mars Oppositions occur when Earth passes between the Sun and planet Mars. Mars oppositions take place approximately every 2 years and 2 months, or every 779.94 Earth days. During these times of opposition, the two planets have the closest distance to each other.

Two useful or interesting dates of closest encounter and closest distance between Earth and Mars are the following ones.

The first date of closest encounter is June 27, 2033. At this date, the distance between Earth and Mars will be approximately 0.428 AU.

To visualize things better, below is an image showing the positions of Earth and Mars and of neighboring celestial bodies on January 29, 2033 (image source: 3D Solar System Simulator):

Below is an image showing the positions of Earth and Mars and of neighboring celestial bodies on June 29, 2033 (image source: 3D Solar System Simulator):

A second date of closest encounter is September 15, 2035. At this date, the distance between Earth and Mars will be approximately 0.381 AU.

The first of these two dates of closest encounter, June 27, 2033 (give or take a few days), could be realistically chosen as the time and date when a human will land on Mars.

People and humans have been planning and wanting to go and set foot on the red planet for the last few decades, some intending to go there in an unprepared and unrealistic way.

In order to ensure the success of the first human mission or trip to Mars, the mission should be the result of international cooperation, everyone taking part in the trip ought to be very well trained and prepared. All the aspects of the mission (technological, scientific, computational, financial, …) ought to be thoroughly taken into consideration, so that the human crew will be able to land on Mars, stay there for a determined short period of time, and return back safely to Earth.

The human mission or trip to Mars is not a game or a one-way voyage with uncertain or harmful results and consequences.This will be a very important event in the history of humankind, and not everyone is ready or able to make the journey to Mars .But those humans who will travel to Mars should be prepared to the maximum.

The human crew would be sent a few months earlier to Mars, so that they would land on Mars at a date approaching the date of closest Earth-Mars distance of June 2033. Hence one of the best dates for humans to set foot on Mars for the first time would be in the summer of 2033.

Among the various factors upon which the progress and success of the mission will depend, one important factor would be the readiness and sagacity of the leader of the first human mission to Mars, who will most likely be the first person to set foot on Mars, and whose decisions will be essential and vital to the suitable choice of dates, and to the successful planning, unfolding, development, and accomplishment of the first human mission to planet Mars.