**A few days ago, S Hayes asked an interesting question. Equipped with a time machine that can only visit the past, and only allowed three trips, where and when would you go? The following are my choices.**

In her article *Time Machine, Three Trips: Where Would You Go?*, S Hayes asks where her readers would go if they had access to a time machine. After careful consideration, here are my three choices and the reasons for them. My trip will take in the pyramids of Egypt, the Tower of London and the home of Pierre de Fermat.

### The Rules

For a full explanation of the rules see the above article, but in summary they are as follows.

- Only three trips are allowed
- The trips are restricted in time to the past only, but not before the earth was formed
- The trips are restricted in space to the earth and its moon
- The trips are for observational purposes and can only be used to gain knowledge

### Difficult Choices

The problem with a task of this nature is that there are thousands of events and people in the past that merit a closer look. Picking just three of these causes a few difficulties.

Try picking your top three favourite songs or books and there may be two that are very easy to choose and have to go on the list. Then there may be another 10 or so to fill the remaining place. The choice becomes not what to select but what to leave out.

The same applies here. To narrow down the range I decided on a theme for my travels. I could have chosen to experience great events for myself, such as Martin Luther King, Jr.’s “I Have a Dream” speech. Or maybe travel into the deeper past to witness species that are now extinct, like dodos or mammoths.

In the end I decided to use my three trips to try to explain some of the mysteries from history. Having chosen the theme, two of my selections were very easy. The third came from a long list of possibilities and deciding what to leave out was difficult.

After a lot of thought, I am finally happy with my selections (for now).

### 2589 BC: Building the Great Pyramid of Giza

The Great Pyramid of Giza, in Egypt, was built for the second king of the 4th dynasty, Khufu (Cheops in Greek). Work started at the beginning of Khufu’s reign in 2589 BC and took at least 20 years to complete.

The Great Pyramid was constructed of approximately 2.3 million blocks of stone, with a total weight of 5,750,000 tons. Most of the stone was yellow limestone, but the outer casing, and the lining of the internal passageways, was white limestone. The burial chamber was lined with granite.

The four sides of the Great Pyramid are 230 metres in length and were aligned to the four cardinal points of the compass. The original height was 147 metres, but with the outer casing plundered it stands at 138 metres today.

Opinions differ about the size of the labour force required to build the Great Pyramid, but it is clear that they were not slaves. Estimates range from 20,000 men, if the workforce was permanent, to 100,000 men, if seasonal.

Most archaeologists agree that a system of ramps would have been used in the construction. The stone blocks would have been dragged up the slopes using sledges and rollers. There are, however, several different types of ramps that could have been employed, ranging from straight or zigzag slopes up one side, to a spiral system around the entire pyramid.

The white limestone of the finished structure would have shone magnificently in the sunlight, and a trip in a time machine would be worthwhile just to see it. But the journey would also answer a number of questions.

- What was the size of the workforce?
- Were the labourers permanent or seasonal?
- How long did the construction take?
- How were the limestone and granite blocks quarried and transported?
- What type of ramp system was used in the construction?
- How would the pyramid have looked before the white limestone casing was stripped off?

### 1483: The Fate of the Princes in the Tower

With the unexpected death of Edward IV on 9 April 1483, his 12-year-old son became Edward V. As Edward made his way from Ludlow to London he was intercepted by his uncle, Richard, Duke of Gloucester. Richard escorted the new king to London and was recognised as lord protector.

Edward IV’s widow, Elizabeth Woodville (sometimes Wydeville) sought sanctuary with her younger son, Richard of York, and her daughters in Westminster Abbey. Convinced that Gloucester was making preparations for Edward V’s coronation, Elizabeth surrendered Richard into his custody on 16 June.

Having removed Edward’s supporters from power, and with the two princes in his custody, Gloucester usurped the crown 10 days later, becoming Richard III.

The princes were housed in the residential apartments of the Tower of London and were officially free. But, after August 1483, they disappeared. The popular view, supported by the writings of Thomas More and dramatised by William Shakespeare, is that the princes were murdered soon after under the orders of Richard III.

There are those that disagree with this view and place the blame elsewhere, including members of the Richard III Society. Even at the time, mystery over the fate of the princes allowed Perkin Warbeck to pretend to be Richard of York during the reign of Henry VII.

In my view, the princes were murdered with the full knowledge of Richard III. If they had left the Tower of London alive they would have been a threat to the new king. The 15th century was a turbulent time, and the Wars of the Roses had taught those in power of the importance of removing threats.

It has been suggested that the princes were murdered after 1485, when Henry VII took the throne. But Richard III had opportunities to quell unrest during his reign when it was claimed that the princes had been killed. All he had to do was show that they were still alive. His refusal to do this suggests that they were dead.

None of these theories are conclusive, and so a trip in a time machine to 1483 could be used to answer many questions.

- Were Edward V and Richard of York murdered?
- When did they die?
- Who was responsible for their murders?
- Did Richard III give the order for them to be killed?
- Were the skeletons found in the Tower of London in 1674 the remains of the princes?

### 1637: Fermat’s Last Theorem

In 1637, Pierre de Fermat wrote a note in the margin of his copy of *Arithmetica*, by Diophantus of Alexandria, that has puzzled mathematicians ever since. Written c. AD 250, *Arithmetica* contained a series of mathematical problems and solutions.

The book also posed the problem of finding solutions to the equation

x ^{n} + y ^{n} = z ^{n}

where x, y, z and n are positive integers and n > 2. The case where n = 2 was already known to produce an infinite series of Pythagorean triples.

Fermat’s note stated (in Latin) that no non zero solution exists for n > 2. The note ends “I have discovered a truly remarkable proof but this margin is too small to contain it.”

Unfortunately, due to Fermat’s reluctance to publish his work, his “remarkable proof” was never seen by anyone else. For over three centuries the search for a proof of what became known as Fermat’s Last, or Great, Theorem occupied the minds of some of the world’s finest mathematicians.

Early work on the problem concentrated on finding proofs for specific values of n. A general proof for all values of n was elusive. By 1993, with the aid of advanced computer processing power, the theorem had been proved for all n < 4,000,000.
The final breakthrough came in 1993, when Andrew Wiles published a partial proof. Several holes were found in the proof, but in 1995, with the aid of Richard Taylor, he published a full and corrected version in the *Annals of Mathematics*.

Given that the solution of Wiles and Taylor ran to 250 pages, and used mathematical tools only developed in the latter half of the 20th century, it is impossible that this is the proof that Fermat had in mind. It is probable that Fermat formulated only a partial solution, or realised later that his idea was incorrect.

So, one last trip in the time machine to 1637 will provide the answers to this mystery.

- Did Fermat find a proof to his own Last Theorem?
- If so, what was it?
- Did his proof work only for specific values of n?
- Was his proof correct?
- If the proof was incorrect, did Fermat realise this?

### Where Next?

With so many places and times to visit, the possibilities for our time machine are endless. S Hayes has thrown down the gauntlet of this challenge, who will pick it up next?

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